All Physics Formula and Glossary Physical Quantity
Formula
Remarks
Weight
W = mg
Force
F = ma
W = weight, N m = mass, kg g = gravitational acceleration, m/s 2 or N/kg F = force, N m = mass, kg a = acceleration, m/s 2
Equations of motion at constant acceleration
Density
Moment of a force about a point
Object in equilibrium with parallel forces acting on it
Work done
W = Fd
W = work done, J F = force, N d = displacement, m
Kinetic energy
K.E.= 1/2 mv2
Potential energy
P.E. = mgh
K = kinetic energy, J m = mass, kg v = velocity, m/s Ep = potential energy, J m = mass, kg g = gravitational acceleration, N/kg or m/s 2 h = gain/loss in height
Efficiency
Power
Pressure
Liquid pressure
P = power, W W = work done or energy transferred, J t = time, s E = energy transferred/used, J Q = thermal energy transferred, J
Boyle's Law
Specific heat capacity
Specific latent heat of vaporization or fusion
Wave equation
Refractive index
n = refractive index i = angle in air/vacuum r = angle in medium c = speed of light in vacuum, m/s v = speed of light in medium, m/s
Critical angle
Amount of charge
Q = It
Q = charge, C t = time, s
Ohm's Law
V = IR
V = potential difference, V I = current, A
Potential difference
V = W/Q
V = potential difference, V W = work done between two points, J Q = charge, C
P = IV = I 2R
P = power, W I = current, A V = potential difference, V (voltage) E = electrical energy, J
emf
Electrical power
Electrical E = VIT energy Resistance
Transformer equations
Glossary
p = resistivity, ohm l = length of wire, m A = cross-sectional area of wire, m2
Concept
Acceleration
Definition
The rate of change of velocity. Value can be found from the gradient of a velocity-time graph.
unit = m/s 2
Gravitational acceleration Alternating current
The rate at which all objects fall towards earth if there were no air resistance, about 10m/s2 near earth's surface An electric current that periodically reverses its direction in the circuit
Ampere (A)
The SI unit for electric current. A flow of 1 coulomb per second is 1 ampere The maximum displacement of a point of a wave from rest position. Height of a crest or depth of a trough measured from the undisturbed position. For a sound wave, the greater the amplitude, the louder the sound.
Amplitude
Angle of incidence
The angle between an incident ray and the normal to a surface
Angle of reflection Angle of refraction
The angle between a reflected ray and the normal to a surface
Atmospheric pressure
The air pressure in the earth's atmosphere. Atmospheric pressure is about 105Pa near sea level and decreases with height above ground.
Average speed Boiling
The total distance traveled divided by the total time taken. A process by which energy supplied changes a substance from liquid to gas without a change in its temperature.
The angle between a refracted ray and the normal to a surface
Cathode ray oscilloscope
An instrument that enables a variety of electrical signals to be examined visually. It is used for measuring direct current and alternating current voltages, short time intervals and frequency and for displaying waveforms
Celsius scale
A temperature scale where the lower fixed point is the ice point and the upper fixed point is the steam point
Centre of gravity The point at which the entire weight of an object appears to act
Condensation Conduction
Convection
A process by which energy released changes a substance from gas to liquid. The process by which thermal energy is transmitted through a medium from one particle to another.
The process by which thermal energy is transmitted from one place to another by the movement of the heated particles of gas or liquid.
Converging lens A lens that can bring a parallel beam of light passing through it focus to a point. It is thicker in the middle than at the edges.
Coulomb (C) Crest
The SI unit of electric charge. The highest points on a wave
Critical angle
The angle of incidence in the optically denser medium for which the angle of refraction in the less dense medium is 90 o Total internal reflection occurs when the angle of incidence is greater than the critical angle.
Density
Mass per unit volume of a substance Density = Mass / Volume
Diverging lens
A lens that causes parallel beams of light to diverge. It is thicker at the edges than at the centre.
Echo Electric current
Reflected sound heard after an interval of silence. The rate of flow of charge. I = Q / t [ I = current, Q = charge, t = time ] SI unit for temperature K = oC + 273 The energy a body possess due to its motion.
Kelvin (K) Kinetic energy
Kinetic theory of All matter is made up of large numbers of tiny atoms or molecules which matter are in continuous motion.
Latent heat of fusion
The energy needed to change a substance from solid to liquid without a change in temperature
Latent heat of vaporization
The energy needed to change a substance from liquid to gas without a change in temperature (See image above) Like charges repel and unlike charges attract 1. The incident ray, refracted ray, and normal all lie in the same plane at the point of incidence. 2. The ration sini/sinr is constant [ i = angle of incidence, r = angle of refraction]
Law of charges Laws of refraction
Law of reflection 1. The incident ray, reflected ray, and normal all lie in the same place at the point of incidence 2. The angle of incidence = angle of reflection
Lenz's law
States that the direction of the induced e.m.f. is in a direction that opposes the change producing it.
Liquid pressure
Longitudinal waves
Pressure due to the weight of a column of liquid is given by pressure = hpg [ h = height of column, p = density, g = gravitational field strength ] Waves which travel in a direction parallel to the direction of vibration eg sound wave
Magnetic materials
Materials that are attracted by a magnet. Iron is easier to magnetise but loses its magnetism easily - soft magnetic material
Steel is harder to magnetise but does not lose its magnetism easily hard magnetic material.
Manometer
Hard magnetic materials are used to make permanent magnets. Soft magnetic materials are used to make temporary magnets. A U-tube containing liquid (mercury or water) used to measure gas pressure
Mass
Melting Moment of a force
Newton's Laws
Newton (N) Normal
Ohm's law
A measure of the amount of substance in an object. W = mg [ W = weight, m = mass, g = gravitational acceleration ] SI unit is kg A process whereby energy supplied changes the state of a substance from solid to liquid without a change in temperature. The turning effect of a force. Moment = Force x Perpendicular distance from the line of action of the force to the pivot SI unit is Nm 1. An object at rest will remain at rest and an object in motion will continue in motion at a constant speed in a straight line if no resultant force acts on it. 2. The resultant force acting on a body is equal to the product of the mass and acceleration of the body; the direction of the force is the same as that of the object's acceleration. 3. For every action, there is an equal and opposite reaction. SI unit for force A line that is perpendicular to a surface Used in reflection and refraction
States that current through a metal conductor is directly proportional to the potential difference across it provided that temperature and physical condition of the conductor remain unchanged. R=V/I
Optical centre Parallelogram law of vector addition
The point midway between the lens' surfaces on its principal axis. Light rays passing through the optical centre are not deviated. If two vectors acting at a point are represented as the sides of a parallelogram drawn from that point, their resultant force is represented by the diagonal passing through that point of the parallelogram.
Parallel circuits
I = I1 + I2 + I3 + ...
V = V1 = V2 = V3
Period
How much time it takes for one cycle (one complete wave) to pass and the units are always in terms of time. The faster a wave moves, its wave period becomes smaller. It is also the time taken for the crests, or any point on the wave, to move a distance of one wavelength.
Pascal Pitch
SI unit for pressure. 1 pascal = 1 N/m2 The pitch of a note depends on its frequency. Higher frequency --> higher pitch The difference between the electrical potential (voltage) between 2 points. The potential difference across a component in a circuit is defined as the work done to drive a unit charge through the component. V = W/Q [V = p.d., W = work done, Q = charge] SI unit is volt (V) A variable resistor used to vary voltage.
Potential difference
Potential divider/ potentiometer Potential energy The energy stored in an object due to its position, state, or shape Power The rate of doing work Power = work done/time taken OR energy change/time taken SI unit is watt (W) 1 W = 1 Joule/s
Pressure Principal axis
Principal focus Principle of conservation of energy Principle of moments Radiation
Ray Real image Rectifier Refraction
Refractive index
The force per unit area, measured in pascals or N/m2 P = F/A [P = pressure, F = force, A = area] A line joining the optical centre of a lens and perpendicular to the plane of the axis
The point on the principal axis whereby incident rays parallel to the principal axis onto a lens are converged to (or diverged from) States that energy cannot be created or destroyed but only changes from one form to another When an object is not rotating or in equilibrium, the sum of anticlockwise moments about any point = sum of clockwise moments about the same point The transfer of energy by electromagnetic waves. Factors affecting rate of energy transfer: 1. Surface temperature 2. Color 3. texture 4. Surface area - higher at higher temperatures - higher when black colour and rough surface - lower when white colour and smooth surface a narrow beam of light An image formed by a lens that can be captured on a screen An arrangement consisting of one or more diodes for converting alternating current to direct current The change in direction of a light wave or water wave as it crosses a boundary at an angle Refraction occurs because the wave changes its speed in different media n = c/v The ratio of the speed of light in vacuum to the speed of light in the medium can be calculated using sini/sinr The greater the value of the refractive index, the greater is the bending
Resistance
of light towards the normal as it passes from air into the medium The ratio of the potential difference across a conductor to the current flowing through it. SI unit is ohm. Factors affecting resistance: 1. length (directly proportional) 2. cross-sectional area (inversely proportional)
Resistors in series Resistors in parallel
Effective resistance = R1 + R2 + R3 +...
Resultant force
When the forces acting on an object are unbalanced, a resultant force acts on the object and it accelerates or decelerates.
Effective resistance =
Right-hand grip rule
Scalar quantities Specific heat capacity
Physical quantities that have magnitude only eg. mass, temperature, time, speed, distance The amount of thermal energy required to raise the temperature of a unit mass of a material by 1 K or 1 oC
Specific latent heat of fusion
The amount of energy required to change a unit mass of a substance from solid to liquid without a change in temperature
Specific latent heat of vaporization Steam point
The amount of energy required to change a unit mass of a substance from liquid to gas without a change in temperature The upper fixed point on the Celsius scale of temperature
Thermal energy The total kinetic energy of the atoms or molecules in a body
Thermocouple
A thermometer consisting of two wires of different metals joined together at the ends to form two junctions. If the two junctions are at different temperatures an e.m.f. is produced. The bigger the temperature difference, the larger the e.m.f. produced.
Temperature Transformer
A measure of the degree of hotness of a body A device used to change the voltage of an alternating current Step-up transformer: has more turns in the secondary coil than in the primary coil --> this increases the voltage step- down transformer: has fewer turns in the secondary coil than in the primary coil --> decreases the voltage. For a transformer that is 100% efficient, output power = input power
Transducer
Transverse wave
A device that transforms energy from one form to another. Input transducers transform other energy into electrical energy eg solar cells, microphones, thermistor, LDR. Output transducers transform electrical energy to other forms of energy eg loudspeakers, LED and electrical meters Waves which travel in a direction perpendicular to the direction of the vibrations. eg rope waves, water waves
Electrostatics Electrostatics is the study of static or stationary electric charges. Charging by friction is a simple way to acquire static electric charges. There are 2 kinds of electric charges: - positive charge (proton, cation) - negative charge (electron, anion) The SI unit for charge is the coulomb, C The charge of a proton is 1.6 x 10 -19 C The charge of an electron is -1.6 x 10 -19 C All charges obey the law of electrostatics which states that - like charges repel - unlike charges attract
The magnitude of the electrical force of attraction or repulsion between charges is increased if - the quantity of charge is increased - the distance between the charges is decreased
Explanation for electrostatics Matter is made up of atoms. In every atom, there are positively charged protons and negatively charged electrons. The electrons orbit around the nucleus which contains the protons (as well as the uncharged neutrons) When an atom is in the uncharged state, the number of protons and the number of electrons are equal. An atom can only become charged by adding or rem oving the negatively charged electrons. Therefore an object becomes negatively charged when it gains electrons and positively charged when it loses electrons.
Electric field An electric field is a region where electrical forces of attraction or repulsion act on any charged object placed in it The pattern of the electric field is illustrated by drawing electric lines of force. The direction of the electric field is defined as the direction of the electric lines of force.
Electrostatic induction Electrostatic induction is a process whereby a conductor becomes charged when a charged body is brought near it but is not in direct contact with it.
Explanation A positively charged rod, when placed near an uncharged aluminium foil, attrots the free electrons inside the foil. This results in the near side of the foil becoming negatively charged, and the other side positively charged. In other words, the positive and negative charges in the foil are separated by the positively charged rod. These separated charges are known as induced charges. Once the rearrangement of the charges is done, following the law of charges, the rod attracts the near side of the foil but repels the far side. However, since the strength of an electrostatic force decreases with distance, there will be an overall attractive force between the rod and the foil. Any object that allows electric charges by induction method is known as a conductor.
The separated charges due to electrostatic induction are known as induced charges. The presence of different types of induced charges explains why the pieces of paper are attracted to a charged comb brough near to them.
Methods of electrostatic charging 1. Charging by friction a. rub 2 different materials together and then separate them quickly b. one of the materials will be positively charged and the other will be negatively charged 2. Charging by electrostatic induction a. charging a conductor by induction
b. charging two conductors by induction
c. charging an electroscope by induction
3. Charging by contact
When a charged conductor is in contact with another neutral conductor or is sliding on an insulator, electric charges will be shared, though not necessarily equally between the 2 objects in contact.
Conductors, insulators, semi-conductors and superconductors conductors
insulators
Allow electric charges to flow through them easily (low
Do not allow electric charges to flow
resistance)
through them easily (high resistance)
eg: metals, acids, bases, salt solutions, graphite, ionized
eg: non-metals, acids, bases and salts in
gases
solid states, diamond and non-ionized gases
solid conductors have free-moving electrons as charge
insulators do not have free-moving
carriers. liquid and gaseous conductors have ions as charge
electrons or ions functioning as charge
carriers
carriers
Semiconductors Eg. germanium and silicone To increase their conductivity, impurities are added to them.
Applications - For making microchips and transistors used in computers and other electronic appliances like radios
Superconductors They have near zero resistance at very low temperatures around 0K. Materials which have superconductivity properties include mercury, tin, lead and some ceramic materials
Van de Graaf generator
Friction between the moving rubber belt and the metal roller produces positive charges on the belt. The positive charges are then carried up to the dome where they attract negative charges to the inside of the dome and repel positive charges to the outside of the dome. This discharges the belt, but leaves an excess of positive charges on the dome. As the amount of positive charges accumulate on the dome, its voltage increases .
MCQ Questions 1. Which of the following statements about an electrical insulator is correct? a. it contains some electrons but more protons b. it contains some protons but more electrons c. it contains electrons but they are not free to move at all d. it contains no electrons at all e. it contains only neutrons 2. When a plastic rod is charged positively by friction, a. it gains electrons b. it gains neutrons c. it gains protons d. it loses electrons e. it loses protons 3. How could the unit of potential difference, the volt, also be written? a. A s b. A/s c. C/A d. C/J e. J/C 4. Two suspended light, aluminium coated with balls have been touched by the same charged perspex rod.. They will a. repel each other but be attacked by the rod b. repel each other and be repelled by the rod c. attract each other but be repelled by the rod d. attract each other and be attracted by the rod
5. A charged rod may be discharged by holding it just above a flame. This is because a. the rod is ionized when heated b. the hot gases in the flame are ionized c. the rod is oppositely charged to the flamed d. the hot gases strike the rod and remove its charge 6. A negatively charged strip is brought near to (but not touching) an uncharged conductor. If the conductor is earthed it a. becomes negatively charged b. becomes negatively charged on one side and positively charged on the other c. is attracted by the strip d. is repelled by the strip 7. What makes metals good conductors of electricity? a. they contain electrons that are free to move b. their molecules are free to move c. they contain excess positive charge d. their atoms are close together and transfer energy when they vibrate 8. Lightning conductors are used to protect tall buildings from the damages due to lightning. Which one of the following statements about a lightning conductor is not true? a. its top must be higher than the highest part of the building b. it has sharp points at its top end c. its lower end is buried in the ground d. it must be insulated from the building 9. Four processes are used to charge an isolated metal sphere. P: The sphere is earthed by touching it Q: The earth connection is removed from the sphere R: A charged rod is brought close to the sphere S: The charged rod is removed In which order should these processes be carried out to charge the sphere? a. P Q R S b. P R S Q c. R P Q S d. R S P Q
MCQ Answers 1. c 2. d 3. e 4. b 5. b 6. c 7. a 8. d
9. c
Structured Question Worked Solutions 1. The diagram shows a metal sphere S mounted on an insulating stand
Describe a simple test you could perform, and which does not alter any charge there may be on the sphere, to determine whether or not the sphere is charged. Given that the sphere is charged, how could you test whether the charge is positive or negative, without altering the charge on the sphere? Solution
1. Bring an uncharged conducting sphere P suspended on an insulating thread close to but not touching S. If P does not move towards S, then S is uncharged. If P moves towards S, then S is charged. Using P with a positive charge, bring it slowly from a far distance towards S. Observe for any deflection of P along the way. If P is deflected away from S, then S is positively charged. If P is attracted towards S, then S is negatively charged. 2. State briefly how you would give an electric charge to a. a glass rod b. a copper disc attached to the end of a nylon rod, assuming that you have available a charged polythene tile. Solution
2a. By rubbing the glass rod with another insulating material such as plastic or a cloth, we can charge the rod by friction.
2b. First place the charged polythene tile close to but not touching the disc and then earth the disc once. The disc now has an induced charge of sign opposite to that of the charged polythene tile. 3. Three copper spheres are placed near each other in air. The large sphere carries a positive charge and the two small spheres touch each other, as shown.
The two small spheres are pulled apart, using their insulated handles, and then taken well away from the large sphere, as shown
a. The charge on the large sphere has been drawn for you. On the diagrams above draw in the charges, if any, on each of the smaller spheres. b. Explain why energy is needed to separate the two small spheres. Solution
a.
b. The two small spheres are oppositely charged, so there is a force of attraction between them. Energy is thus needed to overcome this force to separate these two spheres. 4. An electrically charged sphere C is brought near a small uncharged conducting sphere S suspended as shown in Fig. 1. S is first attracted towards C until it touches the surface of C and then repelled to the position shown in Fig. 2
ai. Explain why S is first attracted towards C aii. Explain why S is repelled after touching the surface of C b. On Fig 2 mark and label each force acting on S c. When a bunsen flame is passed beneath S, the sphere falls back towards C. Suggest why this happens Solution
4ai. Since C is positively charged, it will induce negative charges on the side of S facing C. As unlike charges attract, S is attract towards C. 4aii. Upon touching C, S's negative charges get transferred onto C to neutralise some of the positive charges. S becomes positively charged. The like charges in C and S repel each other. 4b.
4c. The flame ionizes the air surrounding S which neutralises the charges on S. This eliminates the force of repulsion.
Electricity current, I
defined as the rate of flow of electric charge
There is electric current only when there are moving electric charges
I=Q/t
where Q is the amount of charge flows (in C), and t is the time taken (in s)
SI unit is ampere, A
The ammeter, milliammeter, and microammeter are current-measuring instruments and must be connected in series in the circuit
Potential difference V and electromotive force, emf
The potential difference or voltage , V between 2 points is defined as the work done, W in taking 1 C of positive charge from the lower potential to the point of higher potential.
In a circuit, it is the energy sources that supply energy, not the electric charges.
The energy that drives the free electrons around the circuit is known as emf
More than 1 cell can be connected in a circuit (series/parallel)
Cells in series
the combined emf used to drive the electric charges is the sum of all the individual cell's emf
with more cells, the circuit will have more power to drive the electric charges
Cells in parallel
the combined emf used to drive the electric charges is the emf of one individual cell (each cell contributes an equal amount of emf)
with more cells, the circuit will have longer time to drive the electric charges
Potential difference = work done / charge transferred
V=E/Q
where V is potential difference, E is energy, Q is charges flow
SI unit is volt
Example To transfer 2 C of charge from points X to Y in an electrical circuit 50 J of energy is needed. What is the potential difference between X and Y? Solution
Potential difference between X and Y = 50 / 2 = 25 V
1 volt is defined as the potential difference between two points such that one joule of work is done in transferring 1 C of charge from one point to the other.
The voltmeter and millivoltmeter are voltage-measuring instruments and must be connected in parallel to the component across which the potential difference is being measured.
The emf of an electrical source like a battery is equal to the electrical energy provided by the source for every coulomb of charge which flows round the circuit.
The emf of an electrical source can also be defined as the potential difference across the terminals of the source in an open circuit
Voltmeter connected in parallel Ammeter connected in series
Ohm's Law and Resistance
Ohm's Law states that the current I, passing through a conductor is directly proportional to the potential difference, V between its ends provided that the physical conditions and temperature of the conductor remain constant.
a resistor is a conductor with known value of resistance. It can be used to control (reduce) the size of current flowing in a circuit.
Resistance, is therefore a measure of how difficult it is for the current to pass through the circuit.
V / I = constant
Conductors or resistors which obey Ohm's Law are called ohmic.
Eg. pure metal, copper sulphate solution with copper electrodes, metal alloy
Those which do not obey Ohm's Law are called non-ohmic.
The resistance, R of an electrical component is defined as the ratio of the potential difference, V across the component to the current, I flowing through it.
Example The voltage across a lamp is found to be 1.4V when the current in the lamp is 0.2A. Calculate the resistance of the lamp. Solution
Resistance of lamp, R = V / I = 1.4 / 0.2 = 7 ohm
The resistance is also given by the gradient of the graph V vs. I.
Rheostat
a variable resistor used to vary the control of electric current
A rheostat can be used to find the resistance of an unknown resistor.
The voltmeter is connected in parallel
Use the rheostat to adjust the size of the current to a convenient value. Hence, record the readings shown on the ammeter and voltmeter
adjust the rheostat to take 5 sets of readings of I and V
Calculate the resistance from the equation R
=V/I
Factors affecting resistance of a wire 1. Length
for a wire of uniform cross-sectional area, the resistance is directly proportional to the length of the wire
hence, the longer the wire, the higher the resistance
2. Cross-sectional area
for a wire of fixed length, its resistance is inversely proportional to the cross-sectional area
so, the thinner the wire, the higher the resistance
3. Material
resistance depends on the kind of substance
copper is a good conductor and is used for connected wires
nichrome has more resistance and is used in the heating elements of electric heater
4. Temperature
for metallic wires, as temperature increases, the resistance increases
but for some materials like silicon and germanium as temperature increases, the resistance decreases
Electric Circuits An electric circuit is a complete or closed path through which electric charges flow from one terminal of an electrical source to the other, passing through one or more circuit components.
S eries circuit
It has only one path for the current to flow.
the sum of voltages across individual components in the circuit is equal to the voltage across the terminals of the electrical source or the whole circuit.
Application: voltage divider
P arallel circ uit
It has more than 1 path for the current to flow
The sum of the currents flowing in the separate branches of a parallel circuit is equal to the current from the source.
Application: electrical household connections
Short circuit
A short circuit occurs when a large current flows due to the very little or negligible resistance of the circuit
A short circuit leads to
overheating of wires which may cause electric fires
damage of the electrical source (eg battry) and other circuit components
To prevent short circuits, use fuse
- fuses break the circuit if the current flowing through them exceed their respective ratings.
Combined resistance of resistors in series or parallel
In Series: Effective resistance = R1 + R2 + R3 Total voltage = V1 + V2 + V3 + ...
