PH P H Y SICS 1 – Motion Motion
ms
-1
A distance-time graph can make make it easier to represent motion A velocity (speed in a given given direction) – time time graph can show the instantaneous speed DISTANCE-TIME:
VELOCITY-TIME:
Shows distance from start
Gradient shows acceleration
Curved line is acceleration
Straight line is constant speed
Straight line means its stopped moving
Velocity means its stopped
Gradient represents the speed at that
Area under the graph is the distance
oint
travelled
Gradient = change in Y Change in X
the length of the path you have taken – the – the the straight line distance between two places To describe displacement, you need to say how far you are away from the start and
ms
-1
Acceleration is the happens when there is: A change in , or A change in , or A change in speed direction
, so it is also a vector. Acceleration
If an objects speed is constant but its
, we say it is also accelerating
ms -2
With a train travelling at a constant speed in a circle, it is considered to be its average velocity as it goes round the track back to its starting point is zero, as its DISPLACEMENT is ZERO
but
SI units (Systéme Internationale): Metre (m) Kilogram (kg) Seconds (s) Ampere (A)] Kelvin (K) Candela (cd) Mole (mol)
When something decelerates, it is A straight line on a velocity time graph is
, so -1 ms-2 acceleration
The graph shows the motion of a ball being thrown up in the air, falling, and then being caught. A – The ball is at rest A to D – the ball is thrown up with a uniform upward acceleration D to B – it has a negative acceleration as the ball accelerates downwards until resting at B B to E – the same velocity as D to B but it is negative as it accelerates down E – The ball is caught and brought to rest by C
Non-linear graphs (curved graphs) – make strips/rectangles under the graph, calculate the area and add it up this is less accurate than a linear graph
S U V A T s = displacement (m) u = initial velocity (ms-1) v = final velocity (ms-1) a = acceleration (ms-2) t = time (s)
Vectors – the length of the arrow represents represents the of the vector
and the direction of the arrow
You can either the displacement (labelled the resultant) or use or to calculate it The sum of two or more vectors quantities is called their
This rule can be applied whenever vectors act at the same time or from the same point. Relative motion – when an object is moving, it is important to give some sort of information about what its motion is relative to.
Eg. If someone is running along a moving walkway with a velocity of 2 ms -1 relative to the walkway, but if the walkway has a velocity of -2 ms-1, the person will remain in the same positive relative to the ground.
1.2 – Forces
Galileo did the pendulum experiment and found that it rose time. He reasoned that if a ball rolls down a onto an continue moving until something else causes it to stop. GALILEO realised the importance of distinguishing between motions in a
each , it will
and
Newton formed three laws of motion (which sometimes break down under certain conditions) which are very nearly correct under all circumstances
The first law: Every object continues in its state of rest or uniform motion in a straight line unless made to change by the total force acting on it
So, an object has a constant velocity until a acts on it. This law defines what a force – a force is something which can cause acceleration and
The sum of ALL THE forces acting on the body (sigma F) If a body has a number of forces, F 1, F 2 … F n acting on it, it will remain in a state of constant motion only if: . (That is the sum on all the forces from F 1 to F n) is
This can be calculated separately for
and
Because a force can cause acceleration, it is a , with both magnitude and direction. It therefore requires a way of representing both direction and magnitude on a
diagram. A diagram which shows all the forces acting on a body in a certain situation is called a . This doesn’t show forces acting on objects other than the one being considered. CENTRE OF GRAVITY – the weight of an object acting through a single point (the centre) The centre is the point at which gravity appears to act, similar to an objects centre of mass For uniform objects, the centre of the mass will be at the intersection , especially in the middle of the object
Drag forces are made up of two types of forces – result of matter in contact with matter
and
– a
always occurs when two surfaces rub on each other. Although appearing smooth, they are rough, causing friction. Friction
any motion, but cannot actually so does friction
motion. When an object stops,
Friction can be measured using a force meter and moving something across a surface at a constant velocity For an object which is not accelerating, meaning that the frictional force resisting motion must be exactly balanced by the pulling force of the hand
(or ) – caused when a body moves through air. Caused by an object having to push air out of the way in order to move through it. Air resistance depends on , the faster the object moves, the greater the aerodynamic drag (think of a car) As aerodynamic drag increases, objects with a constant driving force tend to reach a max. velocity when they accelerate Free fall and terminal velocity – if someone jumps from a height, they will accelerate due to their own weight (N) and air resistance will affect them Acceleration of free fall or acceleration due to gravity (9.81 ms-2)
In an experiment, the can be measured for various values of the resultant force acting on the trolley while its mass is kept constant. On a graph of , a straight line will show that
There is a
between F and a (a is proportional to F) i.e. F α a
a and m are F α a
( a α 1/m) a
α
F/m
or
F α ma
of F=kma
a α 1/m
Force = kg ms-2 or N
k=1
so
F=ma
– the tendency of an object to stay in its state of rest or uniform moti on
- A car is harder to move than a smaller (in comparison) bike - Without a seatbelt, it can be hard to stop yourself moving in a car when the brakes are applied
An objects
depends on its
. Mass has only size, with no direction (
)
– the force acting on an object due to
All masses have a gravitational field around them. A mass is said to have a around it which causes the mass to attract another mass which is close to it. The size of the field depends on the size of the mass and whereabouts in the field you are. If another mass is put in this field, – caused by
.
