Winter 2010 Review Hosted by Pi Tau Sigma and ASME
Review Material From Barron’s FE Review, 2nd Edition
What is the FE Exam? First step in process to
become licensed Professional Engineer
How to become Licensed? Graduate from ABET
accredited engineering program Pass FE Exam After several years as a practicing engineer Pass PE Exam
How to Apply FE Exam given twice a
year, April and October Contact State Board of Registration to obtain application and registration materials State Board of Registration www.ncees.org
8 Hour – Two 4-hour sessions “supplied reference” exam NCEES Fundamentals of Engineering Reference
Handbook will be provided
Points added from both sessions and 70% (50%) is passing
MORNING EXAM
4 Hours 120 Questions (1 point) 13 Subject Areas
AFTERNOON EXAM (GENERAL)
4 Hours 60 Questions (2 points) 9 Subject Areas
SUBJECT
PERCENTAGE
# OF QUESTIONS
Mathematics
19
Engineering Probability and Statistics
8
Chemistry
11
Computers
8
Ethics and Business Practices
8
Engineering Economics
10
Engineering Mechanics: Statics
6
Engineering Mechanics: Dynamics
7
Strength of Materials
8
Material Properties
8
Fluid Mechanics
8
Electricity and Magnetism
11
Thermodynamics
8
TOTAL QUESTIONS
-
120
SUBJECT
PERCENTAGE
# OF QUESTIONS
Mathematics
6
Engineering Probability and Statistics
5
Engineering Economics
6
Strength of Materials
8
Material Properties
7
Fluid Mechanics
9
Electricity and Magnetism
7
Thermodynamics and Heat Transfer
9
Biology
3
TOTAL QUESTIONS
-
60
IMPORTANT – Download and review prior to taking the exam http://www.ncees.org/Exams/Study_materials/Do
wnload_FE_Supplied-Reference_Handbook.php ▪ Enter valid email address (password will be sent there) ▪ Copy password back into website above ▪ Download PDF (11300KB) and Save
1. 2. 3. 4. 5. 6. 7.
8. 9. 10.
Straight Lines Quadratic Equations Conic Sections Spheres Logarithms Triangle Trigonometry Analytic Trigonometry Complex Numbers Matrices Determinants and Inverses of Matrices
11. 12. 13. 14. 15. 16.
17. 18.
Vectors Sequences and Series Derivatives Maxima, Minima, and Points of Inflection Indefinite Integrals Definite Integrals Differential Equations Laplace Transforms
Find equation for line passing through points (-2,-3) and (2,1)
point (2,1) and perpendicular to 3x-5y=10
Solve quadratic equation for x x2+6x=18
x2+5=2x
Classify the following quadratics as circle, parabola, ellipse, or hyperbola 4x2-4xy+y2-5(5)1/2x+5=0
8y2+6xy-9=0
Sphere with center (1,-3,2) passes through point (4,1,2) Find radius of sphere
Find general-form equation of the sphere
Simplify the following expressions e2ln(x+1)
Log216x-2
Log650+2log64-3log62
Two angles of a triangle are 48 and 62 . The side opposite the unknown angle is 52cm. Find the measure of unknown angle
Find the lengths of the unknown sides
Simplify the following into a single trig function cosθ tan2θ+cosθ
cos2θ /(1-sinθ) -sinθ
Convert 3+3i to polar form
If z1=3+5i and z2=1-5i what is z1z2
If A=
2
5
-3 0 1
2A-B
AT+BT
4
and B=
4
6
-2 -5 0
3
|A|=
1
3 -2
3
0 1
-1 2 -4
3 -1 A if A=
2
4 3
If A=-8i-2j-4k and B=2i+2j+1k |A| |B|
A·B
AxB
Find the sum of the series Σ(4i-3)
Write the following in expanded form Σ(3/2)n
S=120t-16t2 Find instantaneous velocity, v, at any time, t
Find instantaneous acceleration, a at any time, t
For the function f(x)=1/3x3-2x2+3x+1 Find maxima and minima
Point of inflection
Use substitution to evaluate ∫3/(4x-1)dx
Use integration by parts to solve ∫xsin3xdx
Consider the definite integral ∫8xdx Evaluate the integral
Give geometric interpretation of integral
Solve the homogenous linear differential equation y”+8y’+16=0
Perform the following transformations L{5t2-2sin3t}
L-1{4/s+5/s4-1/(2s+8)}
1. 2. 3. 4. 5. 6. 7.