Application: voltage divider
In Parallel: Effective resistance 1/RTOTAL = 1/R1 + 1/R2 + 1/R3 Total current = I1 + I2 + I3 + ...
Application: current divider
Diode - A diode allows the electric current to flow in only ONE direction
The follow arrow on the diode symbol shows that it is forward biased - the current flows easily
The reverse arrow shows that the diode is reverse biased - the current is nearly zero
Rectifier
in a direct current or d.c. circuit, the current only flows in one direction, ie from positive to negative
in a alternating current or a.c. circuit, the power supply can be controlled in such a way that the current alternates between forward and reverse directions, ie from positive to negative for a short period, then from negative to positive for another short period
since a diode only lets current flow in the forward direction and stops all the reverse current, an a.c. can be changed into a d.c. by using a diode
the conversion of an a.c. into a d.c. is called rectification
the diode used to achieve rectification is called rectifier
in half-wave rectification, the diode conducts in the forward half cycle of the a.c. (forward biased) and cuts off the reverse half cycle of the a.c. (reverse biased)
MCQ Questions 1. The diagram shows the magnitude and directions of the electric currents entering and leaving junction X.
What will be the magnitude and direction of the current in the wire XY? magnitude direction a. 1A X to Y b. 1A Y to X c. 5A X to Y d. 5A Y to X e. 8A X to Y 2. The diagram shows a circuit.
What is the reading on voltmeter V2? a. 3V b. 6V c. 9V d. 15V e. 18V 3. Which quantity can be measured in units of joule/coulomb? a. charge b. current c. potential difference d. power e. resistance 4. A current flows in two resistors connected in series as shown. A 1 and A2 are the readings on the ammeter,V1 and V2 are the readings on the voltmeters.
Which of the following correctly describes the ammeter and voltmeter readings? a. b. c. d. e.
ammeter readings A1 < A2 A1 < A2 A1 = A2 A1 = A2 A1 > A2
voltmeter readings V1 < V2 V1 > V2 V1 < V2 V1 = V2 V1 = V2
5. The diagram shows a resistor connected to a cell of e.m.f. 2V.
How much heat energy is produced in the resistor in six seconds? a. 0.4J b. 2.5J c. 4.8J d. 10J e. 60J 6. V represents a potential different, I a current, R a resistance, and t a time. Which of the following has units of energy? a. IRt b. I2R c. V/I d. V2/R e. VIT 7. An electric lamp is marked '240 volts 150 watts'. It is used on a ring main socket marked '30 amps maximum'. Which fuse is best to use in series with the lamp? a. 40 amp b. 30 amp c. 13 amp d. 3 amp e. 1/2 amp 8. A 40 W fluorescent lamp turns half the electrical energy it uses into light energy. How much light does it give out in 10 s? a. 8J b. 20J c. 200J d. 400J e. 800J 9. The diagram shows a circuit.
What is the effective resistance of the three resistors? a. 0.67Ω b. 1.50Ω c. 6.70Ω d. 15.0Ω e. 108Ω
10. The earth wire to an electric toaster should be connected to a. the heating element b. the metal case c. the ON/OFF switch d. the plastic legs e. the toast 11. A battery moves a charge of 60C around a circuit at a constant rate in a time of 20 s. What is the current in the circuit? a. 0.3A b. 3.0A c. 40A d. 80A e. 1200A 12. Which of the following changes to a wire will double its resistance? cross-sectional area
length
a.
double
double
b.
double
no change
c.
no change
halve
d.
halve
halve
e.
halve
no change
13. A heater which is to be used on a 250V mains circuit, has a 5A fuse in its plug. Which of the following is the most powerful heater that can be used with this fuse? a. 50W b. 250W c. 1000W d. 2000W e. 3000W 14. What is the smallest total resistance which can be obtained using only a 6Ω resistor and a 12Ω
resistor? a. 2Ω b. 4Ω c. 6Ω d. 8Ω e. 12Ω
15. Which one of the following is a unit of potential difference?
a. Watt b. Ohm c. Ampere d. Volt 16. The resistances of two wires X and Y are in the ratio 2:1, their lengths are in the ratio 1:2 and their diameters are also in the ratio 1:2. The ratio of the resistivities of X and Y is then a. 1:2 b. 1:1 c. 2:1 d. 4:1 17. A length of resistance wire is connected to the terminals of a cell. Which of the following would decrease the current through the cell? a. using a cell with higher output voltage b. connecting an identical wire in parallel to the first one c. using a thicker wire of the same material and the same length d. using a longer wire of the same material and same thickness 18. In the circuit below, the p.d. between P and Q is 20V. The p.d. between X and Y is
a. 10V b. 20V c. 40V d. 120V 19. A three-pin is connected to the lead for a 1 kW electric iron to be used on a 250V supply. Which of the following statements is not correct? a. the fuse should be fitted in the live lead b. the live wire is coloured brown c. A 13A fuse is the most suitable rating to use d. the yellow and green wire should be connected to the earth pin 20. A torch bulb takes a current of 0.4A from a 3V supply for 2 minutes. How much electrical energy is used? a. 2.4J b. 45J c. 57.6J d. 144J
21. A plug connected to a table lamp contains a 3A fuse. Why is the fuse used? a. to reduce the voltage across the lamp b. to protect the wiring from overheating c. to make it easier for the current to flow d. to reduce the current that flows through the lamp 22. Why is electricity transmitted along power lines at very high voltages? a. to reduce resistance of the cables b. so that transformers can be used c. to ensure that the current is the same all the way along the power lines d. to reduce loss of energy 23. A small heater operates at 12 V, 2A. How much energy will it use when it is run for 5 minutes? a. 30J b. 120J c. 1800J d. 7200J 24. A 1.0 Ω resistor and a 2.0 Ω resistor are connected in series across a 12 V d.c. supply. What is t he
current in the circuit? a. 0.25 A b. 4.0 A c. 6.0 A d. 12 A 25. In an a.c. electric circuit in a house, the switch for any device is always connected to the 'live' lead. Why is this? a. no current ever flows in the neutral lead of the device b. the device will be shorted if the switch is in the earth lead c. the device can never be switched off if the switch is in the neutral lead d. the device can only be isolated (made safe) if the switch is in the live lead 26. The p.d. between the ends of a conductor is 12 V. How much electrical energy is converted to other forms of energy in the conductor when 100C of charge flows through it? a. 0.12 J b. 8.3 J c. 88 J d. 1200 J 27. A combined bathroom unit of a heater and a lamp is controlled by one switch. The unit contains a 2kW heater and a 100 W lamp. In one week, the lamp uses 1 kWh of electrical energy. How much electrical energy is used by the heater alone?
a. 2 kWh b. 4 kWh c. 10 kWh d. 20 kWh 28. An electrical kettle is plugged in and switched on. The fuse in the plug blows immediately. Which single fault could cause this? a. the earth wire is not connected to the kettle b. the live wire and neutral wire connections in the plug are swapped around c. the live wire touches the metal case of the kettle d. the wires connected to the plug are too thin 29. How much electric charge passes through a 12 V battery in one minute when the current is 0.5 A? a. 0.5 C b. 6.0 C c. 30 C d. 360 C 30. When a current of 4 A flows for 1 minute through a lamp, 480 J of energy is transformed. What is the potential difference across the lamp? a. 2 V b. 120 V c. 480 V d. 1920 V 31. A 800 W of electric toaster has been used for 12 hours in a month at a cost of $0.20 per kWh. What is the cost of the electrical energy used in a month? a. $1.60 b. $1.92 c. $13.33 d. $1920 32. Power losses in the grid system are reduced by a. thin wires b. thick wires c. high voltages d. direct current instead of alternating current 33. A 6V cell is connected to a 3Ω resistor. How much charge flows through the resistor in 2 minutes?
a. 4C b. 9C
c. 240C d. 360C 34. A battery drives 30C of charge round a circuit. The total work done is 600J. What is the electromotive force of the battery? a. 0.05V b. 5V c. 20V d. 300V 35. A piece of wire 0.4m long has a cross-section of 2mm2. Which of the following wires of the same material has half its resistance? Length
Area/mm2
a.
0.2
1.0
b.
0.2
4.0
c.
0.8
4.0
d.
0.8
8.0
36. What is the smallest total resistance that can be obtained by using only a 3Ω resistor and a 12Ω
resistor? a. 0.07Ω b. 2.4Ω c. 4Ω d. 15Ω
37. A generator produces 100kW of power at a potential difference of 10kV. The power is transmitted through cables of total resistance 5Ω. What is the power lost in the cable? a. 50W b. 250W c. 500W d. 1000W 38. The resistance of a certain circuit element is directly proportional to the current passing through it. When the current is 1.0A, the power dissipated is 6.0W. What is the power dissipated when the current is raised to 2.0A? a. 6.0W b. 12.0W c. 24.0W d. 48.0W 39. Which of the following is a correct unit for electrical energy?
a. ampere b. coulomb c. joule d. volt e. watt 40. A house-owner replaced a failed fuse for the lights of his house. When the lights were switched on the new fuse also failed. The house-owner put another fuse in with a higher rating than the previous two. Why was this not a sensible thing to do? a. fuses only work if the rating is exactly right b. using a fuse with too high a rating would cause electric shocks c. higher rating fuses only work for power points d. the fuse had already failed because the rating was too high e. a fuse with higher rating might work but the fault would not be corrected 41. Why is a fuse used in an electrical appliance? a. to earth the appliance b. to protect the appliance and its cable c. to change the efficiency of the appliance d. to change the current rating of the appliance e. to change the voltage of the supply to the appliance 42. When using 3-core wiring (live, neutral, earth leads), where should the fuse be fitted? a. only in the live lead b. only in the neutral lead c. only in the earth lead d. in either the live or the neutral lead e. in any lead 43. Which of the following has volt (V) as its unit? a. current + resistance b. power x current c. rate of flow of charge d. the charge in a capacitor e. the electromotive force of a cell 44. A 5 kW immersion heater is used to heat water for a bath. It takes 40 minutes to heat up the water. How much electrical energy has been converted into thermal energy? a. 2.0 x 102 J b. 1.2 x 103 J c. 2.0 x 104 J
d. 2.0 x 105 J e. 1.2 x 107 J 45. A resistor is used in an electronic circuit but it quickly burns out. What is the reason for this? a. a fuse has blown in the circuit b. the current flowing is too low c. the resistor's power rating is too high d. the resistor's power rating is too low e. the voltage of the battery is too low
MCQ Answers 1. b 2. a 3. c 4. c 5. c 6. e 7. d 8. c 9. b 10. b 11. b 12. e 13. c 14. b 15. d 16. b 17. d 18. a 19. c 20. d 21. b 22. d 23. d 24. b 25. d 26. d 27. d 28. c 29. c
30. a 31. b 32. c 33. c 34. c 35. d 36. b 37. c 38. d 39. c 40. e 41. b 42. a 43. e 44. e (energy = power x time) 45. d
Structured Question Worked Solutions 1. A village is 5.00km from the nearest electricity substation. Two conductors are used to connect
the village to the substation. Each metre length of each conductor has a resistance of 0.00120Ω. a. Calculate i. the combined resistance of the 2 conductors from the substation to the village ii. the power loss in the conductors when the current through them is 40.0A b. The voltage between the 2 conductors is 6000 V and the voltage to each house in the village is 240 V. i. Name the device that is used to change the 6000 V supply to a 240 V supply ii Explain why such a high voltage is used for transmitting the electricity
Solution ai. Resistance of a 5.00km length of conductor = (5.00 x 103) x 0.00120 = 6.00 Ω
The conductors must be connected in series in order that a closed circuit can be formed. Combined resistance = 6.00 + 6.00 = 12.0 Ω
aii. Power loss in the conductors = I 2R = (40)2 x 12.0 = 19200W
bi. step-down transformer bii. Since electrical power = current x voltage, a high voltage used means that only a low current is required. For low currents the loss of electrical power as heat in the cables, being I 2R is also low. Besides, cables needed to carry a low current can be relatively thin, thus reducing the cost of the conductor used.
2a. How much electric charge passes through a 12V battery in 1.0s when the current is 1.0A? 2b. How much energy is transferred by a 12V battery in 1.0s when the current is 1.0A? 2c. The figure shows a battery of e.m.f. 12V co nnected in series with a 0.50 Ω resistor and lamps
of resistance 2.5 Ω and 2.0 ohm.
i. calculate the current in the circuit
ii. calculate the voltage across the 3.0 Ω lamp iii. calculate the power developed in the 3.0 Ω lamp Solutions
2a. charge = It = 1.0 x 1.0 = 1.0 C 2b. energy transferred = VIt = 12 x 1.0 x 1.0 = 12 J 2ci. total resistance = 0.5 + 3.0 + 2.5 = 6 Ω
current --> I = V/R = 12 / 6 = 2A 2cii. voltage = IR = 2 x 3.0 = 6 V
2ciii. Power = IV = 2 x 6 = 12 W
3. The figure shows a circuit containing a battery of e.m.f. 3.00V, a resistor of resistance 12.0 Ω and a switch S.
When switch S is closed, what is the a. current through the circuit b. charge passing through the battery in 1.00s c. energy output in the resistor in 1.00s Solutions
3a. current, I = V / R = 3 / 12 = 0.25 A 3b. charge = current x time = 0.25 x 1 = 0.25C 3C. energy = VIt = 3 x 0.25 x 1 = 0.75 J
4. The diagram shows three 6-V filament lamps connected to a 12-V supply of negligible internal resistance. The resistance of each lamp is shown on the diagram. The current through the battery is 2.00A.
a. determine the current through each lamp b. calculate the voltage across each lamp c. lamp L is taken from its socket. State and explain what happens to the brightness of lamp M and what happens to the brightness of lamp N. d. Lamp L is now replaced in its socket and lamp M is taken from its socket. State and explain what happens to the brightness of lamp L and what happens to the brightness of lamp N. Solutions
4a. current through the 3 Ω lamp= 2A current through each of the 6 Ω lamps = 1A 4b. voltage across the 3 Ω lamp = 3 x 2 = 6 V voltage across each of the 6 Ω lamps = 6 x 1 = 6V
4c. both lamps M and N will not light up since the removal of lamp L will cause the circuit to be opened 4d. the brightness of the lamp depends on its power = I 2R. Lamp L will be dimmer since the current passing through it is now 1.33 A. (current = 12/9 = 1.33A) This decrease in current is due to the increase in the resultant resistance ( from 6 Ω to 9 Ω). However, lamp N will be brighter since the current through it is now more than 1A.
5. An isolated farmhouse has its own electrical generator which supplies an output voltage of 250V to each of the following circuits. Circuit A: a lighting circuit containing 8 lamps each rated at 250V, 150W Circuit B: a circuit for an electric cooker rated at 250V, 6.0kW For each circuit, a. determine the maximum current b. suggest a suitable fuse rating Solutions
Circuit A 5a. maximum current = 8(P/V) = 8(150/250) = 4.8A Since the lamps are connected in parallel, total current = sum of individual lamps 5b. suitable fuse rating is 5 A Circuit B 5a. maximum current = P/V = 6000/250 = 24A 5b. suitable fuse rating is 30 A
6. A battery has an e.m.f. of 4.0V and negligible resistance. a. What does this tell you about the work done by the battery in driving 1 coulomb of charge around a closed circuit? b. When a resistor is connected across the terminals of the battery, a current of 0.20A is passed. i. what is the time taken for 1.0C of charge to pass a given point in the circuit? ii. calculate the rate at which heat is produced in the resistor Solutions
6a. work done = 6J
6bi. time, t = Q/I = 1/0.2 = 5s 6bii. rate of heat produced = energy dissipated/time = 4/5 = 0.8W
7. An electric lamp is marked "250V, 100W" and an immersion heater is marked "250V, 2kW" a. calculate the current in each device when operating normally. bi. explain why the filament of the lamp is made to have a larger resistance than the heating element of the immersion heater bii. suggest a reason why the filament is made of a metal with a much higher melting point than that of the element ci. the heat capacity of the filament of the lamp is very small. State one reason why this is an advantage cii. explain why the wire connecting the immersion heater to the supply remains cool even when the heater has been in use for some time Solutions
7a. current in lamp = power/V = 100/250 = 0.4A current in heater = power/V = 2000/250 = 8A 7bi. the power of the lamp is small whereas the power of the heater is large. 7bii. so that the filament would not be easily melted at high operating temperature. the heater element will not rise above 100oC 7ci. the small heat capacity allows the filament to increase in temperature rapidly with minimal heat. In this way, the filament becomes very hot and emits light in a very short time 6cii. the connecting wires have low resistance and are relatively thick, thereby producing little heat
8. A battery is charged for 6 hours using a current of 0.50A. Calculate a. the total charge which flows through the battery b. the work done in passing this charge through the battery if the average voltage between the battery terminals during charging is 11.0V
Solutions
8a. charge, Q =It = 0.5 x 6 x 3600 = 10800C 8b. work done = QV = 10800 x 11 = 118800 J
9a. An electric generator is connected by cables to a small factory. Given that the output power of the generator is 40kW at 5000V and that the total resistance of the cables is 0.5 Ω, calculate i. the current in the cables ii. the voltage drop in the cables iii. the power loss in the cables What happens to this 'lost' power? 9b. if the same power had been supplied at 250V, the current through the same cables would have been 20 times greater. Calculate the power loss under these circumstances 9c. explain why power is better transmitted at a high voltage rather than a low voltage. Solutions
9ai. current in cables, I = P/V = 40000/5000 = 8A 9aii. voltage drop in cable, V = IR = 8 x 0.5 = 4V 9aiii. power lost in cables, P = I 2R = 82 x 0.5 = 32W This 'lost' power is dissipated as heat to the surroundings 9b. power lost, P = I 2R = 1602 x 0.5 = 12800W 9c. at a high voltage, a low current is required. 9ci. power loss in transmission cables is small 9cii. only thin cables are needed, thus it is more economical
10. A number of 8 Ω resistors are available. In the spaces below, draw diagrams to show how you
could connect a suitable number of these resistors to give an effective resistance of
a. 24 Ω b. 4 Ω c. 18 Ω Solutions
10a.
10b.
10c.
11. The element of an electrical heater has a power rating of 1150W when used on a 230V supply. Calculate the cost of operating the heater for 3.0 hours if the cost of 1kWh of energy is 6.0p.
Measurements indicated that 92000J of energy were given out by the heater element in a particular period of time. What quantity of charge passed through the element during that time? Solutions
electrical energy dissipated in 3 hours = Pt = 1.15 x 3 = 3.45 kWh cost at 6p per kWh = 3.45 x 6 = 20.7p Energy = QV 92000 = Q x 230 Q = 92000/230 = 400C
12. A torch uses 3 cells, each of e.m.f. 1.5V and negligible internal resistance, to light a lamp rated 4.5V, 0.5A. In the space below draw a circuit diagram of the cells and lamp when the torch is switched on. Calculate a. the resistance of the filament of the lamp when lit b. the charge flowing through the filament of the lamp per minute Solutions
12a. resistance = V/I = 4.5/0.5 = 9 Ω 12b. Quantity of charge = It = 0.5 x 60 = 30C
13. Electrical power may be transmitted through a system using high alternating voltages. State the advantages gained by using a. high voltages b. alternating voltages
Solutions
13a. the loss of energy as heat in the cable is small. the use of thin cables is more economical 13b. the voltage can be stepped up at the power station and stepped down at the consumer end, using transformers
14. An electric heater is connected, through a correctly wired 3-pin plug, to a mains supply socket. Explain briefly a. the function of the earth wire b. why the fuse is connected to the live wire rather than the neutral wire Solutions
14a. the earth wire is connected to the metal casing. Should an electrical fault develop and the live wire is now connected to the metal casing, a high current now flows to earth. This will cause the fuse to blow and a person would not receive any electric shock from touching the casing 14b. the live lead is at a high alternating voltage whereas the neutral wire is at 0V. If the fuse is connected to the live lead and blows, the circuit will be disconnected from the high voltage. If the fuse is connected to the neutral wire and blows, the circuit is still "live"
15. The battery in the circuit below has an e.m.f. of 16V and negligible internal resistance
Calculate a. the combined resistance of the two resistors connected in parallel b. the current flowing through the 8 ohm resistors Solutions
15a. combined resistance = 1/(1/36 + 1/18) = 12 Ω 15b. current, I = V/R = 16/(8+12) = 0.8A
16. A battery of e.m.f. 9.0V and internal resistance 1.5 Ω is connected in series with a resistor and a current 0.5A passes through the resistor. Calculate a. the resistance of the resistor in the circuit b. the total rate at which chemical energy is transformed by the battery Solutions
16a. p.d. across the internal resistance = 0.5 x 1.5 = 0.75 V p.d. across the resistor = 9 - 0.75 = 8.25 V Resistance = V/I = 8.25/0.5 = 16.5 Ω
16b. total rate of heat transformation = IV = 9 x 0.5 = 4.5W
17. the figure shows a battery of e.m.f. 6.0V connected to a switch S and to two resistors in
parallel, each of resistance 3.0 Ω.
The switch S is closed for 5.0 minutes. Calculate a. the current through each resistor b. the current through the battery c. the total charge which passes through the battery d. the energy supplied by the battery
Solutions
17a. current, I = V/R = 6.0/3.0 = 2.0A 17b. current through battery = total current through resistors = 2 x 2.0A = 4.0A 17c. total charge which passes through the battery = total current x time = 4.0 x (5.0 x 60) = 1200C 17d. energy supplied by battery = VIt = 4.0 x 6.0 x (5.0 x 60) = 7200 J
18. The figure shows the three conductors of a 240V a.c. supply cable, a fuse, a switch and a lamp
T The cable is rated at 240V, 5A continuous working The lamp is rated at 240V, 500W. a. complete the figure to show how the fuse, switch and lamp should be connected to the supply b. what fuse rating should be used? Solutions
18a.
18b. fuse rating = 2.5A (current drawn by lamp = P/V = 500/240 = 2.08A)
19. The figure shows a circuit consisting of a battery of e.m.f. 6.0V and two pairs of 3.0 Ω resistors in series, these pairs of resistors being connected in parallel.
ai. what is the total resistance of the path KLM aii. what is the total resistance of the path KNM aiii. what is the resistance of the circuit between K and M? b. Calculate i. the current through the battery ii. the power developed in the battery Solutions
19ai. total resistance KLM = 3.0 + 3.0 = 6.0 Ω
19aii. total resistance KNM = 3.0 + 3.0 = 6.0 Ω 19aiii. resistance between K and M = (6.0 x 6.0)/(6.0 + 6.0) = 3.0 Ω
19bi. current through battery = V/R = 6.0/3.0 = 2.0A 19bii. Power = IV = 3.0 x 6.0 = 18W
20. An electric iron reaches its steady working temperature 300s after being switched on. The average current flowing through the heating element during this time is 1.3A. Calculate the energy drawn from the 240V mains supply whilst the iron is heating up Explain why this quantity of energy is greater than the heat retained by the iron Solutions
Energy = Power x time = VIt = 240 x 1.3 x 300 = 93600J This quantity is greater than the heat retained by the iron because heat is also lost to the surroundings
21. The diagram shows XY, part of a circuit into which is connected an ammeter of resistance 5.0
ohm. A current flows through the ammeter. A resistor of resistance 0.010 Ω is now connected across the ammeter terminals. Calculate the combined resistance of the ammeter and the resistor.