. The size of the force varies with the strength of the
gravitational field.
- force with both
and
(
)
g= F/m W = mg
g is Nkg -1
Electrical scale – a piece of conducting metal is compressed or deformed by an objects weight, changing its electrical resistance. It measures WEIGHT A beam balance measures MASS as the FORCES have to be balanced
Forces come in pairs
The third law: If body A exerts a force on body B, then body B exerts a force of the same size on body A but in the opposite direction
These forces act on different bodies (i.e. a trolley and the person) The ‘missing’ force is the force of the ground on the person (which would be shown on a
free-body diagram) The push of the ground upwards o our feet is not a member of three thirds law pair, involving the pull of the earth downwards on us. The two third law pairs in this case are different types of force pairs. One is a gravitational pair, the other is caused by contact between two surface (so if you jump, the contact pair doesn’t exist but the gravitational
pair does). Third law pairs of forces are always of the same type – gravitational, electrostatic, contact etc.
When two forces are equal, they cancel each other out and the object they’re acting on is stationary – or in EQUILIBRIUM
VELOCITY diagrams are used to add forces, and to get them into or out of a triangle, then use Pythagoras’ theorem. Principles for adding forces: Draw the forces acting at the same point Construct the parallelogram Draw in the diagonal from the point at which the forces act to the opposite corner of the parallelogram Measure or calculate the size and direction of the resultant
RESOLVING FORCES
The bunting and rope pull on the pole as a result of being pulled tight. The bunting pulls horizontally to the left while the bracing rope pulls down and to the right. When you resolve the forces and work out what components are acting vertically and what are acting horizontally, you can see the effects of the bunting. It pulls the pole sideways and downwards. This is a STATIC EQUILIBRIUM As the pole is at REST it fulfils Newton’s first law. If something changes, then the pole will fall over as the forces aren’t balanced Equilibrium: when an object has balanced forces acting on it and is in a state of rest
ACCELERATION IN THE EARTH’S GRAVITATIONAL FIELD
Projectile – a force acts on an object which starts it moving then it is subject to a constant force while it moves. In most cases this means the object is in free fall in the earth gravitational field An object dropped accelerates vertically downward due to its weight.
2.1 – Fluid flow – a substance that can flow – normally a
or
, but some
can
behave like this
Fluid density is also mass per unit volume
When an object is
in fluid, it feels an
force caused by the
–
The size of the object. –
is
of the fluid that has been displaced by the
The
is equal to
x
is then:
How to answer: (see page 53)
Mass of water displaced is:
Density of water: 1000 kg m-3 If the volume of the brick is: 1.61 x 10-3
This has a weight of:
Weight of brick: 3.38kg So the upward force on the brick is:
If we compare the will be
of the brick with the .
Weight = 3.38 x 9.81 = 33.2N downwards Upthrust = 15.8N upwards Resultant = 33.2 – 15.8 = 17.6 N downwards The brick will until it is at
when it is submerged, the
and
at the bottom
An object floats when it DISPLACES its own weight in fluid. When an object is at the surface of a fluid, there is as no fluid has been displaced. As the object in the fluid, it of fluid, thus acting upon it. When the upthrust and weight are equally, the object will . So if it wants to flo at, it has to sink and displace enough fluid to match its weight.
Used to . The device has a constant weight, so it will sink lower in fluids of lesser density – because a
. Scale markings indicate the density. If used with alcoholic drinks, it there is in it. The the density, the the alcohol content, as alcohol has a lower density than the water it is mixed with.
– (streamline) occurs a lower speeds, and changes to – as the fluid velocity increases past a certain value
This changeover velocity will vary depending on the area through which it is flowing If water is flowing through a pipe slowly, it is flow. Look at the laminar diagram, the arrows closest to the edge of the pipe are shorter than the rest due to friction, meaning this layer moves slower than the other ‘layers’. The next ‘layer’ will experience friction from the outermost one, and so on until we get to the middle layer. . The inner-most layer moves the fastest, as
in question and the
of the
If a liquid follows Newton’s formulae for the frictional force between the layers in streamline flow, then is known as a The laminar flow of water in a pipe continuous
over time
flow – in the same place within the fluid, the velocity of the flow is over time. The of laminar flow are called streamlines; the velocity of the flow will be
, at on any of these over time.
In flow, the fluid velocity in any given place over time. The flow becomes chaotic and eddies form, causing unpredictable and . Turbulent flow on a vehicle and so
7
Streamline flow produces . Thus by altering the of their suits, skiers can raise the velocity at which the air movement past their body will change from laminar flow to turbulent flow. This is designs, such as sports cars and boats the principle behind all ‘
(the friction against you) is greater in water than in air. The frictional force is due to the fluids viscosity.