Measurers of Central Tendency and Dispersion Combinations of Permutations General Probability Probability Distributions Confidence Intervals Goodness-of-Fit Hypothesis Test Regression
Find the mean, median, mode, and standard deviation of the following data 19, 23, 23, 17, 18, 32
How many 5-card hands can be dealt from a standard 52-card deck of playing cards?/
Let E=event of at least 1 tail in 10 coin flips Let F=event the 1st of 10 flips is heads Find P(E)
Find P(E|F)
Coin flipped 20 times what is the probability of the coin landing on heads exactly 10 times?
Find 95% confidence interval for the following data 15.7, 15.8, 16.1, 16.0, 15.8, 16.2, 16.1, 15.8
Test statistic x2=Σ(observed-expected)2/expected Reject null hypothesis if x2>x2a,k-1 where (k-1) is degrees of freedom and k is number of categories Use chi-square table andα if given to solve
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Basic Concepts, Definitions, Notation, and Units Basic Calculations Gas Laws Chemical Reactions Colligative Properties of Solutions Acids, Bases, and Salts Chemical Equilibrium Solubility Product Constants Chemical Kinetics Chemical Thermodynamics and Thermochemistry Electrochemistry Organic Chemistry
Uranium, atomic number Z=92, has 3 isotopes U-234, U-235, U-238. U235 forms cation (+6) when combined with halogen Write symbol for U-235 isotope
Determine number of protons, neutrons, and electrons in one atom of isotope
Write chemical formula for the following Calcium chloride (ionic)
Sulfur trioxide (covalent)
5.75g of unknown gas occupies V=3.40L at T=50 C and P=0.94atm. Find molar mass
50g hydrogen gas and 50g oxygen gas are ignited to form water, calculate the following Mass of H2O formed and any unreacted H2 or O2
Calculate boiling point of solution of 70g NaCl dissolved in 300g of water, KbH2O=0.512 C·kg/mol
0.024M solution of slaked lime Ca(OH)2 [OH-]
pH
Write equilibrium expression for the following reaction at 25 C 2N2O5(g) ↔ 4NO2(g)+O2(g)
What is Δn?
Calculate the molar solubility of calcium flouride, CaF2
Write the rate law equation for the general reaction aA + bB → gG + hH
10 moles ideal gas in piston/cylinder absorb 2,500J of heat and expands from 2.0L to 8.5L against constant external pressure 2.5 atms What is internal energy change of system?
Consider Mg(s)+Sn2+(aq) →Mg2+(aq)+Sn(s) Write two half reactions
Which species is oxidized and reduced
Identify anode and cathode
Using the IUPAC system, name and draw the structures of the following C2H6
CH3-O-CH3
1. 2. 3. 4. 5. 6.
Computer Organization Computer Terms and Definitions Coding Program Design Microsoft Excel Sample Problems
Name 2 Input devices
Name 2 Output devices
Name 5 computer classifications by size and power
What is the difference between Internet and WWW
The Extended Binary Coded Decimal Interchange Code (EBCDIC) Uses ___ bits for each character allowing a maximum of ____different characters
______ware is an executable program kept on disk or tape
______ware is a program placed in ROM (read only memory) or EPROM (erasable programmable ROM)
____ware is the computer
If the value of D1 is (A1+B1+C1)/3 and copied into range of cells D2:D3 and the value of D4 is SUM(D1:D3)/3 what is D4? A 1 1 2 4 3 7 4
B 2 5 8
C D 3 6 9
What is binary number 0101110 in base 10
Base 10 number 135 is equivalent to binary number
Winter 2010 Review Hosted by Pi Tau Sigma and ASME
Review Material From Barron’s FE Review, 2nd Edition
1. 2. 3. 4.
Engineering and Ethics NCEES Model Rules of Professional Conduct Resources for Engineering Ethics Problem-Solving Strategy for FE Exam
Engineers are bound by licensing and ethical rules of their society, and must exercise autonomy in the workplace.