What is the effect of connecting the resistor across the meter on i. the current through the ammeter ii. the total current in the circuit? Explain your answers. State a practical advantage of using an ammeter and a resistor connected in this way.
Define the coulomb. The current indicated by the ammeter was 4.2 A and it flowed for 20s. Calculate the total charge passing through the ammeter. Solutions
21. Combined resistance = 1/(1/5 + 1/0.01) = 0.010 Ω
i. the current through the meter decreases because some of the previous current is now diverted through the resistor. ii. the total current in the circuit will be larger because the effective resistance is lower The ammeter can be used to measure a larger current in the circuit A coulomb is the charge which flows in 1 second past any point in a circuit in which there is a steady current of 1 ampere. Total charge = It = 4.2 x 20 = 84C
22a. The voltage across a 3Ω resistance wire is 6V. How large is the current? 22b. What is the resistance of a filament bulb when a voltage of 3V across it causes a current of 0.5A?
22c. Find the voltage across a manganin wire of resistance 6Ω carrying a current of 2A. Solutions
22a. 2A 22b. 6Ω
22c. 12V
23. Two resistance wires P and Q of the same material and length but of different thickness are connected in parallel to a battery. The cross-sectional area of P is twice that of Q. What is the ratio of:
a. the resistance of P to the resistance of Q b. the current in P to the current of Q Solutions
23a. 1:2 23b. 2:1
24. Two torch bulbs, both marked '0.2A, 3.0V' are connected (a) in series, (b) in parallel, across a 3.0V battery. Assume that the resistance of the filament in the bulbs does not change. In each case of (a) and (b) i. describe the brightness of the bulbs. ii. calculate the currents through each bulb iii. calculate the current supplied by the battery Solutions
24aii. 0.1A 24aiii. 0.1A 24bii. 0.2A 24biii. 0.4A
25. A radio takes 0.1A of current from a 6V battery. a. what is the overall resistance of the radio? b. what is the power of the radio? c. how much energy would be used if the radio is switched on for 30 minutes? Solutions
25a. 60Ω
25b. 0.6W 25c. 1080J
26. if you watched a 120W television for 2 hours and used a 20W table lamp for 4 hours every day for 30 days, how much would you have to pay at the end of 30 days, assuming that electrical
energy costs 15 cents per kWh? Solutions
$1.44
27. An immersion heater has a rating of 3.0kW. What would it cost to use it for 5 hours at the rate of 15 cents per kWh? Solutions
$2.25 28a. How much electric charge passes through a 12 V battery in two minutes when the current is 0.5 A? b. How much energy is transferred by a 12 V battery in two minutes when the current is 0.5A? c. When a 1.5V, 6 W lamp is connected to a 1.5 V battery, calculate the amount of charge passing through the bulb in 10 minutes. di. A consumer buys a 250 V 100 W reading lamp. If the lamp is connected to a 250 V mains supply, what is the current passing through the lamp? dii. If fuses of rating 2 A, 5 A and 13 A are available, which fuse should be used for the lamp? Solution
28a. charge = current x time = 0.5 x (2 x 60) = 60 C 28b. energy = charge x voltage = 60 x 12 = 720 J 28c. I = P/V = 6 / 1.5 = 4 A charge = current x time = 4 x (10 x 60) = 2400 C 28di. I = P / V = 100 / 250 = 4 A 28dii. 2 A fuse should be used
Work - Work is the product of the force on a body and the distance it moves in the direction of the force - Work done = force x distance moved in the direction of the force - Work is done whenever energy is changed from one form into another. - SI unit is joule (J) - Work is a scalar quantity
Energy - energy is defined as the capacity to do work - SI unit is joule (J) - Energy is a scalar quantity - kinetic energy is the energy a body possesses due to its movement - kinetic energy can be classified into -translational kinetic energy: possessed by bodies in translational motion (eg moving train) = 1/2 mv2
-rotational kinetic energy: possessed by bodies in rotational motion (eg rotating merry-go-round) - potential energy is the energy a body possesses due to its position or state - potential energy can be classified into: --gravitational potential energy: possessed by a body due to its position = mgh -elastic potential energy: possessed by a body due to its strained state of being stretched or compressed Eg. A ball of mass 500g is moving at a velocity of 5m/s. What is the kinetic energy of the ball?
kinetic energy = 1/2 mv2 = 1/2 x 0.5 x 5 x 5 = 6.25 J Eg. Billy has a mass of 40kg. He runs up a flight of 20 steps, each of height 0.25m. Calculate his gain in gravitational potential energy
gain in gravitational potential energy = mgh = 40 x 10 x (20 x 0.25) = 2000 J
Principle of Conservation of Energy
States that energy can neither be created not destroyed but can be transformed from one form into another with no change in its total amount. Eg. A ball of mass 3kg is dropped from a height of 5m. i. calculate the gravitational potential energy of the ball before it is dropped ii. calculate the speed of the ball on hitting the ground iii. if the ball bounces to a height of 3m, with what speed does it leave the ground? iv. explain why the ball does not reach its original height when it bounces up again
i. gravitational potential energy = mgh = 3 x 10 x 5 = 150J ii. The kinetic energy of the ball on hitting the ground is equal to the ball's original gravitational potential energy so the kinetic energy of the ball on hitting the ground = 150J If the ball hits the ground with speed v, 1/2 mv2 = 150 v2 = (150 - 2)/3 = 100 v = 10ms-1 iii. The kinetic energy of the ball on leaving the ground is equal to its gravitational potential energy on rising to its maximum height, that is 3m. The gravitational potential energy of the ball 3m above the ground = 3 x 10 x 3 = 90 J The kinetic energy of the ball leaving the ground = 90 J If the ball leaves the ground with speed v, 1/2 mv2 = 90 v2 = (90 x 2)/3 v = 7.746ms-1 iv. Because part of its kinetic energy is changed into other forms of energy like sound and heat when it hits the ground Eg. A pendulum bob of mass 0.5kg is moved sideways until it has risen by a vertical height of 0.2m. Calculate the speed of the bob at its i. highest point ii. lowest point
i. at the highest point, the kinetic energy of the bob = 0 if the speed of the bob at its highest point is v, 1/2 mv2 = 0 1/2 x 0.5 x v = 0
v2 = 0 v=0 ii. according to the principle of conservation of energy, the kinetic energy of at the lowest point is equal to the gravitational potential energy at the highest point. If the speed of the bob at its lowest point is v, 1/2 mv2 = mgh v2 = 2 x 10 x 0.2 = 4 v = 2 m/s
Power and efficiency - power is defined as the rate of doing work - power = work done/time taken - SI unit is watt (W) - Efficiency is the ratio of useful output energy to the total input energy or the ratio of useful power to the total input power. efficiency = (useful output energy / input energy) x 100% Eg. A crane can lift a 200kg mass through a vertical height of 5m in 4s. Calculate i. the power output of the motor driving the crane ii. the efficiency of the motor if the power input is 5kW
i. power output = work done/time taken = (200 x 10 x 5)/4 = 2500W ii. efficiency of motor = (power output/power input) x 100% = (2500/5000) x 100% = 50%
Friction - the net force that slows down moving objects - acts in the opposite direction of motion of object 1. Static friction
- related to objects which are not moving. - amount of force applied = amount of friction 2. Moving friction
- applied force does not affect friction
- it can be affected by surface or sudden change in mass Advantages of friction
- enables walking - brakes of vehicles Disadvantages
- reduce efficiency of machinery - energy wasted as heat Methods to reduce friction
- lubricants - ball bearings -----> so that moving parts are made smoother
Terminal velocity
The greater the velocity of an object, the higher the air resistance.
Definition: The constant maximum velocity reached by a body falling through the atmosphere under the attraction of gravity.
When an object reaches terminal velocity, the force of gravity and air resistance are balanced, the object falls at a constant speed and doesn’t accelerate.
Factors affected: Size, surface area, weight and nature of medium where object is flying.
If an object is falling through a vacuum, there would be no air resistance, thus acceleration is due to gravity alone.
Inertia
Resistance of an object to change.
The greater the mass the more resistant it is.
An object at rest will remain at rest and an object at motion will remain at a constant speed with an absence of a resultant force.
Energy, Work, Power Work
Energy
Power
Definition
Work done on an object is when a constant force is applied on the object producing a distance moving in the direction of the force.
Energy is the capacity to do work.
Power is defined as the rate of doing work
There are many different types of energy like translational, rotational and vibrational kinetic energy.
- Rate of energy transfer / conversion
Watt (W)
SI unit
Joule (J)
Joule (J)
Definition of SI unit
One joule of work is done when a force of one Ne wton moves through a distance of one metre in the direction of the force.
One joule of work is done One watt is produced when 1 when an joule of work is done for 1 object with 1kg moves at 1m/s. second.
Equation
Work = Force x Distance
K.E. = (1/2)(mv2) m = mass v = velocity
Power = Work/Time Power = Energy/Time
P.E. = mgh m = mass g = gravitational acceleration h = height Remarks
Work is done on an object only when the force applied on it produces motion.
The principle of conservation Efficiency = (useful energy of energy states that energy output/total energy input) x cannot be created or destroyed, 100 but can only change from one form to another.
Worked examples 1. a stone of mass 5kg is dropped through a distance of 2.0m. Find the work done by the gravity on the stone. Work done = force x distance = weight x distance = (5 x 10) x 2 = 100J 2. Calculate the work done against gravity in lifting a load of weight 50N through a vertical distance of 30cm Work done = force x distance = weight x distance = 50 x (30/100) J = 15J 3. An object 25kg is moved 2m on a smooth horizontal surface. Find the work done by its weight weight of object = 25 x 10 = 250N acting vertically downwards
work done by weight = 250 x 0 = 0J (because vertical distance moved = 0)
MCQ Questions 1. When a book of mass 2kg was pushed along the horizontal surface of the table, the friction force measured was 5N. When the book was pushed along the same table with a force of 9N, it moved with a constant a. acceleration of 2.0 m/s2 b. acceleration of 25 m/s2 c. speed of 2.0 m/s d. speed of 2.5 m/s2 2. A balloon filled with gas has a total weight of 1800N. The balloon descends with a constant speed of 3 m/s. What is the resultant force acting on the balloon during descent? a. 0N b. 600N c. 1800N d. 5400N 3. A crane lifts a load of 8000N through a vertical distance of 20m in 4s. What is the average power during this operation? a. 100W b. 1600W c. 40000W d. 640000W 4. A toy car A moving with a speed of 30 m/s has a kinetic energy of 900J. Another toy car B has twice the mass of toy car A. If toy car B moves with a speed of 15 m/s, what is the kinetic energy of toy car B? a. 450J b. 900J c. 1800J d. 3600J 5. A 60W fluorescent lamp converts half the electrical energy supplied into light energy. How much light energy does it emit in 1 minute? a. 30W b. 60W c. 1800W d. 3600W
6. A electric motor is used to lift a 200N load through 3m in 5s. If the motor has an efficiency of 40%, what is the total electrical energy used by the motor in one second? a. 48W b. 300W c. 1200W d. 3000W 7. A trolley of mass 1.5kg is placed on a smooth table. If a constant force of 6N acts on the trolley, the acceleration produced by the force will be a. 0.25 ms-2 b. 4 ms-2 c. 4.5 ms-2 d. 7.5 ms-2 8. An object of mass 2kg moves with uniform velocity when a constant force of 10N acts on it. When the force is increased to 20N, the acceleration will be a. 4 ms-2 b. 5 ms-2 c. 6 ms-2 d. 10 ms-2 9. The weight of a rocket in outer space is zero because a. its mass becomes zero b. there is no frictional force c. there is no gravitational force d. the rocket is stationary 10. A ball of mass 0.2kg is thrown to a height of 15m. What is the change in its gravitational potential energy? (g=10N/kg) a. 0.3 J b. 3.0 J c. 7.5 J d. 30 J e. 75 J 11. A boy pushes a toy cart along a level road and then lets it go. As the cart is slowing down, the biggest energy change is from a. chemical to heat b. chemical to kinetic c. heat to kinetic
d. kinetic to chemical e. kinetic to heat 12. A girl weighing 400N takes 4s to run up the stairs 3m high. What is her average speed? a. 0.75 m/s b. 0.8 m/s c. 1.25 m/s d. 1.33 m/s e. 12 m/s 13. How much potential energy does she gain? (from question 12) a. 120 J b. 200 J c. 400 J d. 1200 J e. 2000 J 14. A block of mass 2kg slides from rest through a distance of 20m down a frictionless slope 10m high. What is the kinetic energy of the block at the bottom of the slope? (g = 10ms-2_ a. 20 J b. 40 J c. 200 J d. 400 J e. 800 J 15. What are the main energy changes in a hydroelectric power station? a. electrical -> kinetic -> heat b. heat -> electrical -> kinetic c. kinetic -> light -> electrical d. kinetic -> potential -> light e. potential -> kinetic -> electrical 16. An electric motor runs with a steady input of 250 V and 4 A while raising a load of 1000N. Assuming the motor and transmission to be 100% efficient, what time is taken to lift the load vertically through a distance of 10m? a. 1 s b. 1.5 s c. 4 s d. 10 s e 250 s
17. No work is done by an object at rest because a. no force is acting on the object b. no distance is moved c. heat is not produced d. friction is acting on the object 18. A mass of 40g is raised vertically from the ground to a height of 50cm, the work done in lifting the mass is a. 0.02J b. 20J c. 0.2J d. 2000J 19. During free fall, work is done by a. frictional force b. magnetic force c. gravitational force d. centripetal force 20. Kinetic energy is transformed into gravitational potential energy when a. a raindrop falls from the sky b. a rubber band is stretched c. a stone is thrown upwards d. a bullet is fired horizontally 21. A hammer of a pile-driver is lifted to a height of 2m in 0.5s. If the mass of the hammer is 500kg, the power required for the lifting is a. 500W b. 1000W c. 2000W d. 20000W 22. A car travels at a constant speed of 10m/s. What is the power of the car if the total resistant forces acting on it is 400N? a. 1/40 W b. 40W c. 400W d. 4000W 23. A known force is applied to an object on a horizontal, frictionless surface. What property of the object must be known in order to calculate its acceleration?
a. density b. mass c. surface area d. volume e. weight 24. Which expression is used to calculate force? a. frequency x wavelength b. mass x acceleration c. power + time d. pressure x area e. work x distance 25. Which of the following is a vector quantity? a. energy b. mass c. temperature d. time e. velocity 26. When a force is applied to a body, several effects are possible. Which of the following effects could not occur? a. the body speeds up b. the body rotates c. the body changes direction d. the pressure on the body increases e. the mass of the body decreases 27. A girl weighing 400N takes 4s to run up the stairs as shown in the diagram. What is her average speed?
a. 0.75 m/s b. 0.8 m/s c. 1.25 m/s d. 1.33 m/s e. 12 m/s
28. How much potential energy does she gain? (from qn 27) a. 120 J b. 200 J c. 400 J d. 1200 J d. 2000 J 29. An electric motor can lift a weight of 2000N through a height of 10m in 20s. What is the power of the motor? a. 10 W b. 1000 W c. 2000 W d. 4000 W e. 400 000 W 30. What are the main energy changes in a hydroelectric power station? a. electrical --> kinetic --> heat b. heat --> electrical --> kinetuc c. kinetic --> light --> electrical d. kinetic --> potential --> light e. potential --> kinetic --> electric 31. A spiral spring has a natural length of 10.0cm. When a load of 5N is placed at one end while the other end is fixed on a hook, the length of the spring becomes 11.0cm. What is the new length of the spring if the load is 20N? a. 12.0cm b. 14.0cm c. 20.0cm d. 44.0cm 32. A body whose mass is 4kg, is placed on a frictionless surface. It is being pulled by a spring balance and the acceleration produced is 1m/s2. What is the reading on the spring balance? a. 4N b. 5N c. 36N d. 40N 33. A body weighs 50N on earth where the acceleration due to gravity is 10m/s 2. When taken to the moon, where the acceleration due to gravity is 1.6m/s2, the body would have a weight, in newtons, of a. zero b. 8
c. 50 d. 80 34. A parachutist, whose body and equipment have a total mass of 150kg, descends vertically through the air at a steady speed of 10m/s. Taking g = 10m/s 2, the resultant force acting on him in this descent is a. 1500N upwards b. 150N upwards c. 0N d. 1500N downwards 35. A man weights 600N. He runs up stairs of total height 4 metres in 3 seconds. How much power is exerted by the man? a. 450 W b. 800 W c. 2400 W d. 7200 W 36. When two forces are combined, the size of the resultant depends on the angle between the two forces. Which of the following cannot be the magnitude of the resultant when forces of magnitude 3N and 4N are combined? a. 1 N b. 3 N c. 7 N d. 8 N 37. A rock of mass 20kg is travelling in space at a speed of 6m/s. What is its kinetic energy? a. 60 J b. 120 J c. 360 J d. 720 J 38. A block of mass 6kg is pulled across a rough surface by a 54N force, against a friction force F. The acceleration of the block is 6m/s2. What is the value of F? a. 9 N b. 18 N c. 36 N d. 54 N 39. A girl of weight 500 N runs up a flight of stairs in 10 s. The vertical height of the stairs is 5 m. What is the average power developed by the girl? a. 50 W
b. 100 W c. 250 W d. 1000 W 40. When a block of wood of mass 2 kg is pushed along the horizontal flat surface of a bench, the friction force is 4N. When the block is pushed along the bench with a force of 10 N, it moves with a constant a. speed of 3 m/s b. speed of 5 m/s c. acceleration of 3 m/s2 d. acceleration of 5 m/s2 41. A person exerts a horizontal force of 600 N on a box that also experiences a friction force of 200N. If it takes 4.0s to move the box 3.0m, what is the average useful power? a. 150 W b. 300 W c. 450 W d. 600 W
MCQ Answers 1. a 2. a 3. c 4. a 5. c 6. b 7. b 8. b 9. c 10. d 11. e 12. c 13. d 14. c 15. e 16. d 17. b 18. b 19. c 20. c 21. d
22. d 23. b 24. b 25. e 26. e 27. c 28. d 29. b 30. e 31. b 32. a 33. b 34. c 35. b 36. d 37. c 38. b 39. c 40. c 41. b
Structured Question and Worked Solutions 1. State briefly the energy changes in the production of electricity from a. the burning of coal b. wind-power c. nuclear fission Solution
a. chemical energy -> heat and light energy -> latent energy of vaporization -> kinetic energy of steam -> kinetic energy of turbines -> kinetic energy of generator -> electrical energy b. kinetic energy of air -> kinetic energy of windmill -> kinetic energy of generator -> electrical energy c. nuclear energy of uranium -> heat energy -> latent heat of vaporization -> kinetic energy of steam -> kinetic energy of turbines -> kinetic energy of generator -> electrical energy
2. A boy of mass 30kg runs up a flight of stairs to a floor which is at a height of 5.5m in 6.0s.
Taking the weight of 1 kg = 10 N, calculate a. work done by the boy against gravity b. average power developed by the boy Solution
a. work done = weight x distance = 30 x 10 x 5.5 = 1650 J b. average power = work done/time = 1650/6 = 275 W
3a. Define force and state its SI unit b. Two forces acting at a point have magnitudes 3 N and 4 N. By means of a diagram, show the lines of action of the forces when their resultant is i. 7 N ii. less than 7 N but more than 1 N, iii. 1 N c. Two forces of magnitudes 70 N and 50 N act at a point so that the angle between their lines of action is 40o. By means of a scale diagram, determine the magnitude and direction of the resultant force acting at the point. d. In a study on impact, a bullet of mass 50g penetrates a target and is brought to rest from an initial speed of 500ms-1 in 0.2 s. i. calculate the average deceleration of the bullet over the 0.2 s ii. find the retarding force acting on the bullet during its impact with the target Solution
a. One newton is defined as the force that gives a 1 kg mass an acceleration of 1ms -2. SI unit: newton (N)
C.
di. average deceleration = (500 - 0)/0.2 = 2500 ms-1 dii. retarding force = (50/1000) x 2500 N = 125 N
4. A student Ben, starting at point P, walks due North for 1hr at a constant speed of 4.0km/h and then, at the same constant speed, walks 4.0km due East, finishing at a point Q. In the same total time but at a different constant speed, a second student Tom walks directly from P to Q. Determine
i. the total distance walked by student Ben ii. the distance walked by student Tom iii. the velocity of student Tom Solution
i. 8.0km ii. 5.7km iii. speed = 5.7/2 = 2.85km/h velocity of student Tom is 2.85km/h at 45o to the North
5. A petrol-driven car accelerates from rest to its cruising speed along a straight level road. i. state the principal energy changes in the car and its surroundings ii. the car now climbs a slope with no change of speed. Explain whether the rate of petrol consumption will increase, stay the same, or decrease Solution
i. chemical potential energy -> kinetic energy of car -> internal energy gained by road and air The chemical energy in the fuel is converted into kinetic energy of the car and internal energy gained by the air and road due to friction. ii. rate of petrol consumption increases. When the car climbs a slope, it gains gravitational potential energy because of work done against gravity.