Newton developed a formula for the friction in liquids which includes several factors, one of which is The
factor is called the
The rate of flow of a fluid flowing through a pipe is of the fluid.
Ƞ
to the
In industry, the rate of flow of liquid chocolate through pipes in the manufacture of sweets will vary with the chocolates viscosity.
at
also affects viscosity. In general, liquids have . For gases, viscosity with temperature.
of
In order to calculate an objects actual acceleration when falling, we refer to Newton’s
From this, we can calculate the resulting acceleration for falling objects; we need to include , caused by the object being fluid in air and the force caused by the movement. The changing velocity makes the viscous drag difficult to calculate, so we consider the equilibrium situation, in which the weight exactly balances the sum of upthrust and drag, meaning that the falling velocity remains , thus it is the .
Viscous drag is the friction force between a solid and a fluid. Calculating this can be simple, so long as it is a (otherwise it is difficult as the turbulent flow creates and unpredictable situation)
Viscous drag (F) on a small sphere at low speeds:
r – Radius of the sphere (m) v – Velocity of the sphere (ms -1) Ƞ - coefficient of viscosity of the fluid (Pa s) In such a situation, the drag force is directly proportional to the radius of the sphere and directly proportional to the velocity, neither of which is necessarily an obvious outcome.
Consider this: a ball bearing is dropped through a column of oil Terminal velocity:
weight = upthrust + stokes’ law
Ms is the mass of the sphere and v term is the terminal velocity Mass of the sphere, ms:
Weight of the sphere, W s:
For the sphere, the upthrust = weight of fluid displaced Mass of fluid, mf :
Weight of fluid, W f :
Rearrange:
=
v term
=
Terminal velocity is proportional to the square of the radius. Therefore, a . More complex situations have more complex equations. This isn’t however a
common situation, however the
2.2 – Strength of materials
There is a spring and the
between it exerts
The law states that
a
F exerted by a spring is ,x
K is as the force exerted by the spring is in the OPPOSITE DIRECTION to the extension This law only applies up to a , when this limit is reached, the extension and the spring remains more when the load is removed. This is called the The spring constant, k, is different for different springs. The larger the value of k, the stiffer the spring. Hooke’s law isn’t usually used when considering the stiffness of a particular material;
which the
and
. This provides evidence for a model of solids in forces behave a little like springs.
Beyond the elastic limit, materials no longer obey the law and the permanent deformation is called plastic deformation. Some materials have a Plasticine for example.
The average force used to stretch the spring is: ½F So work done: ½(-kx)x = ½kx2 Elastic energy: Eela = ½Fx = ½kx2
This is the same thing as working out the
– puts something in tension, i.e. tends to pull it apart
If we consider of cross-section If we consider sample
, this takes into account the samples area , this takes into account the length of the
Tensile force per unit area = tensile stress (Nm-2 or Pa) =
Tensile strength = the tensile stress at which the material breaks Extension per unit length = tensile strain =
Many materials, mainly metals, are found to obey Hooke’s
law for small tensile strains. Under these circumstances, the quantity:
This quantity is the The
a material, the
(Nm-2 or Pa) its Young modulus
As the stress increases, the sample begins
– narrowing at one point
– at this point the material stops behaving elastically and begins to
behave plastically. When the stress is removed, the material does not return to its original length – the material shows a large increase in
for a small increase in
– the extension increases rapidly for small increase in force in this
region. Solids which behave in this way are
– the ability for a material to resist a tensile force – the tensile stress at which a material fails
In many situations, the force on a material will be tending to , to squash the material. This is known as a force and puts the mater ial under
Compressive force per unit area =compressive stress (Nm-2 or Pa) =
= the compressive strength at which the Extension per unit length = compressive strain =
Some materials have a very , but are strong when they are subjected to – such as brick and concrete. The strength of a material under is to some extent its . – a materials ability to
, whether is it tensile, compressive or
shear – show – materials that – materials able to withstand – more than one
with without breaking and require a , often gain the
and are good examples – materials which – materials which show . The most malleable material is You can measure hardness by measuring the into the surface with a certain force.
, usually by
of both. , before
or or
by pushing a
A mineral scale by principle that
was used to compare hardness, based on the . This doesn’t provide accurate values so isn’t often used
in engineering
For climbing ropes, the material must be a compromise between and .
,
,
Climbing helmets have also been developed. Traditional, uncomfortable helmets were made from (high density polyethene) but newer ones are made from (carbon-fibre reinforced polymer. These materials are , and not too The helmets are tested thoroughly, investigating , . The compressive stress produced be more than the breaking stress of the material or it will fail. ALSO, by law there must be no more than
the in itself. The
The design is also important, the shell will transfer out evenly over the skull due to . The material it is made out of must also have shows its .