See NCEES Reference Handbook
NSPE’s Board of Ethical Review www.nspe.org
Textbooks on Engineering Ethics
What is the best word to complete the following sentence, “Engineers are to uphold the health, safety, and public ________”? trust good
confidence welfare
The order of ranking of ethical responsibility of the professional engineer, from highest to lowest importance is, Society as a whole, client, profession, oneself Oneself, client, society as a whole, profession
Oneself, client, profession, society as a whole Client, society as a whole, profession, oneself
An engineer working for a large consulting firm has decided to establish his own business. Although the new business is several months from start-up, the engineer should
Tell current colleagues of his new plans Discuss his plans with his current supervisor Resign immediately Start developing promotional literature while he has use of his current employer’s computers
Read the entire problem and make sure you understand the facts and question Eliminate choices that are unethical Pay attention to conflict of interest issues, contract or agreement disputes, accuracy and proper presentation of individual and professional information
1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Fundamental Concepts Nomenclature and Definitions Nominal and Effective (Non-annual Compounding) Interest Rates Cash-Flow Diagrams Interest Formulas and Tables Financial Metrics: Operating Statements and Balance Sheets Depreciation Methods Bonds Benefit-Cost Analysis Capitalized Costs Inflation Methods of Analysis The Factors and the Factor Tables
Define the following: Equivalence –
Future value –
See NCEES FE Reference Handbook
Finance company charges 1.5% per month compounded monthly. What is the nominal and effective interest rates?
Illustrate cash flow diagram for uniform annual receipts, A, from year 0 to year n with a present value, P, and future value, F, at n.
Illustrate cash flow diagram for gradient, G, from year 0 to year n.
See NCEES FE Reference Handbook
What is the difference between Operating (Profit and Loss) Statement and Balance Sheet?
Fundamental accounting equation:
A machine, with 7 year life, is purchased for $20k and has a $3.2k salvage value. According to straight-line depreciation, what is book value at the end of year 4?
Similar to stocks, typically more secure because you may be guaranteed a certain price at maturity. Bond yield is influenced by bond price and computed on basis of comparison of annual interest to current cost. Typically issued to finance construction projects.
B/C ratio> 1 preferred, benefits are greater than costs If two machines initially cost $20k, and $40k to purchase and reduce annual operation costs by $1k and $2k respectively, both have a 10 year life. Which machine is preferred based on benefit-cost analysis?
What is considered a capitalized cost?
Capitalized costs= P=A/i
How do you treat inflation?
If a country experiences 20% inflation per month, what is the effective annual inflation rate?
Present Worth –
Annual Worth –
Rate of Return –
Rate of Return on incremental investment –
Break Even –
What is the factor for converting future worth into present worth?
Where would you find the factor for converting annual cost/revenue into future worth for 10% interest rate? What is the vale if the future worth is estimated at year 5?
1. 2. 3. 4. 5. 6. 7. 8.
Forces Moments Equilibrium of Particles Equilibrium of Rigid Bodies Trusses and Frames Friction Center of Gravity Moments of Inertia
Resolve the forces into their rectangular components y F2=50lb 3
F1=100lb 30°
4
20° F3=80lb
x
Moment produced from a 140N force acting from the origin towards point (6,3,2) about the x axis.
Resultant couple moment of two equal and opposite forces, F1=F2=100lb, at a distance of 3 ft
Determine reaction at each support 500 N 200 N/m A
B 4ft
3ft
3ft
Determine the value of the friction force if µs=0.3 and µk=0.2
250 lb 30°
Determine the center of gravity of the shaded plane area y
8cm
4cm
2cm 4cm 8cm
x
What is the moment of inertia of a slender rod, L=1.5m, about the x, y axis? What is the moment about the end of the rod? y
x z
1. 2. 3. 4. 5.
Kinematics of Particles Kinetics of Particles Work and Energy Rigid Body Motion in a Plane Vibrations
The rectilinear motion of a particle is described by the equation x(t)=6t2-24t+7 where x is in meters. Solve for displacement at the instant when velocity is zero.
5oz baseball vx=110ft/s, vy=0ft/s at instant struck by bat, for 0.15sec, the ball leaves with a velocity 140ft/s at 30° with respect to x-axis. What is the magnitude and direction of average applied force?
600 kg milling machine is removed from factory by being lowered 14 m vertically by rigging cable that has constant tension, 5kN. Determine net work done on machine.
Overhead garage door guided by two rollers at P and Q travel within perpendicular channels. When θ=35°, the velocity of the wheel at Q is .5m/s upward. What is the angular velocity of the centerline PR of the door? P
θ
Q
R
1. 2. 3. 4. 5. 6.
7. 8. 9. 10.
Normal Stress Shear Stress Normal Strain Shear Strain Factor of Safety The Relationship of Stress and Strain Plastic Behavior Thermal Strain Poisson’s Ratio Deformation in Axially Loaded Members
11. 12. 13. 14. 15. 16. 17. 18. 19.