6. The useful power output of a small dc motor is used to raise a load of 0.75kg through a vertical distance of 1.2m. The time taken is 18.0s. The voltage across the motor and the current through it are constant at 6.0V and 0.30A respectively. Assuming that the gravitational force on a mass of 1.0kg is 10N, calculate i. the power input to the motor ii. work done in raising the load iii. useful power output developed by the motor Solution
i.power input to motor = IV = 0.30 x 6.0 = 1.80 W ii. work done = force x distance = 0.75 x 10 x 1.2 = 9 J iii. power output = work done/time = 9/18 = 0.50 W
7. The figure below shows a simple pulley system. Calculate i. the work done by the man in lifting the load ii. the gravitational potential energy gained by the load iii. the efficiency of the pulley system
i. work done = 50 x 3 = 150J ii. gravitational potential energy = 40 x 3 = 120J iii. efficiency = (120/150) x 100% = 80%
8. A motor boat travels due north at a steady speed of 3.0m/s through calm water in which there is no current. The boat then enters an area of water in which a steady current flows at 2.0m/s in a south-west direction as shown. Both the engine power and the course setting remain unchanged.
a. In the space below, draw a vector diagram showing the velocity of the boat and the velocity of the current. Use the diagram to find i. the magnitude of the resultant velocity of the boat ii. the angle between the due North and the direction of travel of the boat b. Calculate the distance the boat now travels in 5.0 minutes c. The mass of the boat is 3.0 x 10 3 kg (3000 kg). Calculate the additional force which needs to be applied to give the boat an initial acceleration of 2.5 x 10-2 m/s2 (0.025 m/s2) Solution
8ai. scale: 1cm = 0.5 m/s
magnitude of resultant velocity = 2.15 m/s 8aii. angle = 42o 8b. distance = 2.15 x 5 x 60 = 645 m 8c. F = ma = 3000 x 2.5 x 10 -2 = 75 N
9. In a laboratory experiment, a small trolley was accelerated from rest by applying a small force to it. The distance travelled by the trolley was measured as 1.1 m in a time of 0.55 s. Calculate its average speed. During this movement, the trolley was uniformly accelerating from rest. Calculate its speed after 0.55 s and its acceleration during this speed. The mass of the trolley is 1.2 kg. What is the force producing this acceleration? Solution
average speed = distance / time = 11 / 0.55 = 2 m/s speed after 0.55 s --> v = (2 x average speed) - u = 4 m/s acceleration = (v - u) / t = (4 - 0) / 0.55 = 7.273 m/s2 force = ma = 1.2 x 7.273 = 8.73 N
10. In a crash test a car of mass 1500kg containing a dummy is driven into a rigid barrier at a speed of 15m/s. The recorded results showed that the interval between the first contact with the barrier and the car coming to rest was 0.12s. a. calculate the average deceleration of the car over the 0.12s b. find the retarding force, assumed to be constant, acting on the car c. One of the man-shaped dummies used in the above test was strapped in place with a safety belt. The dummy was found to have moved forward 0.25m against the force exerted by the belt. Given that the kinetic energy of the dummy just before impact was 7870 J, calculate the average
force which acted in the dummy as it was stopping. d. Explain why it is an advantage for anyone riding in the car to be brought to rest steadily over this distance of 0.25m rather than abruptly. Solution
10a. given u = 15 m/s, t = 0.12 s, v = 0 m/s v = u + at 0 = 15 + a(0.12) a = -125 m/s2 therefore the deceleration of the car is 125 m/s2 10b. F = ma = 1500 x -125 = -1.875 x 10 5 N therefore the retarding force is 1.875 x 105 N 10c. loss in kinetic energy = work done = force x distance 7870 = F x 0.25 --> F = 31480 N 10d. The force acting on the passenger will be much greater and hence drastic injuries could result if the passenger is brought to rest suddenly.
11. A bricklayer lifts 12 bricks each weighing 20 N a vertical height of 1.2 m in 30 s. and place them at rest on a wall. Calculate a. the work done b. the average power needed Solution
11a. work done = total weight x height = 12 x 20 x 1.2 = 288 J 11b. average power needed = work done / time = 288 / 30 = 9.6 W
12. A small, hard ball of mass 0.14 kg is thrown vertically upwards and reaches a height of 12 m
above the point from which it is thrown. Calculate the least energy which it must be given when thrown. (take the force of gravity on 1 kg to be 10 N) On a windless day an inflated ball of much larger volume but having the same mass is propelled upwards with the same energy. It reaches a considerably smaller height. Explain briefly why this is so. Solution
energy required = work done = force x distance = 0.14 x 10 x 12 = 16.8 J A larger volume means that the ball has a larger surface area so it will experience a larger resistance. Hence some energy is lost resulting in a smaller height.
13. An athlete throws a javelin of mass 0.80 kg so that its centre of gravity is raised from a height of 2.0m above ground level at the moment of release, to a maximum height of 14.0 during its flight. Calculate the energy to lift it against gravity to this height. (force of gravity on 1 kg is 10N) Explain why the energy with which the javelin leaves the athlete's hand is considerably greater than the energy calculated above. Solution
vertical distance = 12m Force = 0.8 x 10 = 8 N work done = force x distance = 8 x 12 = 96 J This is because the energy calculated is for the work done to lift the javelin vertically upwards. In the motion, the javelin also moves horizontally. Therefore extra energy is needed to do the work.
14. A steady force of 6.0 N is applied horizontally to a body of mass 4.0 kg, which is initially at rest. In the 2.0 s during which the force is applied, the mass moves 3.0 m in the direction of the force. Assuming that there is no resistance to the motion, find a. the work done by the force
b. the resulting kinetic energy of the body c. the resulting velocity of the body Solution
14a. work done = force x distance = 6 x 3 = 18 J 14b. kinetic energy = work done = 18 J 14c, kinetic energy = 1/2 mv 2 18 = 1/2 x 4v2 v = 3 m/s
15. An empty lift is counterbalanced by a heavy piece of metal. Some people of combined mass 350 kg enter the lift and operate it. The lift rises 50 m in 60 s. Calculate a. the work done in raising the people b. the power required to do this (take weight of 1kg to be 10N) Solution
15a. work done = force x distance = 3500 x 50 = 175 000 J 15b. power = work done / time = 175 000 / 60 = 2916.7 W
16. A stunt man has one end of a thick elastic cord attached to him. The other end of the cord is firmly attached to a point on a high bridge. When the man jumps from the bridge he falls freely under gravity for 2.5s. Take the acceleration of free fall to be 10m/s2 and assume that the man is initially at rest. a. Calculate i. the vertical speed the man acquires during his free fall ii. the vertical distance fallen Suggest one reason why, in a real jump, the distance fallen in 2.5 s and the speed reached would be less than your calculated answers, even though the cord was slack throughout the 2.5 s. b. After this time the cord begins to stretch and the man falls with continually reducing downward acceleration. Why is this?
c. Eventually his downward acceleration becomes zero. Explain why this happens. If the mass of the man is 80 kg, suggest a value for the tension in the cord when his downward acceleration is zero. Without making any further calculation, describe his motion after the point where his downward acceleration has become zero. Solution
16ai. vertical speed, v = u + at = 0 + 10(2.5) = 25 m/s 16aii. vertical distance fallen = (u + v) / 2 x 2.5 = (25/2) x 25 = 31.25 m The existence of the air resistance brought about a smaller resultant force. 16b. As the stunt man falls further, the tension in the cord increases and together with air resistance reduce the resultant force. 16c. This is because the tension in the cord equals the man's weigh; no net forces is present at this time. tension in the cord = weight of man = 80 x 10 = 800 N The man begins to oscillate up and down about this point.
17. A spring has a length of 5.0cm when it has no load hanging on it. When a load of weight 30N is hung from it, its length becomes 11.0cm. How long will it be if the weight of the load is changed to 20N? Solution
9.0cm
18. A boy riding a bicycle has a total mass of 60kg and an acceleration of 0.6m/s 2. Calculate the accelerating force acting on the boy and the bicycle. Solution
36N
19. A mass of 8kg is given an acceleration of a. 5m/s2. b. 40cm/s2. What is the force acting in each case? Solution
19a. 40N 19b. 3.2N
20. An object experiences 2 forces. A force of 3N pulls it horizontally to the right and one of 6N is
applied at 60˚ to the horizontal. Draw a scale diagram to find the resultant and its direction Solution
7.9N at 41˚ to the horizontal
HEAT AND MEASUREMENT OF TEMPERATURE
MCQ Questions 1. If the two wires in the thermocouple are made from the same metal and are placed in different temperatures, the voltage produced will be a. the minimum b. the maximum c. zero d. constantly changing 2. Thermocouples are used to measure high temperatures provided the temperatures measured a. do not exceed the melting points of the wires in the thermocouple b. are equal to the melting points of the wires in the thermocouple c. are not more than the boiling point of water d. are above 0K 3. Which one of the following is suitable for measuring rapidly changing temperatures? a. alcohol-in-glass thermometer
b. mercury-in-glass thermometer c. clinical thermometer d. thermocouple 4. Which of the following determines the range of a mercury thermometer? a. length of the stem b. thickness of the bulb c. volume of the bulb d. volume of the stem e. volumes of the bulb and stem 5. The lengths of mercury thread in the uniform tube above the bulb of a mercury thermometer are: 20mm when the bulb is in melting ice 170mm when the bulb is in the steam above boiling water 50mm when the bulb is in liquid X. What is the temperature of liquid X? 6. If heat energy is removed from an object, its temperature will normally a. fall b. fall then rise c. stay the same d. rise e rise then fall 7. How can the sensitivity of a liquid-in-glass thermometer be increased? a. use a liquid which is a better conductor of heat b. use a thinner-walled bulb c. use a longer tube d. use a liquid of higher boiling point e. use a tube with a narrower bore 8. Which of the following determines the range of a mercury thermometer? a. length of the stem b. thickness of the bulb c. volume of the bulb only d. volume of the stem only e. volumes of the bulb and stem 9. Thermal expansion and contraction of metals are used in each of the following except a. riveting steel plates b. fixing axles for wheels c. pressure cooker d. fire alarm 10. A biimetallic strip is used in temperature control devices because the two metals used in a bimetallic strip a. expand unequally when heated b. are good conductors of heat c. conduct heat at different rates
d. can bend easily 11. The density of a solid decreases when it is heated because a. its mass decreases b. its mass increases c. its volume decreases d. its volume increases 12. The reason for the bursting of water pipes during very cold weather is that a. water pipes contract when cooled b. water expands on freezing c. ice expands on melting d. the structure of the material for the pipe is weakened at low temperature 13. The volume of a gas when heated increases much more than for a solid or liquid because a. the particles of a gas expand more b. the attractive forces between particles of a gas are negligible c. the particles of solids and liquids cannot move d. the molecules of gas are lighter 14. When a narrow-necked glass vessel containing water at room temperature is immersed in hot water, the level of the water is seen to go down a little before it begins to rise. This is because a. the initial heating causes water to contract b. the glass vessel expands c. the water evaporates d. glass is a poor conductor of heat 15. Which of the following types of energy remains constant during a change of state? a. internal energy b. potential energy c. kinetic energy d. heat energy 16. The energy required for a change of state is called a. chemical energy b. state energy c. latent energy d. heat energy 17. If a substance expands on melting, increased pressure acting on it will a. not change its melting point b. increase its melting point c. decrease its melting point d. condense the substance 18. The reversed process of melting is a. condensing b. freezing c. sublimation
d. burning 19. The boiling point of water in a pressure cooker is raised by a. increasing the volume of water in the cooker b. increasing the internal volume of the cooker c. increasing the pressure in the cooker d. increasing the pressure outside the cooker 20. If a sample of water boils at a temperature above 100ºC, the water a. is pure b. contains impurities c. boils at a pressure lower than normal atmospheric pressure d. boils in vacuum 21. Which one of the following properties of a liquid is determined by comparing its boiling point with its standard value? a. purity of the liquid b. density of the liquid c. mass of the liquid d. pressure in the liquid 22. A liquid evaporates at a. temperatures above its boiling point b. its boiling point c. temperatures below its boiling point d. temperatures above and below its boiling point 23. A liquid that evaporates easily is called a. an evaporating liquid b. a volatile liquid c. an unstable liquid d. a saturated liquid 24. The rate of evaporation is higher on a windy day because a. the temperature of a windy day is higher b. the temperature of a windy day is lower c. the particles which escape are carried away by the wind d. the liquid particles move faster 25. Which one of the following factors does not affect the rate of evaporation of water? a. density of water b. humidity of the surrounding air c. motion of the surrounding air d. temperature of the water 26. Which one of the following liquids is used as the cooling agent in a household refrigerator? a. alcohol b. ether c. freon
d. liquid hydrogen 27. The specific latent heat of fusion is absorbed by a substance when it changes from a. a liquid to a gas b. a gas to a liquid c. a solid to a liquid d. a liquid to a solid 28. The latent heat of fusion supplied to a substance is used a. to keep its particles in their fixed positions b. by particles to break away from their fixed positions c. to increase the average speed of its particles in their random motion d. to decrease the average speed of its particles in their random motion 29. Steam at ordinary atmospheric pressure has more energy than boiling water because it has a. a high specific heat capacity b. a low specific heat capacity c. the latent heat of fusion d. the latent heat of vaporization 30. Ab evaporating liquid feels cool because it a. gives out latent heat of fusion b. absorbs latent heat of fusion c. gives out latent heat of vaporization d. absorbs latent heat of vaporization
31. In a vacuum flask, which methods of heat transfer are prevented by the vacuum? a. conduction only b. convection only c. conduction and convection only d. conduction, convection, and radiation
32. The temperature shown by a mercury-in-glass thermometer increases. Which of the following is constant? a. density of the mercury b. internal energy of the mercury c. mass of the mercury
d. volume of the mercury
MCQ Answers 1. c 2. a 3. a 4. e 5. a 6. a 7. e 8. e 9. c 10. a 11. d 12. b 13. b 14. b 15. c 16. c 17. b 18. b 19. c 20. b 21. a 22. c 23. b 24. c 25. a 26. c 27. c 28. b 29. d 30. d 31. d 32. c
Terms
Heat capacity is the amount of heat required to raise the temperature of a body by 1 K (or 1°C)
Specific heat capacity is the amount of heat required to raise the temperature of 1kg of the
substance by 1 K (or 1°C)
Latent heat of fusion of a solid substance is the heat energy needed to change it from solid to
liquid state without any change in temperature
Specific latent heat of fusion of a solid substance is the heat energy needed to change 1kg of it
from solid to liquid state without any change in temperature
SI unit: J/kg
Latent heat of vaporisation of a substance is the heat energy needed to change it from liquid
vapour state without any change in temperature
Specific latent heat of vaporisation of a substance is the heat energy needed to change 1kg of
it from liquid to vapour state without any change in temperature
SI unit: J/kg
Heat Change Formula
Q = mcθ
m = mass (kg) c = specific heat capacity (J kg -1 oC-1) θ = temperature change ( o)
Electric heater Energy Supply, E = Pt Energy Received, Q = mcθ
Energy Supplied, E = Energy Receive, Q Pt = mcθ E = electrical Energy (J or Nm) P = Power of the electric heater (W) t = time (in second) (s) Q = Heat Change (J or Nm) m = mass (kg) c = specific heat capacity (J kg -1 oC-1) θ = temperature change ( o)
Mixing 2 liquids
Heat Gain by Liquid 1 = Heat Loss by Liquid 2 m1c1θ1 = m2c2θ2 m1 = mass of liquid 1 c1 = specific heat capacity of liquid 1 θ1 = temperature change of liquid 1 m2 = mass of liquid 2 c2 = specific heat capacity of liquid 2 θ2 = temperature change of liquid 2
Specific Latent Heat Q = mL Q = Heat Change (J or Nm) m = mass (kg) L = specific latent heat (J kg -1)
Example 1. A mass of 0.20kg of water at 0°C is placed in a vessel of negligible heat capacity. An electric heater with an output of 24 W is placed in the water and switched on. When the temperature of the water reaches 12°C, the heater is switched off. a) Calculate the time for which the heater is switched on. Assume that the heat capacity of water is 4200J/kgK b) An ice cube of mass 0.020kg is added to the 0.20kg of water at 0°C in the same vessel and the heater is switched on. Assuming that all the ice is at 0°C, calculate how long it will take for the water to reach 12°C. Assume that the specific latent heat of fusion on ice is 0.34 MJ/kg Solutions
a) Heat supplied by heater = heat absorbed by water E = mcθ
E = Pt 24 × t = 0.20 × 4200 × 12 t = 420 --> The heater is switched on for 420 s.
b) Heat absorbed by ice = Heat used to melt ice + Heat used to raise temperature of ice water from 0°C to 12°C = ml + mcθ
= (0.020 × 340000) + (0.040 × 4200 × 12) = 8816 J Time t = 8816/24 = 367 s
MCQ 1. When the temperature of a body increases, its… a. internal energy decreases b. internal energy remains constant c. internal energy increases d. heat capacity increases
2. The internal energy of a body is measured in… a. kg b. °C c. J d. JK-1
3. The heat capacity of a bottle of water is 2100 J°C -1. What is the amount of heat required to heat the water from 30°C to 50°C? a. 2100J b. 4200J c. 42000J d. 63000J
4. If the same amount of heat is supplied to 2 metal rods, A and B, rod B shows a smaller rise in temperature. Which of the following statements is true about the heat capacity of rods A and B? a. The heat capacity of A is less than that of B b. The heat capacity of B is less than that of A c. The heat capacity of A is zero d. The heat capacity of B is zero 5. The heat capacities of 10g of water and 1kg of water are in the ratio… a. 1 : 10
b. 10 : 1 c. 1 : 100 d. 100 : 1
6. 1 kg of substance X of specific heat capacity 2 kJkg -1°C-1 is heated from 30°C to 90°C. Assuming no heat loss, the heat required is…
a. 7.5 kJ b. 18 kJ c. 80 kJ d. 120 kJ
7. How much heat is required to raise the temperature of 20g of water from 10°C to 20°C if the specific heat capacity of water is 4.2 Jg -1°C-1? a. 1.68 J b. 84 J c. 840 J d. 1680 J
8. 4000 J of energy are given out when 2kg of a metal is cooled from 50°C t0 40°C. The specific heat capacity of the metal, in Jg-1°C-1, is… a. 40 b. 50 c. 200 d. 400
9. What is the temperature rise when 42 kJ of energy is supplied to 5kg of water? (specific heat capacity of water is 4200 Jkg -1°C-1 a. 2°C b. 5°C c. 8.4°C d. 10°C
10. A piece of copper of mass 2kg is cooled from 150°C to 50°C. The specific heat capacity of copper is 400 Jkg-1°C-1. The heat loss is… a. 800J b. 4000J
c. 40000J d. 80000J 11. 2 kg of oil is heated from 30°C to 40°C in 20s. The specific heat capacity of oil is 8 kJkg -1°C-1. The power of the heater is…
a. 8 W b. 8 kW c. 24 kW d. 32 kW
12. An immersion heater rated at 200 W is fitted into a large block of ice at 0°C. The latent heat of fusion of ice is 300J/g. How long does it take to melt 20g of ice? a. 13s b. 15s c. 30s d. 60s 13. An immersion heater rated at 150 W is fitted into a large block of ice at 0°C. The specific latent heat of fusion of ice is 300J/g. How long does it take to melt 10g of ice? a. 2s b. 5s c. 20s d. 150s e. 4500 s 14. Aniline melts at -6°C and boils at 184°C. At which temperature would aniline not be a liquid? a. -9°C b. -3°C c. 25°C d. 100°C e. 102°C 15. A 2 kg mass of copper is heated for 40 s by a heater that produces 100 J/s. The specific heat capacity of copper is 400 J/kgK. What is the rise in temperature? a. 5 K b. 10 K c. 20 K d. 50 K
MCQ Answers
1. c 2. c 3. c 4. a 5. c 6. d 7. c 8. c 9. a 10. d 11. b 12. c 13. c 14. a
Structured Question Worked Solutions 1. A 12-kW electric heater, working at its stated power, is found to heat 5kg of water from 20°C to 35°C in half a minute. The specific heat capacity of water is 4200 Jkg-1°C-1 a. Calculate i) the heat produced by the heater in half a minute ii) the heat absorbed by the water in the half minute Solution
1i. 12000 x 30 = 360 kJ 1ii. 5 x 42000 x 15 = 315 kJ 1b. There is heat lost to the surroundings b. Account for the difference in the answers to ai and ii. [1] 2. A lead cube of mass 0.25kg falls from rest from a height of 12m to the ground. Calculate, neglecting frictional loss, a. the loss of potential energy of the cube b. the gain in kinetic energy of the cube c. the speed the cube has when it hits the ground d. the rise of the temperature of the cube after it hits the ground, assuming that all the kinetic energy is converted into internal energy of the cube. [8] The gravitational force on the mass of 1kg=10N The specific heat capacity of lead=0.13 kJ/(kgK) Solution
2a. loss of p.e. of cube = mgh = 0.25 x 10 x 12 = 30 J 2b. gain in k.e. of cube = loss of p.e. of cube = 30 J 2c. 1/2 mv2 = 30 1/2 x 0.25 x v2 = 30 v = 15.5 speed of cube when it hits the ground = 15.5 m/s
2d. internal energy of cube = gain in k.e. of cube mcθ = 30 0.25 x 130 x θ = 30 θ = 0.923oC 3. Lemonade can be cooled by adding lumps of ice to it. A student discovers that 70g of ice at a temperature of 0°C cools 0.30kg of lemonade from 28°C to 7°C. The latent heat of fusion of ice is 0.33 MJ/kg. The specific heat capacity of water is 4.2 kJ/kgK. Determine a. the energy gained by the ice in melting b. the energy gained by the melted ice c. the enegy lost by the lemonade d. a value for the specific heat capacity of the lemonade Solution
3a. energy gained by ice in melting = ml = 0.07 x (3.3 x 10 5) = 23100 J 3b. energy gained by melted ice = mcθ = 0.07 x 4200 x 7 = 2058 J 3c. energy lost by lemonade = 23100 + 2100 = 25200 J 3d. energy lost by lemonade = 25200 J mcθ = 25200 0.3 x c x 21 = 25200 c = 4000 J/kgK 4. A gas burner is used to heat 0.50kg of water in a beaker. The temperature of the water rises from 15oC to 60oC in 60s. Assuming that the specific heat capacity of water is 4200J/kgK, calculate the average rate at which heat is transferred to the water. Solution
4. Heat gained by water = 0.5 x 4200 x (60 - 15) = 94500J Average rate of heat transfer = heat gained / time taken tak en = 94500 / 60 = 1575 J/s 5. The heater of an electric kettle is rated at 2.0kW. ai. Calculate how long it would take to raise the temperature of 1.5kg of water in the kettle iron from 15oC to 100oC. The specific heat capacity of water is 4200 J/kgK. Ignore heat losses and the heat needed to raise the temperature of the material of the kettle aii. Calculate the cost of heating the water assuming that 1kWh of energy costs 6.0p b. The heating element works from a 250 V a.c. supply. Calculate i. the current through the heating element ii. the resistance of the heating element Solution
5ai. heat required = 1.5 x 4200 x (100 - 15) = 535500 J Power = 2000W Power = Energy / Time Time = 535500 / 2000 = 267.75s aii. energy consumed = power x time = 2 x (267.75/3600) = 0.14875 Cost = 2 x 0.14875 x 6 = 0.89p bi. current in the heating element = power / voltage = 2000 / 250 = 8A bii. resistance = voltage / current = 250 / 8 = 31.25 ohm 6a. What is meant by the term latent heat of fusion of a solid? 6b. Thermal energy is supplied to a melting solid at a constant rate of 2000W. Calculate the mass of the solid changed to liquid in 2.0 minutes. Assume that the specific latent heat of fusion of the solid is 95 000 J/kg and that heat exchange with the surroundings may be neglected. Solution
6a. It is the heat required to change 1g of the solid at its melting point to liquid state at the same temperature. 6b. heat supplied by thermal energy = heat absorbed to convert solid to liquid heat supplied in 2 minutes = ml 2000 x 2 x 60 = 95 000 x l l = 2.526 kg 7. 2.0 kg of ice is placed in a vacuum flask, both ice and flask being at 0°C. It is found that exactly 14 hours elapse before the contents of the flask are entirely water at °C. Given that the specific latent heat of fusion of ice is 3.4 x 105 J/kg, calculate the average rate at which the contents gain heat from the surroundings. Suggest a reason why the rate of gain of heat gradually decreases after all the ice has melted. Solution
quantity of heat required to melt the ice = ml = 2 x 3.4 x 10 5 = 6.8 x 105 J rate of heat gain = total heat gain / time = (6.8 x 105) / (14 x 60 x 60) = 13.49 J/s After all the ice has melted, m elted, the temperature of water rises. The gap of difference diff erence in temperature between the water and the surroundings reduces and hence the rate of heat gain decreases.
Transfer of Thermal Energy
When 2 objects are placed in contact with one another, their temperature eventually becomes the same, known as thermal equilibrium.
Heat travels from a region of high temperature to low temperature.
Conduction Heat is transmitted layer by layer through a medium from one particle to another.
Mechanism - collision between neighbouring particles
a. Particles nearer to heat source gain energy and vibrate faster. b. Particles collide into less energetic neighbouring particles which gains kinetic energy. c. The less energetic particles vibrate faster, collides into other particles. d. Process continues layer by layer to spread the heat to cooler parts. - flow of free electrons in conductors only
a. Electrons near heat source gain energy, move faster. b. Free electrons can move between the particles and collide with other electrons, allowing the less energetic electrons to gain energy and move faster. c. Process continues to spread the heat to cooler parts.
Convection Process whereby heat is transmitted from one place to another by the movement of heated particles of a gas/liquid.
Mechanism - change in density
a. fluid nearer to heat source gains heat and expands. b. Expansion causes decrease in density for the fluid nearer to heat source, causing it to rise. c. The hotter fluid rises over the cooler fluid while the cooler fluid rushes in to take the space. d. The process continues and a convection current is formed. e. Convection is faster than conduction as there is bulk movement (all the molecules get hot and move
up, thus it is faster than conduction.
Radiation A method of heat transfer where the source of heat transmit transm it energy through electromagnetic waves. A medium is not required.
Factors affecting radiation - Temperature of object - surface of object - surface area of object - Good emitters are also good absorbers of radiation.
MCQ Questions 1. How may heat be transferred though a vacuum? a. by convection only b. by radiation only c. by conduction only d. by convection and radiation 2. Which of the following is the poorest conductor of heat? a. air b. brass c. vacuum d. water e. wool 3. How is heat transferred through the walls of a steel radiator? a. conduction only b. convection only c. radiation only d. conduction and convection e. convection and radiation 4. Which of the following will be the best absorber of infra-red radiation? a. dark animal fur b. shiny metal tray c. white plastic bag
d. window glass e. writing paper 5. A vacuum will prevent heat transfer by a. conduction only b. convection only c. radiation only d. conduction and convection e. conduction, convection, and radiation
MCQ Answers 1. b 2. c 3. a 4. a 5. d
Structured Question Worked Solutions 1. State briefly how energy is transferred in the following processes a. conduction b. convection c. radiation Solution
1a. Conduction occurs only in all solids whereby the heat energy is transferred via increased vibrations from one layer of molecules to its neighbouring layer and so on. For solids which are good conductors of electricity, free electrons can carry heat energy quickly by diffusing from the hotter end of the solid to the colder sections 1b. Convection occurs only in fluids whereby the fluid at the heat source warms up and becomes less dense than the surrounding fluid. This causes the fluid to rise carrying the heat quickly away from the source. The process is repeated as colder fluid move in to replace the moving warmer fluid 1c. In radiation, the heat energy travels in the form of waves from one place to another without any medium.
Solution 2. A bunsen burner is used to heat a beaker full of water a. explain how energy is transferred through the bottom of the beaker b. explain how energy is transferred through the water c. A student's hand, several cm to one side of the bunsen burner, starts to feel hot. Name the process by which energy is transferred from the burner to the student's hand
2a. the glass molecules gain energy which is passed on to neighbouring molecules 2b. the water near the bottom of the beaker heats up first, expands, and rises up to the top. The colder water, being denser sinks to the bottom to be heated up. Thus, a convection current is set up which transfers heat energy through the water 2c. radiation 3. A saucepan with a thick copper base contains water and is placed on a flat electric hot plate. a. state the process by which energy is i. transferred from the hot plate to the water ii. spread through the water b. state one reason why the water would reach boiling point more rapidly with a lid on the pan c. the sides of saucepans are often polished. How does this reduce heat loss? Solution
3ai. conduction aii. convection b. heat lost by convection is reduced by the lid c. polished surfaces are poor emitters of heat. Hence heat lost by radiation is minimized. 4a. A curved metal mirror focuses the heat energy from the Sun on to a small tank containing water. The area of the mirror is 1.2 m 2, Assuming that the average amount of energy received from the Sun at the mirror per square metre per second is 550 J, calculate the minimum time taken to raise the temperature of 5 kg of water from 20 oC to 100oC. The energy needed to raise the temperature of 1 kg of water by 1 oC is 4200 J. 4b. Only some of the energy incident on the mirror actually reaches the water. Give two reasons why this is so.
4c. The graph illustrates how the temperature of the water changes with time when the mirror is used.
Suggest explanations for the forms of sections AB and BC of the graph 4d. Explain why the temperature of the water rises to 100 oC whereas the surface of the mirror remains quite cool.
Solution 4a. energy supplied per second by the mirror = 550 x 1.2 J quantity of heat required = 5 x 4200 x (100 - 20) = 1680000 minimum time taken = energy/power = 1680000/(550 x 1.2) = 2545.45 s or 42.42 min 4bi. some energy is absorbed by the water container 4bii. some energy is absorbed by the metal mirror 4c. AB: The temperature of water rises slowly with increase in temperature due to greater loss of heat at higher temperature BC: The temperature of water is at 100oC. Temperature remains constant when water is transformed into steam.
4d. Only a small amount of the incident energy is absorbed by the mirror which has a larger area. The heat can be conducted away quite easily. The small tank holds a small amount of water which absorbs most of the incident energy. This leads to a rapid rise in temperature.
Scalar vs Vector quantities
Scalar quantities:described by a magnitude only.
eg. distance, mass, length, temperature
Vector quantities: quantities described by a magnitude and direction
eg. displacement, weight, acceleration, force, momentum
Some terms
Displacement: The distance measured along a straight line in a stated direction w.r.t. the
original point (vector).
Velocity: Rate of change of displacement
Acceleration: Rate of change of velocity
Note: Negative Acceleration = Retardation
Acceleration of free-fall
The acceleration of free-fall near the surface of the Earth is constant and is approximately 10m/s2. It is derived from the gravitational force felt by objects near the Earth surface and independent of the mass of any object.
Speed of a free-falling body (experiencing no other forces other than gravity) increases by 10m/s every second or when the body is thrown up, it decreases by 10m/s every second.
The higher the speed of an object, the greater the air resistance.
Terminal Velocity: When an object is moving at constant velocity, acceleration is 0.
As an object falls, it picks up speed, increasing air resistance. Eventually, air resistance becomes large enough to balance the force of gravity where the acceleration of the object is 0, reaching constant velocity.
Displacement-Time Graphs
Used to show displacement over time.
Horizontal line: Body at rest.
Straight line with positive gradient: Uniform velocity.
Straight line with negative gradient: Uniform velocity in the opposite direction.
Curve: Non – uniform velocity.
The gradient of the tangent of this graph gives the instantaneous velocity of the object.
Velocity-Time Graphs
Used to show velocity over time.
Such a graph can be used to find:
Velocity
Acceleration: Gradient
Distance travelled: Area under the graph
Ticker Tape
The Equations They are called the 'suvat' equations because the quantities s, u, v, a and t are used in the equations, with four of the symbols used in each equation. = displacement (measured in metres) = initial velocity (measured in metres per second, ms-1) = final velocity (also measured in ms-1) = acceleration (measured in metres per second per second, ms-2) = time (measured in seconds, s) Below are the equations:
Note
It is important to bear in mind that these equations can only be used for CONSTANT ACCELERATION ONLY. When acceleration is not constant, these equations do not work. For variable acceleration, either graphical methods or calculus would be needed.
Furthermore, these equations can only be used for motion in a straight line or one-dimensional motion.
Thus these equations are known as the equations of rectilinear motion.
Rectilinear motion is one-dimensional motion with uniform acceleration.
MCQ Questions 1. Which of the following is a vector? a. area b. volume c. density d. force 2. The displacement of an object from a fixed point is the distance moved by the object a. in a particular interval of time b. in a particular direction c. at a constant speed d. at a constant velocity 3. A car accelerates from rest at 5ms-2 for 0.5 minute. The final velocity of the car is a. 150ms-1 b. 5.5ms-1 c. 10ms-1 d. 2.5ms-1 4. When the brakes of a bicycle were applied, the bicycle was brought to rest from 4ms -1 in 2 minutes. What is the acceleration of the bicycle? a. -1/30 ms-2 b. 1/30 ms-2 c. -2ms-2 d. 2ms-2 5. A free falling object is said to be in linear motion. This is because the object is falling a. due to its weight b. at constant velocity c. at constant acceleration d. in one direction 6. An object has been falling freely from rest for 3 s. The maximum velocity of the object is
a. 30ms-1 b. 3.3ms-1 c. 10ms-1 d. 13ms-1 7. A body is moving in a circle at a constant speed. Which of the following statements about the body is true? a. There is no acceleration b. There is no force acting on it c. There is a force acting at a tangent to the circle d. There is a force acting towards the centre of the circle e. There is a force acting away from the centre of the circle
8. What must change when a body is accelerating? a. the force acting on the body b. mass of the body c. speed of the body d. velocity of the body
MCQ Answers 1. d 2. b 3. a 4. a 5. c 6. a 7. d 8. d
Structured Questions Worked Solutions 1. A car accelerates uniformly from a speed of 20ms-1 to a speed of 25ms-1 in 2s. Calculate a. the average speed for this period of 2s b. the distance travelled during this period c. the acceleration
Solution
1a. 22.5 m/s 1b. 45 m 1c. 2.5 m/s2
2.
Describe the motion of the lorry over the following sections of graph along... a. PQ b. QR c. RS Solution
2a. moving with decreasing speed 2b. stationary/zero speed 2c. moving with increasing speed 3.
a. How far has the object travelled during the first 5 seconds? b. What is the acceleration of the object c. For how long does the object move at uniform velocity? d. What is the average speed of the object during the first 15 seconds? Solution
3a. 25 m 3b. 2 m/s2 3c. 0 3d. 11.7 m/s2 4. In an experiment, a student measured the accelerations of a steel ball and a feather falling freely. Will the two accelerations be the same or different? Give a reason for your answer. Solution
The two accelerations are different. The air resistance slowed the downward motion of the falling feather much more than that of the falling steel ball. 5. The figure below shows the velocity of a bus moving along a straight road over a period of time.
a. What does the portion of the graph between O and A indicate? b. What can you say about the motion of the bus between B and C? c. What is the deceleration of the bus between C and D? d. What is the total distance travelled by the bus in 100 s? e. What is the average velocity of the bus? Solution
5c. 1 m/s2 5d. 2000 m 5e. 20 m/s 6. Two cyclists, A and B, start a race. A accelerates for the first 5 s, until his velocity reaches 12ms-1, after which he travels with constant velocity. B accelerates for the first 10 s, until his velocity reaches 15ms-1, after which he travels with constant velocity. a. Sketch the velocity-time graphs for the two cyclists b. Calculate the distance travelled by both cyclists in the first 10 s c. Who is in the lead after 10 s? Solution
6b. 90 m; 75 m 7. A car travels along a straight road. The speedometer reading after every 5 s is tabulated below
Time/s
0
Velocity 0 m/s
5 10
10 20
15
20
25
30
35
40
30
30
30
30
15
0
a. Draw a velocity-time graph to show the variation of velocity with time b. Describe the motion of the car c. How far from the starting point is the car after 20 s d. What is the total distance travelled by the car e. What is the average velocity of the car for the whole journey Solution
7c. 373 m 7d. 825 m 7e. 20.6 m/s 8. Find the average velocity of a car which travels 360km in 6 hours in a. km/h b. m/s Solution
8a. 60 km/h 8b. 16.7 m/s 9. Find the average velocity of an athlete who runs 1500m in 4 minutes in a. m/s b. km/h Solution
9a. 6.25 m/s 9b. 22.5 km/h 10. The graph below shows the speed-time graph for a child on a swing
a. Write down i. the maximum speed ii. the time at which the maximum speed occurs bi. On the graph, mark with 'Z' the point where the magnitude of acceleration of the child is maximum. bii. Mark with 'M' one point at which the acceleration is zero c. Estimate the distance travelled by the child in 1.2s d. Describe briefly the changes in acceleration during the period shown on the graph Solution
10ai. 6.0 m/s 10aii. 0.60 s 10b.
10c. 3.6 m 10d. The acceleration increases from zero initially to a maximum and decreases to zero. The body then decelerates with deceleration increasing to a maximum and decreases to zero. 11. A body is accelerated uniformly from rest and in the first 8.0s of its motion it travels 20m. Calculate a. the average speed of this period of 8 s b. the speed at the end of this period c. the acceleration Solution
11a. 2.5 m/s 11b. 5 m/s 11c. 5/8 m/s2 12. A car of length 6.0m accelerates from rest along a straight level road as shown.
The car takes 2.0s to pass the point P. 10.0s later the car has just passed point Q.
The car takes 0.40s to pass point Q. Calculate ai. the average speed of the car as it passes P aii. the average speed of the car as it passes Q aiii. the average acceleration of the car between P and Q bi. Estimate the distance between P and Q bii. What assumption did you make when you estimated the distance between P and Q? Solution
12ai. 3 m/s 12aii. 15 m/s 12aiii. 1.2 m/s2 12bi. 90 m 12bii. The car accelerates uniformly between P and Q. The acceleration remains constant. 13a. What is meant by the period of a simple pendulum? 13b. The period of a simple pendulum 1 m long is approximately 2 s. State accurately how you would determine the period of such a pendulum as accurately as possible, using a stopclock accurate to within 0.1 s. Solution
13a. The period of a simple pendulum is the time taken for one complete oscillation made by the pendulum. 13b.
The pendulum as shown above is slowly brought to point X and then released. Simultaneously, the stopclock is started. For every time the bob returns to X, it is considered one oscillation. Count to 30 oscillations and read the time taken. The whole experiment is repeated three times. Then average the three readings. The period is found by taking average time over 30. 14. Students, investigating motion down an inclined plane, measure the speed of a steel ball at one second intervals after the ball starts to roll from rest down one such plane:
time in s
0.00
1.00
2.00
3.00
speed in m/s
0.00
0.60
1.20
1.80
a. calculate the average acceleration over the first 3.00 s b. calculate the average speed over the first 3.00 s c. what was the distance travelled by the ball in the first 3.00 s? d. how do the numbers in the table show that the acceleration was constant? Solution
14a. average acceleration = (final speed - initial speed) / time = (1.80 - 0.00) / 3.00 = 0.60 m/s2 14b. average speed = 1/2 x (u + v) = 1/2 x (0.00 + 1.80) = 0.90 m/s 14c. distance travelled = average speed x time = 0.90 x 3 = 2.7 m 14d. The speed increases by a constant value of 0.60 m/s every one second, hence the acceleration can be seen to be constant. 15. A metal box, attached to a small parachute, is dropped from a helicopter. a. Explain in terms of the forces acting, why i. its velocity increased immediately after being dropped ii. it reached a uniform velocity after a short time b. The total force opposing the motion of the box and parachute at a particular instant during its fall is 30N. The combined mass of the box and parachute is 5.0kg. Calculate the resultant downward force on the box and parachute. (g = 10 N/Kg)
Briefly describe the motion of the box and parachute at this time c. At the end of this fall the parachute is caught on a tall tree. The box is then cut loose and falls from rest to the ground. The time of fall is 2.4 s. Calculate i. the velocity with which the box strikes the ground ii. the average velocity during its fall iii. the distance fallen (g = 10 m/s2) Solutions
15ai. This is because at the moment the box left the helicopter, the force of gravity pulled it downwards, causing an increase in velocity 15aii. The presence of the parachute increased the air resistance which acted as a constant retarding force on the box. Once this force was equal to the weight of the box, velocity became constant. 15b. resultant downward force = (5 x 10) - 30 = 20 N From Newton's Second Law of Motion, the box and parachute at this time will accelerate at a rate of 4 m/s2 15ci. given t = 2.4 s, u = 0, g = 10 m/s 2, v = u + at v = 10(2.4) = 24 m/s 15cii. average velocity = (u + v)/2 = (0 + 24)/2 = 12 m/s 15ciii. distance = 12 x 2.4 = 28.8m
Pressure-Volume Relationship of a Gas
Increasing the volume of the container lowers the pressure Decreasing the volume of the container increases the pressure Increasing the pressure of a gas sample decreases its volume Decreasing the pressure of a gas sample increases its volume
Boyle's Law
States that for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume P1V1 = P2V2 Explanation When randomly moving gas molecules hit the wall of the container, they exert a force on the wall. Since pressure is defined as force per unit area, a gas exerts pressure. If the volume of the gas is halved by halving the volume of the container, the number of molecules per cm3 in the container will be doubled. The number of collisions of molecules with the wall in one second will also be doubled. Thus the pressure is doubled
Example 1
An air bubble at the bottom of a lake 40m deep has a volume of 1 .5cm3. What is the volume of the air bubble when it rises to the surface of the lake? (1 bar of pressure is approximately equivalent to the pressure exerted by 10m of water) Solution
Pressure at surface = p1 = 1 bar = pressure exerted by 10m of water Pressure at bottom = p2 = p1 + pressure exerted by 40m of water = 50m of water Volume at surface = v1 Volume at bottom = v2 = 1.5cm3 Boyle's Law: P1V1 = P2V2 10 x v1 = 50 x 1.5 v1 = 7.5cm3
MCQ Questions 1. Brownian motion provides evidence that a. smoke particles consist of molecules b. smoke particles are lighter than air molecules c. air molecules are in continuous random motion d. air molecules attract smoke particles 2. At room temperature the particles in a solid are best described as a. stationary and far apart b. stationary and close together c. vibrating and close together d. moving randomly and far apart 3. Liquids have a definite volume because a. the molecules are held in fixed positions b. forces between the molecules do not allow them to leave the liquid c. the molecules do not vibrate d. the molecules are packed close together in a regular pattern 4. The volume of a certain gas in a piston is reduced to 2/3 of its original value. What happens to the pressure of the gas? a. increases by 2/3 b. increases by 3/2 c. decreases by 2/3 d. decreases by 1/3
5. The pressure of a gas in a piston is 1.5 bar when the volume is 10cm3. The volume is increased and the pressure falls to 1.2 bar. By how m uch was the volume increased? a. 2.5cm3 b. 12.5cm3 c. 8.0cm3 d. 1.8cm3 6. In one minute, a diver breathes 1 litre of air at an atmospheric pressure of 100 kPa. To breathe in the same mass of air in one minute, how much air would he need to breathe when the total pressure on him under water is 300 kPa? a. 1/3 litre b. 1/2 litre c. 1 litre d. 2 litres e. 3 litres 7. The air in a large paper bag is heated. The bag is then found to rise through the surrounding cold air. This is because a. the air in the bag has become less dense b. the mass of the paper bag has decreased c. heat always rises d. the mass of air in the bag has increased e. the chemical compositions of the air in the bag has changed 8. The motion of the molecule of two gases causes them to mix. What is this motion called? a. Brownian motion b. conduction c. diffusion d. evaporation e. radiation 9. A student observes the Brownian motion of smoke particles in air with a microscope. She sees moving points of light. These points of light come from a. air particles only moving randomly b. air particles only vibrating c. smoke particles only moving randomly d. smoke particles only vibrating e. both smoke and air particles moving randomly 10. Some gas trapped in a cylinder is compressed at constant temperature by a piston. Which of the following will not change? a. density
b. mass c. molecular spacing d. pressure e. volume 11. A given mass of air occupies 12 m3 at normal atmospheric pressure. If the pressure is increased to 4 times the original value without changing the temperature, what volume will the air occupy? a. 3 m3 b. 6 m3 c. 24 m3 d. 48 m3 e. 192 m3 12. When the temperature of a gas rises at constant volume, its molecules a. move closer together b. move with greater average speed c. collide with one anther less ofte n d. exert smaller forces on one another e. expand
13. What is a property of both liquids and gases? a. they always fill their containers b. they are incompressible c. they can flow d. they have molecules in fixed positions
Answers 1. c 2. c 3. b 4. b 5. a 6. a (use v1p1 = v2p2) 7. a 8. c 9. c
10. b 11. a 12. b 13. c
Additional Notes Speed of light: 3 x 108 m/s Light ray: Path in which light travels. Can be parallel beam, converging beam or
diverging beam. Luminous object: Objects which give out light Non-luminous object: those which do not give out light Reflection of light Incident ray: Light ray hitting the reflecting surface. Reflected ray: Light ray reflected from the reflecting surface. Normal: The perpendicular to the reflecting surface at the point of incidence. Angle of incidence (i): The angle between the incident ray and the normal. Angle of reflection (r): The angle between the reflected ray and the normal. Law of Reflection
The incident ray, reflected ray and the normal of the reflecting surface lie on the same plane. Angle of incidence = Angle of Reflection
Regular reflection
Occurs at smooth surfaces. Parallel light rays incident on the surface are reflected in one direction only (all rays have the same incident/ reflected ray). The normals of all points of incidence are equal.
Diffuse reflection
Occurs at rough surfaces (sandpaper, burnt boots). Parallel light rays incident on the surface is reflected in all directions. The normals are not parallel.
Characteristics of image formed by plane mirror
Same size as object Laterally inverted Upright Virtual (not real, cannot be captured on screen) The distance of the image from the mirror = distance of object from the mirror.
Applications of mirrors
optical testing blind corners periscopes
Refraction of light
the bending effect of light as it passes through another medium of different density. Refraction occurs as the speed of light varies in different media
Conditions
The light must pass from one optical medium to another of different optical density Angle of incidence more than 0°.
Laws of refraction
The incident ray, the normal and the refracted ray all lie on the same plane. For 2 particular transparent media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. sin i / sin r = constant
When light travels from a less dense medium to a denser medium, the ray of light moves towards the normal. Likewise, when light travels from a denser to a less dense medium, the ray of light moves away from the normal. When light enter a medium perpendicularly, regardless of its density, no deviation of the ray is observed. Refractive index
The value of the constant ratio sin i/sin r for a ray passing from air/vacuum to a give medium is known as the refractive index of the medium. The greater the value of the refractive index, the greater the bending of light, the more the light is slowed down and the denser the medium is.
Dispersion of white light
This is due to different colours travelling different speeds in glass.
Red deviates (slows down) the least.
Violet deviates (slows down) the most.
Converging lens
Features
Optical Centre (C): The midway point between the lens surface on the principal
axis
Principal axis: The line passing symmetrically through the optical centre of the
lens
Principal focus (F): Point on the principal axis where rays of light converge after
passing through the lens Focal length (f): Distance between the optical centre, C and the principal focus F. Focal plane: Plane which passes through F and P. It is perpendicular to principal axis.