Torsion Bending Transverse Shear Stress Combined Loading Principal and Maximum Shear Stresses Thin-Walled Pressure Vessels Columns Deflection of Beams Failure Theories
Determine the normal stress in each section
2”
C
5 kips B 1” A 10 kips
If the allowable shearing 200kN stress in the bolt is 350MPa, determine the minimum diameter of the bolt.
200kN
P
l
δ
τ y γ τ
x
F.S. –
F.S.=Pfail/P__ F.S.=σfail/ σ __ F.S.=τfail/ τ __
Draw a stress strain curve and identify the the elastic zone σ (stress)
ε (strain)
What is the difference between plastic behavior and linear elastic?
Determine the change in temperature required to close the 2mm gap Brass
Steel 2mm
600mm
500mm
Poisson’s Ratio is a material property. How is it related to modulus of rigidity, G, and modulus of elasticity, E?
Determine the total elongation for the composite structure P1=10kips, P2=5kips
E1=E2=30x106psi
D1=2in, D2=1in
L1=20in, l2=15in
E1, A1
l1
P1 E2, A2
l2
P2
For the hollow cylinder, determine the torque, T, that causes a maximum shearing stress of 400MPa 1.5cm
T
24cm 2cm
Determine the shear force and bending moment at a point 2m to the right of point A 500 N
1000 N
200 N/m A
B 5m
2m
2m
1m
Determine maximum transverse shear stress for 40x60cm rectangular beam with loading 200 N/m
A
B 6m
4m
Structural members subjected to combination of axial, bending, and torsional loading.
Determine the principal and maximum shear stresses σx=-24,828psi, σy=0 τxy=-6,369psi τ
σ
σ
τ
Pressure at any location along the wall is given by the following equation
2m long pin-ended column of square cross section, for which each side is 10cm, has E=12GPa and σall=15MPa. Determine maximum allowable load that can be applied.
Winter 2010 Review Hosted by Pi Tau Sigma and ASME
Review Material From Barron’s FE Review, 2nd Edition
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Atomic Structure Bonding Crystallography Phase Equilibrium Ferrous Metallurgy Solid Solubility in Metal Alloys Chemical Diffusion Corrosion Mechanical Behavior Magnetic Behavior Electrical Behavior Engineering Materials
Atomic Structure: arrangement of _________ Electron Configuration s
Hydrogen, H Helium, He Lithium, Li Boron, B Magnesium, Mg Aluminum, Al Chlorine, Cl Zinc, Zn
Covalent
Electromagnetic interaction between delocalized electrons
Ionic
Bonding between atoms with half-filled orbitals
Metallic
Electrostatic attraction between oppositely charged ions
FACE-CENTERED CUBIC
BODY-CENTERED CUBIC
HEXAGONAL CLOSE-PACKED
What is the theoretical density of nickle? Structure: FCC Atomic Mass: 58.71 amu
Atomic Radius: .125 nm
Alloy containing 24 wt % Ni heated to liquid region then cooled to 1,200 C What phase(s) is (are) present? If more than one,
how much of each is present?
What is the diffusion coefficient of carbon in iron at 700 C
In regard to corrosion, which of the following is NOT true? The cathode loses mass Oxidation occurs at the anode The anode and cathode must be electrically
connected Water usually plays an important role
Diamagnetism
Electron magnetic moments oppose applied magnetic field
Paramagnetism
Magnetic moments align within material and become permanent magnet
Ferromagnetism
Weak permanent magnetic moments align with applied magnetic field
Metals
Insulators
Semi Conductors
Super Conductors
Glasses
Polymers
Composites
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Definitions Fluid Properties Fluid Statics Fluid Dynamics Internal Flow External Flow Devices Fluid Measurements Dimensional Analysis – Dimensional Homogeneity Similitude
______ deforms continuously when shear stress is applied. Can be a ______ or ______.
Control Volume is
Forces on fluids include ______ and _______.
What is the Mach number of a jet of oxygen gas at standard conditions (1 atm, 25 C) with a speed of 450 m/s? k=1.40, R=0.260kJ/kg·K
What is the density of an oil if its specific gravity is 0.86?
Static pressure = An open manometer is used to measure pressure in an air tank. The manometer fluid is mercury and the height difference is 14cm, what is the pressure in the vessel? ρmercury=13,550 kg/m3
Air enters a diffuser, D1=12cm and D2=30cm, at v1=2.25 m/s. What is the average speed at point 2?
What is the hydraulic diameter of a rectangular duct 24 in wide and 15 in high?