As light rays can pass through the lens from both sides, each lens has 2 principal foci and 1 focal length on each side of the lens. A thicker lens has a shorter focal length and bends light rays to a greater extent whereas a thinner lens has a longer focal length and bends light rays to a shorter extent. Linear magnification = height of image / height of object OR image distance / object
distance Object distance
Properties of image
Object distance is at infinity (parallel rays)
- inverted - real - diminished Object distance is - inverted more than 2 focal - real lengths - diminished Object distance is 2 - inverted focal lengths - real - same size Object distance - inverted between 1 and 2 focal - real length - magnified Object distance is 1 - upright focal length - magnified - virtual Object distance is - upright less than 1 focal - magnified length - virtual
Image distance
Uses
- Focal length - opposite of lens
Object lens of a telescope
- Between 1 and 2 focal length - opposite lens - 2 focal lengths opposite lens
- camera - eyes
- More than 2 focal length - opposite lens - infinity - same side of lens - image behind object - same side of lens
- projector - photograph enlarger
photocopier (equal size copy)
spotlight
magnifying glass
Constructing ray diagrams Step
Rules
1
An incident ray through the optical centre C passes without bending
2
An incident ray parallel to the principal axis is refracted by the lens to pass through F An incident ray passing through F is refracted parallel to the principal axis
3
Principle axis - the principle axis is defined as a line perpendicular to the curved surface
of the lens at its center...ie - a line running horizontally through the center of the lens. Principle focus - related to the focal length of the lens... ie - one focal length away from
the center of the lens (therefore there are two principle foci, one on either side, usually designated F on the far side, and F' on the same side as the object.) Parallel rays of light entering the lens either converge towards the principle focus (convex lenses) or diverge from it (concave lenses). Focal length - Focal length is the shortest distance between the principle axis and the
principle focus.
Paraxial rays - Paraxial rays are those that are close to the principle axis and parallel to
it. Magnification - the magnification is usually defined as image height/object height,
representing in effect how much bigger the image is. This is also be directly related to image distance/object distance
MCQ Questions 1. The diagram below shows a plane mirror placed at a distance of 400cm in front of a girl. If the doctor's test card is fixed at 70cm behind the eyes of the girl, what is the distance of the image from the girl?
a. 470m b. 800m c. 870m d. 940m 2. The diagram shows a ray of light moving from air to plastic. Which ratio is the refractive index of plastic?
3. The image seen on the translucent screen of a pinhole camera is
a. real and inverted b. real and upright c. virtual and inverted d. virtual and upright 4. An object is placed in front of a pinhole camera. An image is seen at the centre of the translucent screen when viewed from behind. If the object is now moved slightly nearer and to the observer's right, the image becomes a. larger and moves to the observer's right b. larger and moves to the observer's left c. smaller and moves to the observer's right d. smaller and moves to the observer's left 5. A light ray does not undergo refraction at a boundary between two media of different optical densities if its angle of incidence is a. zero b. 45o c. 90o d. 180o 6. An object is placed in front of a lens at a distance less than the focal length of the lens. The image formed will be a. real, inverted and diminished b. real, upright and magnified c. virtual, inverted and magnified d. virtual, upright and magnified 7. If the size of the image formed by a converging lens is the same as the object, the object distance is a. less than the image distance b. equal to the image distance c. less than the focal length of the lens d. equal to the focal length of the lens 8. Which of the following instruments does not contain lenses? a. microscope b. camera c. binoculars d. periscope 9. A boy walks at a speed of 5m/s towards a plane mirror. The boy and his image in the mirror are moving a. towards each other at a speed of 5m/s b. away from each other at a speed of 5m/s c. towards each other at a speed of 10m/s d. away from each other at a speed of 10m/s 10. The size of an image formed in a pinhole camera may be increased by a. placing the object nearer to the camera b. reducing the size of the object c. decreasing the distance between the pinhole and the screen d. making the pinhole bigger 11. In total internal reflection, the angle of incidence is a. less than the critical angle b. greater than the critical angle c. less than the angle of reflection
d. greater than the angle of reflection 12. Total internal reflection can take place in glass and not in air because glass is a. optically denser than air b. less transparent than air c. more transparent than air d. as optically dense as air 13. The image formed by a slide projector is usually a. real, inverted and diminished b. real, inverted and magnified c. virtual, upright and magnified d. virtual, inverted and diminished 14. Red light cannot be dispersed by a glass prism because it a. has a high frequency b. has a long wavelength c. does not have component colours d. is not refracted in glass 15. White light is dispersed using a prism by means of a. reflection b. refraction c. diffraction d. interference 16. A student uses a converging lens to produce an enlarged virtual image of a scale she wishes to read accurately. The focal length of the lens is 10cm. What is a suitable distance between the scale and the lens? a. 8cm b. 10cm c. 15cm d. 20cm
MCQ Answers 1. c 2. c
3. a 4. b 5. a 6. d 7. b 8. d 9. c 10. a 11. b 12. a 13. b 14. c
15. b 16. a A magnetic field is a region of space where a north magnetic monopole experiences a force.
Properties of magnets - can attract magnetic materials such as iron, steel, cobalt and nickel - has 2 poles: North and South poles - a freely suspended magnet always points in a fixed direction - like poles repel and unlike poles attract Note: repulsion is a sure test of the polarity of a magnet
Magnetic induction - the process of inducing magnetism in an unmagnetised magnetic material
Magnetic materials: - iron - cobalt - steel - nickel Use of magnetic materials
- permanent magnets - compasses - magnetic door stops - loudspeakers - electric meters - Electromagnets - magnetic relays
- electric bells - audio or video tapes
Non-magnetic materials - glass - plastic - wood - rubber
Electromagnetic induction An experiment to show that a changing magnetic field can induce an e.m.f. in a circuit
When a magnet is pushed into the solenoid, the pointer of the galvanometer deflects momentarily. induced current flows in the solenoid momentarily The experiment shows that induced current (or induced e.m.f.) is produced in the coil due to the changing magnetic field of the magnet This process by which induced current is produced is called electromagnetic induction When there is a change in the magnetic flux (field lines) linking a conductor, an electromotive force is induced between the ends of the conductor. This is called electromagnetic induction. If the conductor forms part of a circuit, the induced e.m.f. produces an induced current The change in the magnetic flux linking the conductor can be caused by relative movements between the conductor and the magnet (as shown above) changes in the magnetic strengths surrounding the conductor The size of the induced e.m.f. and hence the induced current, obeys the Faraday's law of electromagnetic induction which states that the induced e.m.f. in a conductor is proportional to the rate of change of magnetic lines of force linked to the conductor, or the rate at which the magnetic lines of force are being cut by the conductor
Factors affecting magnitude of induced e.m.f Induced e.m.f. increased when
1. the magnet moves at a faster speed in and out of the coil 2. a stronger magnet is used 3. the number of turns in the coil is increased Making a magnet by electrical method - most efficient method
a steel bar to be magnetised is placed inside a solenoid direct current is passed through the solenoid, it becomes a magnet
- polarity of the magnet determined by
viewing from one end of the solenoid if current flows in an anticlockwise direction, that end will be the North pole viewing from one end of the solenoid if current flows in a clockwise direction, that end will be the South pole
Methods of demagnetisation
Heating Hammering Using alternating current - most efficient method
A magnet to be demagnetised is placed inside a solenoid connected to an alternating current supply. The magnet will be demagnetised when it is slowly removed from the solenoid with the alternating current flowing in it.
An experiment to plot the magnetic field of a bar magnet
Place the bar magnet at the centre of a piece of paper with its N-pole facing North Place the compass near the magnet and mark the positions (X and Y) of the ends of the compass needle. Move the compass until the S-pole end of the compass needle is exactly at Y. Repeat the process of marking the dots. Join the dots to give a plot of the field lines of the magnetic field.
Change in the direction of the induced current when a Spole is inserted into the solenoid instead of a N-pole
When the N-pole of a magnet is pushed into the solenoid, the galvanometer deflects.
When the S-pole of a magnet is pushed into the solenoid, the galvanometer deflects in the opposite direction
Note: induced current flows in the opposite direction Lenz's Law: Direction of an induced e.m.f. opposes the change producing it.
Change in the direction of the induced current when a Npole of the magnet is withdrawn from the solenoid instead of being inserted into it
When the N-pole of a magnet is pushed into the solenoid, the galvanometer deflects.
When the N-pole of a magnet is withdrawn from the solenoid, the galvanometer deflects in the opposite direction.
Note: induced current flows in the opposite direction. Note: If the solenoid is moved while the magnet is stationary, there will also be induced current flowing in the solenoid.
Electromagnetic Effects Generator
A device in which a coil is rotated in a magnetic field to produce electricity The kinetic energy of a rotating c oil in a running generator s converted mainly into electrical energy
DC Generator
Diagram of a d.c. generator
consists of a rectangular coil of wire connected to a pair of slip rings. coil is placed between the N-pole and S-pole of a magnet when the coil is rotated, the magnetic field linked with the coil changes and an e.m.f. is induced in the coil. the slip rings (or commutator) connect the same carbon brush to the same end of the coil so that current can flow to an external load.
AC Generator
As the coil is rotated, the two sides of the coil move up and down in the magnetic field between the permanent magnets The cutting of magnetic lines of force by the two sides produces an induced current in the coil The induced current flows in the direction in accordance with Lenz's Law Each time the plane of the coil passes through the vertical, the curre nt in the coil changes its direction of flow while the commutators change over. These two changes cancel each other out, so the current will continue to flow in 1 direction.
Diagram of an a.c. generator
As the coil is rotated, the two sides of the coil moves up and down in the magnetic field between the permanent magnets The cutting of magnetic lines of force by the sides produces in induced current in the coil The induced current flows in the direction in accordance with Lenz's Law Each time the plane of the coil passes through the vertical, the curre nt in the coil changes its direction of flow. So does the direction of flow of the current in the external circuit. The output is therefore an alternating current as shown in the graph below.
Graphs of a.c. and d.c. outputs against time
The induced e.m.f. or current of a d.c. or an a.c. generator is increased by incre asing the rate of cutting the magnetic lines of force, by: increasing the speed of rotation of the coil increasing the number of turns in the co il winding the coil on a soft iron core so as to concentrate the magnetic lines of force through the coil. This increases the strength around the coil using stronger magnets
Fleming's right hand rule - for generators/dynamo To determine the direction of induced current in the coil (Generators)
Factors affecting the magnitude of induced e.m.f. The induced e.m.f. of the ac generator can be increased by
increasing the speed of rotation of the coil increasing the number of turns of the coil winding the coil on a soft iron core using stronger magnets
Pattern of a magnetic field due to a current in a straight wire
The magnetic field forms concentric circles around t he wire. The circles are closer together near the wire than when further away from the wire The direction of field can be determined by using the right hand grip rule below.
When current flows through a conductor a magnetic field forms. The field lines form concentric circles around the conductor.
Right hand grip rule
Hold a straight wire in your right hand with your thumb pointing in the direction of conventional current (positive flow).
Your fingers circle the wire in the direction of the magnetic field. The compasses in the following diagram indicate the direction of the magnetic field near the conductor. Use your left hand for electron flow.
The following diagram shows a conductor carrying conventional current out of the page (toward the observer), and the direction of the field near the conductor.
Pattern of a magnetic field due to a current in a solenoid
- The magnetic field resembles that of a bar magnet - The direction of the magnetic field can be determined by the r ight hand grip rule - The other method is by viewing at one end of the solenoid - if current flows in anticlockwise direction --> North pole - if current flows in clockwise direction --> South pole
Increasing magnetic field strength by - increasing magnitude of current - increasing number of turns per unit length of solenoid - using a soft-iron core within the solenoid
Fleming's Left Hand Rule - For Motors
Thumb: Motion/Direction of force Forefinger: Direction of magnetic field Centre finger: Direction of current
Current-carrying coil in a magnetic field experiences a turning effect (d.c. motor)
The coil is connected to a split-ring commutator When current flows through the coil, the force acting on the coil will turn the coil in a clockwise direction until the coil is in the vertical position There is no current flowing in the vertical position, but due to its momentum, the coil continues to rotate past the vertical position This reverses the direction of current in the coil. Thus, the coil continues to rotate in a clockwise direction The purpose of the split-ring commutator is to reverse the direction of current in the coil whenever the commutator changes its contact from one carbon brush to another, This ensures that the coil will rotate in a fixed direction
Turning effect of the wire coil increased when 1. 2. 3.
the number of turns of the coil of wire is increased the current is increased the coil of wire is wound on a soft-iron core
MCQ Questions 1. It can be deduced that a piece of metal is already a magnet if a. copper wire is attracted to it b. both ends of a compass needle are attracted to it c. a magnet is attracted to it d. one end of a compass needle is repelled by it e. copper wire is repelled by it 2. Which two materials are most likely to be used for the coil and core of an electromagnet? coil core a. copper air b. copper iron c. copper steel d. iron iron e. iron steel 3. Which of the following statements describes an example of induced magnetism? a. two north poles repel each other, but a north pole attracts a south pole b. a bar magnet, swinging freely, comes to rest pointing north-south c. a bar magnet loses its magnetism if it is repeatedly dropped d. a bar magnet attracts a piece of soft iron e. it is hard to magnetise steel, but easy to magnetise soft iron 4. A small compass is placed beside a bar magnet.
In which direction will the compass needle point?
5. The diagram shows a sheet X of material used to provide magnetic shielding for a sensitive meter near a transformer.
Which material is suitable for X? a. copper b. glass c. iron d. lead e. perspex 6. Which of the following could be used for the needle of a plotting compass? a. aluminium b. brass c. copper d. iron e. steel
7. A direct current I flows upwards in a vertical wire. Which diagram shows the direction and shape of the magnetic field in the region of the wire?
(hint: use right hand grip rule) 8. In which device is a permanent magnet used? a. electric bell b. electromagnet c. plotting compass d. relay e. transformer 9. Which of the following is the best way to demagnetise a magnetised steel needle? a. break it into two pieces b. make it red hot and then let it cool c. leave it next to another strong magnet d. leave it inside a solenoid carrying direct current e. slowly pull it out of a solenoid carrying alternating current 10. Which of the following methods of magnetising a steel rod will produce the strongest magnet? a. bringing a permanent magnet near to the rod b. holding the heated rod in an N-S direction and tapping strongly c. passing an electric current through the rod d. placing the rod in a solenoid carrying a large direct current e. stroking the rod with a permanent magnet 11. A coil of copper wire wrapped around a core could be used as an electromagnet. Which of the following combinations would produce the strongest electromagnet? number of turns core a. few soft-iron b. few steel c. many copper d. many soft-iron e. many steel
12. The diagram shows a beam of electrons about to enter a magnetic field. The direction of the field is into the page.
What will be the direction of the deflection, if any, as the beam passes through the field? a. towards the bottom of the page b. towards the top of the page c. into the page d. out of the page e. no deflection (hint: use Fleming's left-hand rule) 13. The diagram shows a piece of iron 3cm long placed near the S-pole of a magnet.
Which diagram best represents the magnetic field pattern?
14. Which of the following proves that a piece of soft iron is magnetised? a. a magnet is attracted to it b. the ends of a compass are attracted to it c. an aluminium foil is attracted to it d. one end of a magnet is repelled by it 15. A transformer has half the number of turns on the secondary coil than that on the primary coil. Which of the following statements about the output voltage is true? Types of voltage Maximum output voltage Frequency a. alternating doubled no change b. alternating halved no change c. direct doubled halved d. direct halved doubled 16. There are 1000 turns in the secondary coil of a transformer and 500 turns in the primary coil. What will be the voltage across the secondary coil if an alternating voltage of 240 V is applied across the primary coil? a. 60 V b. 120 V c. 480 V d. 960 V 17. The direct current flows downwards in a vertical wire. Which diagram shows the direction and shape of magnetic field in the region of the wire?
18. The diagram shows a coil in a magnetic field.
The coil is part of a d.c. motor which is connected to a d.c. supply. The current, I, flows in the coil. Which direction will the coil rotate and what must be connected directly to P and Q of the coil? Direction of rotation of coil Part connected to P and Q a. clockwise split-ring commutator b. clockwise split-rings c. anticlockwise split-ring commutator d. anticlockwise split-rings 19. The strength of the magnetic field produced by a current-carrying wire depends on the a. direction of the current b. magnitude of the current c. length of the wire d. shape of the wire 20. An alternating current flowing through a coil produces a magnetic field having a. zero strength b. constant strength but alternating directions c. constant directions but alternating strengths d. alternating strengths and directions 21. Fleming's left-hand rule is also known as the a. ampere rule b. force rule c. dynamo rule d. motor rule 22. The magnetic field pattern produced by a coil carrying a direct current is similar to the magnetic field pattern of a. two straight parallel wires carrying direct current in the same direction b. two straight parallel wires carrying direct current flowing in opposite directions c. a permanent bar magnet
d. a horseshoe permanent magnet 23. A current-carrying coil in a magnetic field will experience a. a force of attraction b. a force of repulsion c. forces of attraction and repulsion d. a turning effect 24. When a d.c. motor is connected to an a.c. supply, the coil will a. rotate faster b. stop rotating c. rotate at uniform speeds d. rotate at different speeds 25. In a d.c. motor, no force is acting on the coil when it is perpendicular to the magnetic field. This is because a. no current is flowing through the coil b. a small current is flowing through the coil c. a large current is flowing through the coil d. there is no magnetic field in the vertical position 26. Which one of the following appliances does not use the motor effect? a. loudspeaker b. microphone c. galvanometer d. ammeter 27. The function of the commutator in a d.c. motor is to a. decrease the resistance of the coil b. reverse the direction of the current in the coil c. increase the strength of the magnetic field d. increase the magnitude of the current flowing into the motor 28. Magnetic induction produces a. a magnetic force b. permanent magnetism c. temporary magnetism d. an induced e.m.f. 29. Which one of the following does not change the magnetic flux linking the conductor? a. pulling the conductor away from a magnet b. pushing the conductor and a magnet with the same velocity c. pushing a magnet towards the conductor d. pulling a magnet away from the conductor
30. There is no induced current in the coil when the magnet in the coil stops moving. This is because a. the magnet loses all its magnetism b. the magnetic strength in the coil is not changing c. the magnetic strength in the coil is maximum d. the magnetic strength in the coil is zero 31. The direction of the induced e.m.f. is given by a. the induced e.m.f. rule b. the cockscrew rule c. Ampere's swimming rule d. Fleming's right-hand rule 32. The main function of the commutator is to a. enable the induced current to flow in the same direction through the external circuit b. enable the coil to be rotated in the same direction c. reduce the resistance of the coil d. enable the induced current to flow in the same direction through the coil 33. Which of the following will not induce an e.m.f. in a coil? a. moving a bar magnet towards a coil b. moving a coil away from a bar magnet c. passing a constant direct current through a coil d. passing an alternating current through a coil 34. Each of the following changes will increase the output voltage of a simple generator except a. increasing the speed of rotation b. increasing the number of turns in the coil c. increasing the distance between the two poles of the magnet d. winding the coil on a soft iron core 35. There are 500 turns and 2000 turns in the primary and secondary coil of a transformer respectively. If the output voltage is 1000V, how large is the input voltage? a. 250V b. 500V c. 2000V d. 4000V 36. A transformer which is 80% efficient gives an output of 12V and 4A. What is the input power? a. 13W b. 38W
c. 60W d. 154W
37. Which of the following will prove that a metal bar is a permanent magnet? a. it attracts another magnet b. it attracts both ends of a compass needle c. it conducts electricity d. it repels another magnet
38. Which of the following has no effect on the size of the turning effect on the coil of an electric motor? a. size of the current in the coil b. direction of the current in the coil c. number of turns in the coil d. strength of the magnetic field
39. When a magnet was pushed towards a solenoid, the sensitive meter connected to the solenoid deflected to the right.
When the same magnet was pulled away from the solenoid at the same speed, what was the deflection on the meter? a. the same and to the right b. greater and to the right c. zero d. greater but to the left e. the same but to the left
40. Why is electrical energy usually transmitted at high voltage? a. the resistance of the transmission cables is as small as possible b. the transmission cables are safer to handle c. as little energy as possible is wasted in the transmission cables d. the transmission system does not require transformers e. the current in the transmission cables is as large as possible
MCQ Answers 1. d. 2. b 3. d 4. e 5. c 6. e 7. b 8. c 9. e 10. d 11. d 12. a (note: since the electron beam enters from left to right, the direction of current is from right to left) 13. b 14. d 15. b 16. c 17. b 18. c 19. b 20. d 21. d 22. b 23. d 24. b 25. a 26. b 27. b
28. d 29. b 30. b 31. d 32. a 33. c 34. c 35. a 36. c 37. d 38. b 39. e (Lenz's law) 40. c
Structured Questions - Worked Solutions 1. Two magnets A and B are placed with their poles as shown below.
a. draw arrows to show the directions of the forces exerted on the north pole of magnet A by each of the poles of magnet B b. draw arrows to show the directions of the corresponding forces exerted on the south pole of B by each of the poles of A c. draw an arrow to show the direction of the resultant force exerted by magnet B on magnet A. Label the arrow with letter R d. explain why the resultant force acts in the direction you have shown in c.
Solution
a.
b. since the like poles are nearer to one another, the repulsive forces are stronger than the attractive forces. hence the resultant force is a repulsive force. 2a. Explain what is meant by i. magnetic field ii. electric field b. Complete the diagram to show the pattern and direction of the magnetic field in the space around a bar magnet.
c. The figure below shows the electric field around two small charges.
Describe a simple experiment which could be used to confirm the presence of the field. di. The figure below shows a positively charged sphere S placed near to an initially uncharged isolated conductor AB. Complete the diagram to show the charges induced in the conductor.
dii. Complete the diagram below to show the corresponding charges when S is negatively charged.
diii. Describe the motion of the electrons in AB when the charge on S alternates from positive to negative several times per second. State one effect this motion will produce.
Solution
ai. A magnetic field is a region in which a free pole (North) experiences a force aii. An electric field is a region in which a charge experiences a force.
b.
c. A positively charged body is suspended by an insulating thread near the negative charge. It is observed to be attracted to the negative charge. This shows that the body experiences a n electric force and that an electric field is present. di.
dii.
diii. The electrons will move back and forth between the ends of AB at the same frequency as the charge on S alternates. This changing distribution of electrons heats up the conductor AB. If AB was freely suspended on a non-conducting thread, it would oscillate back and forth. 3. A large electric current is passed, in the direction indicated, through the vertical wire shown below.
Sketch on the card shown the pattern of the magnetic field around the wire (ignore the magnetic field of the earth). Indicate with an arrow the direction of the magnetic field at any one point. How would you check this direction experimentally? Solution
Place a compass on the card. The direction in which the North end of the compass needle points indicates the direction of the magnetic field at that point. 4. The diagram shows a coil of wire wound on a soft iron core. A current is passed through the coil in the direction indicated by the arrows.
a. Mark the N and S poles produced in the iron core. b. Show by an arrow the direction in which the N end of a compass needle would point when placed at A. c. A beam of electrons flow through the point B in a direction that is perpendicularly downwards into the paper. Show clearly by an arrow labelled F, the direction of the force exerted by the magnetic field on the electron beam. Solution
5. The diagram shows a rectangular current-carrying coil mounted on a freely-pivoted horizontal shaft between the poles of a permanent magnet. The connections to a battery and the direction of the current in each side of the coil are shown: the sides of the coil are labelled J, K, L and M.
a. On the diagram, draw arrows to show the directions of forces, if any, acting on the sides, J, K, L, and M. b. State what will happen to the coil as a result of these forces acting on it. Solution
a.
b. The coil will make a half turn in the anticlockwise direction and the sides J and L interchange in positions. As such, the coil will rotate in the anticlockwise direction again for the next half turn. Hence the coil rotates alternately in the anticlockwise direction and then in the clockwise direction for each half turn.
6. The diagram shows a simple a.c. generator
a. Explain i. why an e.m.f. is induced in the coil as it rotates ii. how we know that at the instant shown in the diagram, the slip-ring P is positive b. The coil rotates 2.5 times in each second. At this speed, the maximum value of the induced e.m.f. is 20mV. On graph paper, sketch a graph of e.m.f. against time for a time interval of 1 s from the instant shown in the diagram. Solution
ai. When the coil is rotated, the magnetic field linked with the coil changes and an e.m.f is induced in the coil. aii. Using Fleming's Right Hand Rule, the current flows in the anticlockwise direction in the coil. As the current leaves the coil at slip-ring P, it is thus positive. b.
Additional Notes
1. What kind of electricity is caused by friction?
Static Electricity is caused by friction. 2. How are charged particles in matter affected when two objects are rubbed tog ether?
All matter is made up of tiny particles that have electric charges. Some of these particles have a positive charge. Other particles have a negative charge. Rubbing two objects together may cause some of the negative
charges to rub off one object. The charges move to the second object. This gives the second object a greater negative charge than the first object. 3. How is current electricity produced?
Current electricity is produced when negative charges move along a path. 4. What is a circuit? What are the parts of a circuit?
A circuit is the path along which negative charges move. There are four parts to a circuit: (1) There is a source of electricity Example: A battery (2) There is a path along which charges can move. Example: A wire (3) There is a switch that opens and closes the circuit. Example: A knife switch (4) There is some object that uses the electricity. Example: A light bulb 5. Explain the difference between a complete circuit and an incomplete circuit.
When a switch is closed or turned on, the path of electricity is complete. The charges move. A c ircuit whose path is complete is called a complete circuit. When the switch is open, or turned off, the path is broken. The movement of charges stops. The path is incomplete. A circuit whose path is incomplete is called an incomplete circuit. 6. Explain how electricity is produced in a flashlight.
A dry cell battery is the source of electricity in a flashlight. 7. What are the three ways to make electricity?
Electricity can be made from chemical energy in dry cell batteries and wet cell batteries, and from mechanical energy in generators. 8. How is energy produced in a hydroelectric power plant?
A generator is a machine that uses a magnet to produce electricity. Power plants use large generators to make electricity for whole towns. Generators have moving parts. They need a sourc e of energy to move the parts. Generators usually use fossil fuels, water, wind, or nuclear generated power. 9. What would show the magnetic field of a magnet?
A magnetic field can be seen when iron filings are sprinkled near a magnet. The iron filings form a pattern of lines. These lines are called lines of force. Lines of force show where the magnetic field is and what it looks like. 10. Explain the difference between the two poles of a magnet.
The ends of a magnet are called the poles. A magnetic field is strongest at the poles. A magnet has two poles a north pole and a south pole. The poles are equal in strength. The north pole of one magnet attracts the south pole of another magnet. The south pole of one magnet attracts the north pole of another magnet. But the north pole of one magnet repels, or pushes away, the north pole of another magnet. In the same way, the south pole of one magnet repels the south pole of a second magnet.
11. How are particles in magnetized iron different from those in unmagnetized iron?
Most magnets are made of iron. The particles that make up iron are like tiny magnets. In a normal piece of iron the particles are all mixed up. They point in different directions. In a magnetized piece of iron the particles point in the same direction. 12. How is magnetism used to produce electricity?
Magnetism can be used to produce electricity. This can be done by moving a magnet through a coil of wire. Electricity is produced as long as the magnet moves through the coil. A generator produces electricity this way. 13. What are some uses of electromagnets?
Electromagnets are often used in scrap yards to lift metal and move it. Many electromagnets are strong enough to lift heavy objects, such as cars. Electromagnets are also used in telephones. 14. In what ways are electricity and magnetism alike?
Electricity and magnetism both produce a force that can pull or push things without touching them. They both have opposite states: electricity has positive and negative, and magnetism has north-seeking and southseeking. In both, opposite states attract and same states repel. 15. What will happen if you put a compass next to an electromagnet that is switched on?
The compass needle will turn because an electromagnet produces a magnetic field. The magnetized compass needle will move to line up with the field lines.
Summary Measurement
length
Example
Instrument
accuracy
very short
diameter of thin wire
micrometer screw gauge
0.01mm
short
diameter of coin
vernier calipers
0.01cm
medium
length of pendulum
metre rule
0.1cm
long
length of classroom
measuring tape
1cm
name
power
symbol
giga
109
G
mega
106
M
kilo
103
k
hecto
102
h
deca
101
da
none
100
none
deci
10-1
d
centi
10-2
c
milli
10-3
m
micro
10-6
u
nano
10-9
n
Measurement of time: using pendulum, clock or stopwatch Period: time taken for 1 complete oscillation frequency : number of complete oscillations per second the period increases with the length of the pendulum
MCQ Questions 1. 0.05km written in the standard form is a. 5/100 km b. 0.5 x 10-1km c. 5 x 10-2km d. 40 x 10-3km 2. To measure length using a metre rule, wrong positioning of the eye leads to a. parallax error b. eye error c. zero error
d. metre error 3. Which of the following instruments is most suitable for measuring the internal diameter of a 100ml beaker? a. metre rule b. vernier calipers c. measuring tape d. external calipers 4. The mass of an object is reduced if its a. state is changed b. amount of matter is decreased c. surface area is decreased d. volume is increased 5. A cuboid with length 3cm, width 4cm and height 10cm is made from wood of density 0.5gcm -3. The mass of the cuboid is a. 17.5g 60g 120g 240g 6. It is easier to float in the sea than in a swimming pool because a. the seawater is denser than the water in the pool b. the seawater is less dense than the water in the pool c. the seawater is warmer than the water in the pool d. the seawater is cooler than the water in the pool 7. To correct a fast-running pendulum clock, a. decrease the length of the pendulum b. increase the length of the pendulum c. increase the mass of the pendulum bob d. decrease the mass of the pendulum 8. A ticker-tape timer vibrates 10 times a second. What is the time interval between two consecutive dots? a. 0.1s b. 1s c. 2s d. 10s 9. The bob of a simple pendulum takes 18.8s to swing from P to Q and back to P again twenty times. What is the period of the pendulum? a. 0.47s b 0.94s c. 1.88s d. 3.96s 10. A box weighs 100N on Earth. Given that the acceleration due to gravity is 10ms -2 on Earth and the acceleration due to gravity is 4ms-2 on Mars, what is the mass and weight of the box on Mars? Mass Weight a. 10kg 100N b. 10kg 40N c. 25kg 100N d. 25kg 40N
MCQ Answers 1. C 2. A 3. B 4. B 5. B 6. A 7. B 8. A 9. B 10. B
Structured Question Worked Solutions 1. What is the reading on the vernier calipers?
Solution
5.47cm 2. What is the reading on the micrometer screw gauge?
Solution
6.5mm+0.18mm=6.68mm 3. The mass of 600 spherical lead pellets is found to be 66g and the total volume of the pellets is found to be 5.7cm 3. Calculate
a. the total weight of the pellets b. the volume of one pellet (the force of gravity acting on a mass of 1.00kg is 10.0N) Solution
a. 0.66N b. 0.0095cm3 4a. What is meant by the period of a simple pendulum? b. The period of a simple pendulum 1m long is about 2s. State clearly how you would determine the period of such a pendulum as accurately as possible, using a stopclock accurate to within 0.1s. Solution
a. Period is the time taken for a pendulum to swing one complete oscillation. b. Set a simple pendulum to oscillate, ensuring that the angular displacement does not exceed 5°. Ignoring the first few oscillations,, time only the steady oscillations. Obtain the time for 20 oscillations, and divide this time by 20 to calculate the period. For better accuracy, the experiment can be repeated a few times to obtain the average value of the period. 5. When a block of metal is hung in air from a spring balance, the reading is 9.6N. a. What is the weight of the block of metal? b. Assuming that the weight of a 1kg mass is 10N, what is the mass of the block of metal? Solution
a. 9.6N b. 0.96kg 6. A rectangular block measures length 1.00cm, width 2.50cm, and height 4.00cm. a. Name the instrument used to measure the sides of the rectangular block b. Calculate the volume of the rectangular block c. If the mass of the rectangular block is 300g, find the density of the block Solution
a. vernier calipers b. 10cm3 c. 30gcm‐3 7. State one advantage and one disadvantage of using the micrometer screw gauge for measuring length. Solution
advantage: high accuracy, accurate to 0.01mm disadvantage: has a short range usually between 0 to 25mm 8. State 4 advantages of using the measuring tape as an instrument for measuring lengths. Solution
can be very long can be used to measure bent lines
can be used to measure circumference portable
9. The internal and external diameters of a hollow silver sphere are 7cm and 14cm respectively. Find the mass of the sphere, given that the density of silver is 10 500 kgm -3 Solution
10. Explain why the density of gas is usually stated together with its temperature. Solution
Density is the mass per unit volume. As the volume of gas changes with temperature, the density also changes with temperature. Hence, the density of gas is usually stated with its temperature.
MCQ Questions 1. Which of the following types of energy remains constant during a change of state? a. internal energy b. potential energy c. kinetic energy d. heat energy 2. The energy required for a change of state is called a. chemical energy b. state energy c. latent energy d. heat energy 3. If a substance expands on melting, increased pressure acting on it will a. not change its melting point b. increase its melting point c. decrease its melting point d. condense the substance 4. The reversed process of melting is a. condensing b. freezing c. sublimation d. burning
5. The boiling point of water in a pressure cooker is raised by a. increasing the volume of water in the cooker b. increasing the internal volume of the cooker c. increasing the pressure in the cooker d. increasing the pressure outside the cooker 6. If a sample of water boils at a temperature above 100oC, the water a. is pure b. contains impurities c. boils at a pressure lower than normal atmospheric pressure d. boils in vacuum 7. A liquid evaporates at a. temperatures above its boiling point b. its boiling point c. temperatures below its boiling point d. temperatures above and below its boiling point 8. Which of the following liquids is used as the cooling agent in a household fridge? a. alcohol b. ether c. freon d. liquid hydrogen 9. The specific latent heat of fusion is absorbed by a substance when it changes from a. a liquid to a gas b. a gas to a liquid c. a solid to a liquid d. a liquid to a solid 10. The latent heat of fusion supplied to a substance is used a. to keep its particles in their fixed positions b. by particles to break away from their fixed positions c. to increase the average speed of its particles in their random motion d. to decrease the average speed of its particles in their random motion
MCQ Answers 1. c 2. c 3. b 4. b 5. c 6. b 7. c 8. c
9. c 10. b
Structured Questions 1a. Name the following processes i. a solid changes into a liquid ii. a liquid changes into a solid iii. a liquid changes into a gas at a particular temperature iv. a liquid changes into a gas at ordinary room temperature v. a gas changes into a liquid b. What would you expect the boiling point of water to be if its freezing point is less than 0oC? c. Describe how the melting point of ice is affected by i. presence of sugar ii. altitude Solution
1ai. melting aii. freezing aiii. boiling aiv. evaporation av. condensation b. more than 100oC ci. lowered cii. increased 2a. Explain why we feel cooler when wind blows over us and evaporates the sweat ob our skins b. Using your knowledge of the kinetic theory, explain why evaporation produces a cooling effect c. An immersion heater with an output of 240W is embedded in a large block of ice at 0 oC. After the heater has been switched on for 11 min and 12 s, it is found that 480g of ice has melted into water at 0oC. Calculate the specific latent heat of fusion of ice. d. Why is the specific latent heat of vaporization of a substance much greater than its specific latent heat of fusion? Solution
2a. Evaporation of sweat which is a liquid produces a cooling effect. Furthermore, the rate of evaporation is increased by the movement of air 2d. 240 x 672 = 0.48 l
l = 336000 j kg-1 3. A 200W heater is used to melt ice at 0 oC in a filter funnel. After 300s, the mass of water collected is 0.188kg. If 0.088kg of the ice melted purely due to heat taken in from the surroundings (and not from the heater), calculate the specific latent heat of fusion of ice. Solution
3. 200 x 300 = (0.188 - 0.088) l 60 000 = 0.1 l l = 600 000 Jk/kg 4. A 100g packet of frozen peas at 0 oC is taken from the cold compartment of a fridge. After 20min, the ice has completely melted and produced 5g of water a. assuming that the peas and the water are still at 0oC, calculate the rate at which heat has been gained from the surroundings to melt the ice. Assume that the specific latent heat of melting ice is 340 J/g bi. suggest why the rate of gain of heat might have been larger than the value you have calculated bii. if the peas and water are left for several more minutes, the rate of gain of heat decreases. Suggest why this is so. Solution
4a. amount of heat absorbed by ice = ml = 5 x 340 = 1700J rate of heat gained = 1700/20 = 85J/min bi. heat must be conducted from the packet to the contents. This means the packet must be at a higher temperature and would need to absorb some heat from the surroundings bii. this is because the difference in temperature between the system and the atmosphere has reduced. The rate of heat gain depends on this temperature difference 5.
The figure shows a graph of temperature against time obtained by cooling a vapour. Explain how the energy is given out in the portions of the graph labelled a. AB b. BC c. CD d. DE Solution
5a. latent heat of vaporization is given out when the vapour condenses into a liquid b. heat is given out when the hot liquid cools c. latent heat of fusion is given out when the liquid freezes and becomes solid d. heat is given out when the hot solid cools
Pressure - Pressure is force acting normally per unit area.
If the amount of applied force is the same, then
Larger area --> Lower pressure
Smaller area --> Higher pressure
Examples of Pressure
Skis have a large area to hold up the weight of the skier on the snow
Flat bottomed shoes are comfortable to wear due to reduced pressure acting on our feet
A sharp knife can cut easily because the very high pressure under the cutting surface is more than the object can withstand
Atmospheric Pressure
Atmospheric pressure exists because of MOLECULAR BOMBARDMENT of energetic air molecules (from the air around us)
Under normal conditions, there are large numbers of air molecules and these molecules move with high velocities. They make frequent collisions with things around us
The pressure exerted by the air molecules is almost equivalent to putting a 1 kg mass on an area of 1 cm2
Normal atmospheric pressure= 1 atm (about 1.013 x 105 pa or 101300 pa)
101300 Nm-2 = 10.13 Ncm -2 = 1.013 kgcm -2
Applications of atmospheric pressure
Drinking with a straw
Drawing a liquid into a syringe by withdrawing the plunger
Holding a rubber sucker on a smooth surface
Removing dust with vacuum cleaner
Pressure due to a liquid column
The taller the liquid column (with narrow base), the larger the amount of liquid contained, the greater the weight of the liquid to exert pressure
The amount of pressure in the SAME liquid column is DIFFERENT at DIFFERENT DEPTHS.
The greater the depth, the greater the weight of the liquid above it, the greater the pressure
The pressure in a liquid depends on the HEIGHT of the liquid
The amount of pressure increases with DEPTH
2 cases of liquid pressure 1. With atmospheric pressure
p = p0 + ρgh
Pressure at bottom = atmospheric pressure + pressure due to liquid column In this case, when the container is open, there is atmospheric pressure acting on the liquid as well.
2. Without atmospheric pressure
p = ρgh
Pressure at bottom = pressure due to liquid column only In this case, when the container is closed, air is removed (vacuum), so there is no atmospheric pressure.
Factors affecting pressure in a liquid
1.Density of liquid 2.Depth of liquid 3. Gravitational acceleration
When it is at equilibrium, pressure must be the same at any point along the same depth (h). Note: pressure does not depend on the shape of the liquid column.
Measurement of pressure
Simple Mercury Barometer - Used to measure atmospheric pressure How to construct
A thick-walled glass tube (about 1m long) is filled with mercury completely
The open end of the tube is covered with a finger and inverted
Place the inverted tube in a trough of mercury
Observation: The height of the mercury column found to be about 760mm or 76cm Atmospheric pressure = 1 atm or 760 mmHg or 76 cmHg Reasons for using mercury in a barometer
Mercury does not wet glass
Mercury has a high density
Manometer - Used to measure gas pressure How to construct
The manometer consists of a U-tube containing a column of liquid
The liquid can be mercury, water or oil
How to measure?
When both arms are open, same atmospheric pressure is exerted on the liquid surfaces (same horizontal level)
To measure the pressure of a gas, left side is connected to a gas supply
The gas exerts pressure on the surface at L. The gas pressure must be greater than atmospheric pressure to cause the right side to rise
Pressure at L given by p = p0 + ρgh
Hydraulic System
Pressure can be transmitted throughout a liquid in hydraulic presses
When a small force is applied to the smaller piston, pressure is exerted on the liquid
This pressure is transmitted in the liquid (oil) and is the same everywhere within the oil. Thus the pressure at the bigger piston must also be p.
Since area at the bigger piston is bigger, force must also be greater
A small force applied to the smaller piston can lift a greater load on the bigger piston
Additional Notes
Pressure is the force acting normal or perpendicularly per unit area
SI unit: Pascal (Pa) or N/m2
Pressure in:
Solid
Liquid
Gas
Equation
Pressure = Force/Area
Pressure = hpg
The air surrounding us exerts a pressure in all
h = depth of liquid (m)
directions which is about
p = density of liquid
105 Pa.
3
(kg/m ) g = gravitational field strength
Remarks
This formula can only
- A liquid exerts pressure
- A barometer is used to
be used for solids.
because of its weight.
measure pressure. It
- Liquid pressure acts
consists of an inverted
equally in all directions.
tube in a dish of mercury.
This is because particles
The space above the
of the water can flow and
mercury in the tube is
wrap around the object.
vacuum. - Liquid mercury is used as its density is very high and a shorter barometer can be used to show atmospheric pressure. - An object can be bent/sucked in due to the production of vacuum and due to the difference in pressure; the atmospheric pressure will press on the object.
MCQ Questions 1. Stiletto heels can exert great pressure mainly due to a. the large force acting on it b. the small force acting on it c. its large surface area d. its small surface area 2. Which of the following places has the highest atmospheric pressure? a. on the top of a hill b. in a cable car c. on the roof top of a tall building d. at the bottom of the sea 3. Wind blows a. from areas of high atmospheric pressure to low pressure areas b. from areas of low atmospheric pressure to high pressure areas c. only at areas above normal atmospheric pressure d. only at areas below normal atmospheric pressure
4. The pressure in a liquid decreases with a. increase in surface area b. decrease in surface area c. increase in depth d. decrease in depth 5. A simple barometer filled with water has to have a minimum length of a. 1cm b. 10cm c. 10m d. 100m 6. A block of wood measuring 6m by 3m by 0.5m is placed on a table. If the mass of the block of wood is 4500kg, what is the pressure on the table due to the block? take gravitational force acting on a mass of 1kg to be 10N a. 2500Pa b. 5000Pa c. 9000Pa d.22500Pa 7. A man stands on snow wearing a pair of skis. The total mass of the man is 60kg and each of the skis has an area of 0.2m 2 in contact with the snow. A 1kg mass has a gravitational force of 10N acting on it. What pressure does the man exert on the snow? a. 15N/m2 b. 30N/m2 c. 1500N/m2 d. 3000N/m2 8. Which of the following does not cause the height of the mercury column of a simple mercury barometer to vary? a. changes in atmospheric pressure b. changes in temperature of the mercury c. changes in the value of g d. evaporation of mercury from the barometer reservoir e. leakage of air into the tube 9. In which of the following examples is the greatest pressure exerted? a. a barefooted person standing on the beach b. a brick resting on the ground c. a book resting on a table d. an elephant standing on the ground
e. a knife cutting a piece of meat 10. A tank 3 m long, 1 m wide, and 0.5 m deep is filled with oil which weighs 12 000 N. What is the pressure on the base of the tank due to the oil? a. 4000 Pa b. 6000 Pa c. 8000 Pa d. 18 000 Pa e. 24 000 Pa
11. Water of depth 10m exerts a pressure equal to atmospheric pressure. An air bubble rises to the surface of a lake which is 20m deep. When the bubble reaches the surface, its volume is 6cm 3. What was the volume of the air bubble at the bottom of the lake? a. 2m3 b. 3m3 c. 12m3 d. 18m3
MCQ Answers 1. d 2. d 3. a 4. d 5. c 6. a 7. c 8. d 9. d 10. a 11. a
Structured Question Worked Solutions
1. The figure shows a mercury barometer on a day when the atmospheric pressure is 750mmHg. What is the pressure at point B, at the bottom of the mercury reservoir?
Solution
Pressure = 750 + 80 = 830 mmHg
2. The figure shows a manometer with limbs of cross-sectional area of 0.0015m2. It contains a liquid which exerts a pressure of 5000Nm -3. Calculate i. the volume of liquid between the levels PQ and RS in the left-hand tube ii. the weight of the volume of liquid in i. iii. the excess pressure, in Nm-2, of the gas supply above the surrounding atmospheric pressure
Solution
i. volume = 0.0015 x 0.5 = 0.00075m 3 ii. weight = 0.00075 x 5000 = 3.75N iii. pressure = 3.75/0.00015 = 2500Nm-2 3. When a block of metal of mass 1.2kg stands on a horizontal surface, the area of contact between the block and the surface is 8.0cm2. Assuming that the force of gravity acting on a mass of 1kg is 10N, calculate the pressure exerted by the block on the surface. Solution
pressure = force/area = (1.2 x 10)/8 = 1.5Nm -2 4. The figure shows a U-tube manometer connected to a gas cylinder of large volume. The atmospheric pressure is 76cm of mercury.
ai. What is the pressure at A in the right-hand tube? aii. What is the pressure at B in the left-hand tube? b. The tap is opened and mercury is run out until the level in the left-hand tube drops to the 60cm mark. i. assuming that the pressure in the gas cylinder remains constant, what is the new position of the level in the right-hand tube? ii. Explain how you arrived at your answer.
Solution ai. 76cmHg. (because A is exposed to the atmosphere so it experiences atmospheric pressure) aii. 106cmHg (because the pressure at B equals the point in line with it i n the other tube. The pressure there is atmospheric pressure + pressure due to t he column of mercury) = 76 + 30 bi. The new position in the right-hand tube is at the 30cm mark bii. The pressure of the gas cylinder remains the same, hence the difference between the levels of mercury in A and B remains constant. Since B drops by 20cm, A likewise will drop by 20cm from the 10cm mark to the 30cm mark.