What is the coefficient of drag for 50cm square plate, placed in a 12m/s air stream? What is the total drag force on the plate? ρair=1.225kg/m3, viscosity=2x10-5 N·s/m2
Find the power of an impulse turbine if 25 kg/s of water leaves the nozzle with a speed of 65m/s, and the turbine is spinning at 500rpm. The radius of the turbine is 50cm, and blade angle, α, is 120º.
What is the stagnation pressure of the fluid if hp=13.6cm, hs=8cm? What is the fluid speed? Fluid is water, ρatm=1,000kg/m3, patm=101.3kPa hp hs
Dimensionally homogeneous – relationship is one whose value is independent of fundamental values (mass, length, time)
If a one-fifth-scale boat model is to e tested in a tow tank, at what speed should the model be towed if a speed of 15 knots (11.72m/s) is to be simulated?
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Current, Voltage, and Power Resistance Direct-Current (DC) Circuit Analysis Inductance Capacitance Resistor-Capacitor (R-C) and Resistor-Inductor (RL) Circuits Alternating-Current (AC) Circuit Analysis Operational Amplifiers Electric and Magnetic Fields DC Motors
1 ampere=
1 volt=
Quantity Symbol Unit q Coulomb Current i v Energy w Joule p
Equation i(t)=dq/dt v(t)=dw/dq p(t)=dw/dt p(t)=v(t)∙i(t)
Ohm’s Law: Resistors in Series Kirchhoff’s Voltage Law:
Resistors in Parallel Kirchhoff’s Current Law:
3 resistors in series, R1=5Ω, R2=6 Ω, R3=9 Ω, if the voltage applied is 10V, what is the current?
3 resistors in parallel, R1=2Ω, R2=6 Ω, R3=4 Ω, if the voltage applied is 12V, what is the equivalent resistance?
Determine number of loops Assign loop currents Apply Kirchhoff’s voltage law to each loop
Voltage/current relation for inductor:
Energy stored in inductor:
Inductors in Series:
Inductors in Parallel:
Voltage/current relation for capacitor:
Energy stored in capacitor :
Capacitors in Series:
Capacitors in Parallel:
A switch, resistor, capacitor and battery are in series with one another. The capacitor is initially uncharged, VT=10V, R=2Ω, C=1/8F. What is the voltage across the capacitor 0.5s after switch closed.
What is the average value of voltage for square wave with 2V amplitude, 4Hz frequency?
Two point charges, q1 and q2, are 36cm apart. What is the magnitude of the force acting on q1 if q1=-2x10-6C and q2=+3x10-6C?
1. 2. 3. 4. 5.
Definitions of Terms Laws and Principles Material Systems Applications Heat Transfer
System
Changes in state of system
Property
Two main classifications open, closed
State
Evolution of system from one state to another
Interaction
Condition at an instant of time
Process
Attribute of system
A container holds 3kg of water and is stirred with a mixer that is powered by the lowering of a 50kg mass 8 meters. The mixing raises the internal energy of the water which is accompanied by a change in temperature. If temperature is related to internal energy of liquid water as such, ΔU=mcvΔ T, what is the change in temperature?
What is the gas constant for argon?
An ideal gas has the following compositions in terms of mole fractions, what is the mass fraction of butane? Butane 0.39 Methane 0.42 Propane 0.19
A 30 kg/s stream of steam enters a turbine at 800kPa and 600ºC, and exits the turbine at 50kPa and 300ºC. What is the rate of energy transferred through turbine work? What is the rate of entropy production?
What is the heat transfer rate of a slab of lead, k=35W/mK, if the front is kept at 110ºC, the back at 50ºC, area=0.4m2, and thickness is 0.03m?
Cellular Biology (e.g., structure, growth, cell organization) 2. Toxicology (e.g., human, environmental) 3. Industrial Hygiene (e.g., personnel protection equipment (PPE), carcinogens) 4. Bioprocessing (e.g., fermentation, waste treatment, digestion) 1.
Calculate the carrying capacity for a bacterial culture growth, if the following is known : initial
concentration=1.8g/L Initial growth rate=0.4g/Lh Growth constant=1.5/h
The risk of excess cancer for a known carcinogen is 0.01. What is the carcinogen potency factor, if the daily intake averaged over the lifetime of an average recipient is 6ppm/day?
A noise reading at 8m from the source was recorded to be 72 dB. What will be the approximate reading at a distance of 24 m from the source?
What is the kinetic constant of the degradation reaction of a contaminant with half-life of 12h?