5. The figure shows two vertical tubes P and Q, each closed at the upper end. The pressure in the space above the mercury meniscus in tube P is negligibly small. There is a small amount of air in this space in the tube Q. The density of mercury is 13.6 x 10 kg/m 3. The gravitational force on a mass of 1.00kg is 10.0N. Determine i. the atmospheric pressure, in Pa, at that time. ii. the pressure, in Pa, exerted by the air in the space at the top of tube Q
Solution
i. Atmosphere pressure = hpg = (75.0/100)(13.6 x 103)(10.0) = 1.02 x 105 Pa ii. air pressure at top of tube Q = atmospheric pressure - liquid pressure due to 60.0cm of mercury = 1.02 x 105 - (60.0/100)(13.6 x 10 3)(10.0) = 2.04 x 104 Pa 6. The tyres of a car are in contact with the ground over a total area 3.0 x 10 -2 m2. The total weight of the car is 6300N. Calculate the pressure exerted by the tyres on the ground. Why would you expect the temperature of the tyres to have risen after the car has been in motion for some time? Solution
Pressure exerted by the tyres = weight/area = 6300/3.0 x 10 -2 = 210 000 N/m 2 The temperature of the tyres rises because the work done in overcoming friction with the road is transformed to heat energy A wave is a phenomenon in which energy is transferred through vibrations Properties of waves:
1. The source of any wave is a vibration or oscillation. 2. Waves transfer energy from 1 point to another. 3. In waves, energy is transferred without the medium being transferred.
Transverse waves
Transverse waves are waves that travel perpendicular to the direction of motion.
Examples of such waves include rope waves and water waves.
The crest is the highest points of the wave whereas the trough is the lowest points of the wave.
Longitudinal waves
Longitudinal Waves are waves that travel parallel to the direction of motion.
Examples are sound wave and pressure waves.
They form compressions and rarefactions.
Compressions are region where the air particles are close together, creating high pressure.
Rarefactions are areas where the air particles are far apart, creating low pressure.
Wavelength
A wavelength is the shortest distance between any 2 corresponding points in a wave.
SI unit: metre.
Amplitude is the maximum displacement from the rest or centre position (high of a crest or depth
of a trough).
SI unit: metre.
Period
This is the time taken for 1 point on the wave to complete 1 oscillation.
it is the time taken to produce 1 wave.
The SI Unit is seconds (s).
Frequency
Frequency (f):It is the number of complete waves per second.
the number of occurrences within a given time period. When there is a higher frequency, more waves are produced in 1 second, thus the period will be shorter.
SI unit: Hertz (Hz).
Wave speed
the distance of the wave moved in 1 second in the medium.
It is dependent of the medium itself.
For example, for sound, the wavespeed is always the same unless the medium is changed from solid to liquid.
measured in metre per second.
Wavefront
an imaginary line on a live that joints all points that are in the same phase.
It is usually drawn by joining the wave crests.
Reflection of waves
When water waves get reflected, the only thing that changes is the direction.
The wavelength, frequency and speed remains the same throughout.
Sponges are used to absorb the reflections of the water waves.
Refraction of waves
When water waves get refracted (move from deep to shallow water), the speed and the wavelength changes.
The frequency of the wave does not change
Electromagnetic Spectrum
Electromagnetic waves are transverse waves. They are electric and magnetic fields that oscillate at 90° to each other.
They transfer energy from one place to another.
They can travel through vacuum (do not require any medium to travel)
They travel at 3.0 x 108 per second in vacuum. They will slow down when travelling through water or glass.
The wave equation is applicable here too.
They obey the laws of reflection and refraction.
They carry no electric charge (they are neither positively or negatively charged)
Their frequencies do not change when travelling from one medium to another. Only their speeds and wavelength will change.
Most important equation Speed = frequency x wavelength
Sound
Sound is a form of energy.
The energy is passed from 1 point to another as a wave.
Sound is an example of longitudinal wave.
Sound is produced by vibrating sources placed in a medium (air).
It travels in air through a series of compressions or rarefactions.
Compressions: Air molecules are close together, forms high pressure.
Rarefactions: Air molecules are far apart, forms low pressure.
Speed of sound differs in different medium
Air: 330 - 340m/s Water: 1500m/s Glass: 5000m/s Speed of sound differs because:
Differences in strength of interatomic forces
Closeness of atoms in the 3 states
Temperature
- The Wave Equation can also be used to find the speed of sound - The speed of sound is solids like metals are so fast that we can assume/ignore the time it takes to travel a distance. Echoes
Echoes refer to the repetition of a sound resulting from reflection of the sound waves.
Echoes are formed when a sound is reflected off a hard and flat surface.
Reverberation occurs when the surface is too close, causing any reflected sound to follow closely behind the direct sound and prolonging the original sound.
Ultrasound
The range of frequencies which a person can hear is known as the range of audibility.
Human: Between 20 Hz and 20 kHz
Dog: <20 kHz
Bats: Between 10 kHz and 120 kHz.
Ultrasound is the sounds with frequencies above the upper limit of the human range of audibility.
Its small wavelength means less diffraction and the echo formed is more precise in direction.
Applications for ultrasound include:
Determining depth of seabed
Locating sunken ships / shoals of fish
Cleaning small dirt from jewellery
Quality control (checking for cracks) in concrete
Medical applications (development of foetus)
Loudness
a factor distinguishing between various sounds.
The larger the amplitude of vibration, the louder the sound
Sound is measured by decibels (dB).
Pitch
a factor distinguishing various sounds
The higher the frequency of a note, the higher the pitch
Pitch is measured in hertz (Hz).
MCQ Questions 1. Which of the following waves cannot pass through a vacuum? a. light b. sound c. X-rays d. radio waves 2. The distance between 2 successive wavefronts is equal to a. half the distance between a crest and a trough b. the distance between a crest and a trough c. the distance between two successive crests d. the distance between three successive crests 3. A ripple tank with a vibration hitting the surface of the water at a frequency of 50Hz produces 10
complete waves in a distance of 20cm. The velocity of water wave produced is a. 0.1 m/s b. 10 m/s c. 1 m/s d. 100 m/s 4. A crest of a water wave travels 40cm in 5s. If the distance between 2 successive crests is 5mm, what is the frequency of the wave? a. 0.2 Hz b. 1.6 Hz c. 8 Hz d. 16 Hz 5. In a ripple tank, circular waves are reflected from a straight barrier. Which one of the following shapes best describes the shape of the reflected waves? a. circular b. planar c. parabolic d. square 6. Which one of the following is changed when the wave is reflected? a. wavelength b. frequency c. speed d. velocity 7. Which of the following is not changed when the wave is refracted? a. wavelength b. frequency c. speed d. velocity 8. All electromagnetic waves in vacuum have the same a. amplitude b. frequency c. wavelength d. velocity 9. Which of the following waves has the longest wavelength? a. gamma rays b. infra-red
c. ultraviolet d. X-rays 10. A dipper dips into the water in a ripple tank at a frequency of 20 Hz produces plane water waves which travel at a speed of 40cm/s. What is the wavelength of the waves? a. 0.02m b. 2m c. 40m d. 800m 11. A wave source of frequency 2000Hz emits waves of wavelength 0.2m. How long does it take for the waves to travel 4000m? a. 0.4s b. 0.5s c. 2s d. 10s 12. Two notes are played on a piano. The second note is louder and has a lower pitch. The second note is a. higher in amplitude and higher in frequency b. higher in amplitude and lower in frequency c. lower in amplitude and higher in frequency d. lower in amplitude and lower in frequency 13. An instrument on a ship that is used to measure the distance between the ship and a cliff sends out a pulse of sound and receives an echo 5s later. If the speed of sound in air is 330m/s, how far is the ship from the cliff? a. 66m b. 825m c. 1650m d. 3300m 14. During a thunderstorm, an observer sees a lightning flash. 6 s later he hears the thunder. The speed of sound is 330m/s. Approximately how far away is the observer from the lightning? a. 1/20 km b. 1/3 km c. 1/2 km d. 2 km e. 30km 15. A dolphin emits an ultrasonic wave with a frequency of 150 000Hz. The speed of the ultrasonic wave
in water is 1500m/s. What is the wavelength of this wave in water. a. 0.0001m b. 0.01m c. 0.1m d. 10m e. 100m 16. A marine survey ship sends a sound wave straight to the seabed. It receives an echo 1.5s later. The speed of sound in seawater is 1500m/s. How deep is the sea at this position? a. 500m b. 1000m c. 1125m d. 2250m e. 4500m 17. Water waves were produced in a ripple tank using a vibrator of frequency 3Hz. Which of the following values of speed and wavelength could the waves have had? a. speed = 1cm/s; wavelength = 3cm b. speed = 2cm/s; wavelength = 1cm c. speed = 5cm/s; wavelength = 15cm d. speed = 6cm/s; wavelength = 3cm e. speed = 12cm/s ; wavelength = 4cm 18. A surf board moves at 5m/s on the crest of a wave. The distance between wave crests is 10m. The frequency of the wave motion is a. 0.5Hz b. 1Hz c. 2Hz d. 5Hz e. 10Hz 19. Which of the following cannot travel through glass? a. ultraviolet waves b. water waves c. sound waves d. light waves 20. Which of the following is a property of electromagnetic waves? a. they are reflected by mirror only b. they travel at a speed of 330m/s through air c. they are deflected by magnet
d they can travel through a vacuum 21. The figure shows a sea-wave that causes a small cork (z) to rise up and down through one complete oscillation every 4 seconds. Refer to this for questions 21 to 23.
The amplitude of the wave is a. 0.5m b. 1.0m c. 1.5m d. 3.0m 22. The horizontal speed of the wave is a. 0.25m/s b. 0.75m/s c. 4m/s d. 12m/s 23. If the wave is moving to the right, after 4 seconds the cork z will be at position a. P b. Q c. R d. S 24. A large ripple tank with a vibrator working at a frequency of 30 Hz produces 25 complete waves in a distance of 50cm. The velocity of the wave is a. 1500cm/s b. 750cm/s c. 60cm/s d. 5/3 cm/s 25. A source of frequency 500 Hz emits waves of wavelength 0.2m. How long does it take the waves to travel 600m? a. 3s b. 6s c. 12s d. 60s
26. A wave of frequency 1000 Hz travels between two points P and Q with a velocity of 300m/s. How many wavelengths are there in PQ if the length of PQ is 600m? a. 0.3 b. 3.3 c. 600 d. 2000 27. Which one of the following statements about ultraviolet radiation and visible light is not true? a. they are emitted by the sun b. they have the same frequency c. the vibrate transversely d. they can be reflected by polished sheets of metal 28. A VHF radio station broadcasts at a frequency of 100 MHz (1.0 x 10 8 Hz). The speed of radio waves is 3.0 x 108 m/s. What is the wavelength of the waves broadcast by the station? a. 0.33m b. 3.0m c. 4.0 x 1015m d. 3.0 x 1015m 29. Which of the following is an example of longitudinal wave? a. blue light b. water ripples c. radio wave d. sound wave 30. A boy, using a stopwatch, notes that there is a 3s delay between the flash of lighting and the sound of thunder. How far is he from the thunderstorm? Assume speed of sound is 330m/s a. 990m b. 110m c. 3.3km d. 1.1km
31. Which type of electromagnetic radiation travels at the highest speed through a vacuum? a. gamma rays b. light waves
c. radio waves d. none - all travel at same speed
MCQ Answers 1. b 2. c 3. b 4. d 5. a 6. d 7. b 8. d 9. b 10. a 11. d 12. b 13. b 14. d 15. b 16. c 17. e 18. a 19. b 20. d 21. a 22. b 23. d 24. c 25. b 26. d 27. b 28. b 29. d 30. a 31. d
S tructured Ques tion Worked S olutions 1. A gramophone record was made to play at 45 r.p.m. Explain why the frequency of the notes heard is decreased when the record is played at a speed of 33 1/3 r.p.m Solution
1. As the wavelength of the notes are recorded permanently on the record, a reduction in speed reduces the frequency of the notes heard.
2. Name the part of the electromagnetic spectrum as described in the following a. its wavelengths are shorter than those of visible light and it is used to treat cancer b. its frequencies are lower than those of visible light and it is reflected by layers in the upper atmosphere during its transmission c. its wavelengths are shorter than those of visible light and it is used to detect cracks in lead beams d. its frequencies are higher than those of visible light and it is absorbed by glass to produce fluorescence Solution
2a. gamma rays 2b. radio waves 2c. X-rays 2d. ultraviolet rays
3. The speed of light in air is 3.00 x 10 8 m/s. The speed of sound in air in 0.34km.s. An observer is 5.00km away from the lightning discharge. a. calculate the travel time to the observer of i. light from the lightning flash ii. sound from the thunder b. what is the time interval between the observer seeing the lightning and hearing the thunder?
Solution
3ai. travel time to the observer of the light from the lightning = 5000 / (3 x 10 8) = 1.67 x 10-5 s 3aii. travel time to the observer of the sound from the thunder = 5000/340 = 14.7 s 3b. time interval = 14.7 s
4.
A student sits in the middle of a rectangular hall which is 17m wide, as shown above. When the student hits a drum, two echoes are heard, 50 ms and 80 ms respectively, after the bang. Assuming that there is no echo from the ceiling, calculate a. the speed of sound in air b. the length of the hall Solution
4a. consider the first echo, where the sound travelled a distance of 17m in the time 50 ms (0.05s) Speed = 17/0.05 = 340 m/s 4b. distance = time x speed = 0.08 x 340 = 27.2 length of hall = 27.2 m
5a. A loudspeaker and microphone are set up facing each other several metres apart. Explain how the vibrations of the cone of the loudspeaker produce sound waves in the air and how these waves are transmitted through the air to the microphone 5b. The separation of the loudspeaker and the microphone in (a) is 6.8m. When the cone of the loudspeaker vibrates at a frequency of 200Hz, there are exactly 4 complete waves in the air
between the loudspeaker and microphone i. calculate the speed of sound as it travels in the air between the loudspeaker and microphone ii. estimate the number of waves between the loudspeaker and microphone when the frequency of 2.00kHz iii. state the effect on the sound heard by a normal healthy ear if the frequency is changed from 200Hz to 2.00kHz Solution
5a. When the cone of the loudspeaker vibrates, the layer of air molecules next to the cone also vibrates at the same frequency. When the cone moves to the right, the layer of air molecules nearest to it is compressed, forming the compression. When the cone moves to the left, the layer of air molecules nearest to it is pulled further apart forming the rarefaction. Hence as the cone vibrates, a series of alternate compressions and rarefactions travels outwards from the cone of the loudspeaker which is along the same direction as the vibration of the cone. Thus the sound wave is transmitted through air to the microphone 5bi. wavelength = distance / number of waves = 6.8 / 4 = 1.7m speed of sound = frequency x wavelength = 200 x 1.7 = 340 m/s 5bii. the speed of sound in air remains constant. Frequency of a sound wave is inversely proportional to its wavelength. The sound of a frequency of 2000Hz is 10 times higher than that of sound at a frequency of 200Hz. The corresponding wavelength of the sound wave at a frequency of 2000Hz is reduced to 10 times smaller than 1.7m. Since the distance between the loudspeaker and microphone remains unchanged, the number of waves is thus increased by 10 times to 40. 5biii. when sound at a frequency of 200Hz is produced, a lower pitched humming sound is heard. As the frequency of the sound is increased to 2000Hz, a higher pitched sound is heard.
6.
The diagram shows a metal rod, 2.4m long, being struck a sharp blow at one end using a light hammer. The time interval between the impact of the hammer and the arrival of the sound wave at the other end of the rod is measured. Four measurements of the time interval are 0.44ms, 0.50ms, 0.52ms, and 0.47ms a. Determine the average value of the four measurements b. Hence, calculate a value for the speed of sound in the rod. Solution
6a. 0.00048s 6b. 2.4 / 0.00048 = 5000m/s
7a. The sound wave from a source of frequency 400Hz travels in air at a speed of 340m/s. Calculate the wavelength of this sound wave 7b. At any instant there are compression and rarefactions along the path of the sound wave i. explain briefly the meaning of compression and rarefactions ii. what is the distance from the centre of a compression to the centre of the nearest rarefaction in the wave described in a? Solution
7a. 0.85m 7bi. at compression, the air molecules are brought closer than that in normal positions. At rarefaction, the particles are further apart than in their normal position
7bii. 0.425m
8.
The figure shows a boy setting up waves on a long elastic cord. The student's hand makes one complete up-and-down movement in 040s, and in each up-and-down movement the hand moves through a height of 0.30m. The wavelength of the waves on the string is 0.80m For this wave, find the a. amplitude b. frequency c. speed
[0.15m; 2.5Hz; 2m/s]
9. A source of frequency 500 Hz emits waves of wavelength 0.2m. How long does it take the waves to travel 400m?
[4s]
10. A wave of frequency 500 Hz travels between two points P and Q with a velocity of 300m/s. How many wavelengths are there in PQ if the length of PQ is 600m?
[1000]
11. A vibrator of frequency 3 Hz produces waves with an amplitude of 0.5m and a wavelength of 12cm. What is the velocity with which the waves travel across the surface?
[36cm/s]
12. A stick dips steadily into a pond 30 times each second. 50 complete waves are counted on the water surface over a distance of 1m. How fast is the wave travelling?
[60cm/s]
13. A gun is fired between two parallel vertical walls. The echo from one wall is heard after 0.1s; the echo from the other wall is heard after 3.0s later. How far apart are the walls if the speed of sound in air is 340m/s?
[680m] 14. A popular speaker is addressing a very large crowd of people. The public address loudspeakers are mounted on the front of the speaker's platform. The speech is also broadcast by radio. An observer in the crowd notices that he receives the radio broadcast on his radio 1.6s before he hears the same word from the loudspeakers. Estimate the distance of the observer from the platform. State any assumption that you make in arriving at your estimate. (take speed of sound in air to be 330m/s) Solution
Distance of observer from platform = time x speed of sound = 1.6 x 330 = 528m It is assumed that there is no wind and the time lapse between the time the sound leaves the radio and enters the ear is negligible.
Moment The moment of a force is the turning effect of a force, or the ability of the force to making something turn. Moment of a force (M) about a point O is the product of the force (F) and the perpendicular distance (D) from the point to the line of action of the force. Moment = Force x Distance
SI Unit: Newton Metre (Nm) The turning effect of a force depends on - location of applied force
- perpendicular distance between the point of application of the force and the pivot
Type 1,2,3 Levers
Principle of Moments When a body is in equilibrium, the sum of clockwise moments about the balanced point is equal to the sum of anticlockwise moments about the same point (pivot). Total clockwise moment = Total anticlockwise moment
When the clockwise moment is not equal to the anticlockwise moment, there is a resultant moment and the object will rotate in the direction of resultant moment. If there is no resultant moment, the object is balanced.
Centre of gravity The centre of gravity (CG) of a body is an imaginery point where the whole weight of the body seems to act in any orientation. The CG of a regular object is at the centre. The CG of an irregular object is determined using a plumb line. If a body is hanging freely at rest, its CG is always vertically below the pivot, thus the plumb line method works. It can only be used for flat, irregular objects.
Stability Stability is a measure of the body's ability to maintain its original position. 3 types of stability: 1. Stable equilibrium
Object will return to original position after slight disturbance. 2. Unstable equilibrium
Object will fall after slight disturbance 3. Neutral equilibrium
Object remains in new position after slight disturbance.
To increase the stability of a body, its base area should be increased, and the height of its centre of gravity should be decreased.
Example A light metre rule is allowed to pivot freely at the zero end. The other end is supported by a sprin g balance. A weight of 200N is then hung at the 40cm mark. The metre rule stays horizontal. What is the reading on the spring balance?
Solution
By the principle of moments, taking moments about the pivot Anticlockwise moment = Clockwise moment F x 1m = 200N x 0.4m F = 80N
The reading on the spring balance is 80N.
MCQ Questions 1. Which one of the following activities does not apply the turning effect of a force? a. swinging on a swing b. sliding down a slide c. moving up and down on the see-saw d. rowing a boat 2. Which one of the following quantities is zero when a uniform rod is supported in the middle? a. mass b. weight c. pressure d. moment 3. When a body is at rest, it obeys the a. principle of momentum b. Archimede's principle c. principle of moments d. principle of inertia 4. A uniform metre ruler of weight 0.2N balances at the 60-cm mark when a weight W is placed at the 80cm mark. What is the value of W? a. 0.1N b. 0.15N c. 0.2N d. 0.2667N 5. Which one of the following measuring instruments works on the principle of moments? a. spring balance b. single pan beam balance c. micrometer d. vernier calipers 6. A uniform rod of weight 5N and length 1m is pivoted at a point 20cm from one of its ends. A weight is hung from the other end so that the rod balances horizontally. What is the value of the weight? a. 0N b. 0.05N c. 5N d. 7.5N 7. An object will not turn if the applied force on it a. does not reach its maximum b. does not produce a moment c. passes through its centre of mass
d. passes through its centre of gravity 8. Levers are classified into different types according to the position of its a. fulcrum, load and effort b. centre of gravity c. centre of mass d. moment and load 9. Which one of the following statements does not describe a pair of scissors? a. its fulcrum lies between the load and the effort b. it is a lever of type 1 c. it works on the turning effect of a force d. it does not have a centre of mass 10. Which of the following levers is of type 2? a. wheelbarrow b. scissors c. fishing rod d. ice tongs 11. The centre of mass of a body a. has a fixed position b. depends on the pull of gravity c. is always outside the body d. must be in a solid part of the body 12. A drinking glass has a low centre of gravity because a. it is heavy b. it is tall c. it has a broad base d. its contents are heavy 13. When a body is in neutral equilibrium, any displacement will a. raise its centre of gravity b. lower its centre of gravity c. neither raise nor lower its centre of gravity d. return the body to its original position
MCQ Answers 1. b 2. d 3. c 4. a 5. b 6. d 7. b 8. a
9. d 10. a 11. a 12. c 13. c
Structured Questions 1. A uniform metre rule AB is supported at its centre of gravity by a knife edge. A force of 5N is applied at a point which is 30cm from end A of the rule. Calculate the force which must be applied to point B to restore equilibrium.
[2.0N] 2. A boy of weight 600N sits on the see-saw as shown at a distance of 1.5m from the pivot. What is the force F required at the other end to balance the see-saw?
[450N] 3. A very light rod 40cm long is pivoted at the centre. A weight of 50N is placed at one end. Where is the place to put a weight of 200N in order that the rod is in equilibrium?
[5cm from the centre] 4. A very light rod 20cm long has weights of 60N and 40N at its ends. About which point can the rod balance horizontally?
[8cm from the 60N weight] 5. A uniform rod 1m long has masses of 100g and 40g at its ends. If it balances 30cm from one end, what is the weight of the rod?
[0.1N] 6. The figure shows a uniform metre rule pivoted at the 50cm mark. 125g and 200g weights hang from the rule as shown.
a.
Calculate where you would hang a 25g mass in order to balance the rule horizontally b. State, without calculation, how the rule with the two masses hanging as shown in the figure could be balanced without using any extra mass.
[40cm from the pivot on the side of the 200g mass]
Alpha decay
Beta decay
Gamma emission