FE Other Disciplines Practice Problems

Problem 1 · Differential equations

The Laplace transform of f(t) = 3e^(−2t) sin 4t is:

1. A.12/[(s + 2)² + 16]
2. B.12/[(s² + 16)(s + 2)]
3. C.12/[(s − 2)² + 16]
4. D.3(s + 2)/[(s + 2)² + 16]

Problem 2 · Analytic geometry

Two straight pipe runs cross in plan. One follows y = 2x + 3 and the other follows y = 0.25x − 1 (x and y in meters). The acute angle between the two runs is most nearly:

1. A.49.4°
2. B.60.3°
3. C.74.1°
4. D.130.6°

Problem 3 · Sample distributions and sizes

A lab wants to estimate the mean strength of a material to within ±2 MPa at 95% confidence. The standard deviation is known to be 6 MPa, and z(0.025) = 1.96. The minimum number of specimens required is:

1. A.6
2. B.25
3. C.35
4. D.139

Problem 4 · Statistics

Daily water demand in a town is normally distributed with a mean of 18.0 MGD and a standard deviation of 2.4 MGD. For the standard normal distribution, Φ(1.645) = 0.950. The demand that is exceeded on only 5% of days is most nearly:

1. A.14.1 MGD
2. B.21.1 MGD
3. C.21.9 MGD
4. D.22.7 MGD

Problem 5 · Chemical reactions

Octane (C8H18, M = 114.23 g/mol) burns completely: 2C8H18 + 25O2 → 16CO2 + 18H2O. Take M(CO2) = 44.01 g/mol and M(H2O) = 18.02 g/mol. The mass of CO2 produced per kilogram of octane burned is most nearly:

1. A.0.841 kg
2. B.1.42 kg
3. C.3.08 kg
4. D.8.00 kg

Problem 6 · Chemical reactions

For the gas-phase reaction N2O4 ⇌ 2NO2 at a certain temperature, the equilibrium concentrations are [NO2] = 0.030 mol/L and [N2O4] = 0.0045 mol/L. The equilibrium constant K_c is most nearly:

1. A.0.150
2. B.0.200
3. C.5.00
4. D.6.67

Problem 7 · Data acquisition

A pressure transmitter spans 0 to 600 kPa gauge with a 4 to 20 mA output. The logger reads 13.6 mA, and local atmospheric pressure is 101.3 kPa. The absolute pressure is most nearly:

1. A.360 kPa
2. B.389 kPa
3. C.461 kPa
4. D.509 kPa

Problem 8 · Sensors and transducers

A strain-gauge load cell has a capacity of 500 kg and a rated output of 2.0 mV/V at full capacity. It is excited at 10.0 V and reads 12.6 mV. Assuming a linear response, the load on the cell is most nearly:

1. A.63.0 kg
2. B.315 kg
3. C.794 kg
4. D.3,150 kg

Problem 9 · Societal impacts

Select all that apply.

An engineer is preparing a cradle-to-gate life-cycle assessment of an aluminum bicycle frame. Which stages fall inside the system boundary? Select all that apply.

1. A.Bauxite mining and alumina production
2. B.Smelting and alloying the aluminum
3. C.Tube forming and welding the frame at the factory
4. D.Riding the bicycle during its service life
5. E.Recycling or landfilling the frame at end of life

Problem 10 · Codes of ethics

Under the NCEES Model Law, the engineer in 'responsible charge' of engineering work is the licensee who:

1. A.Signs the services contract on behalf of the firm
2. B.Exercises direct control and personal supervision of the work and makes the independent professional decisions
3. C.Reviews the drawings once they are complete, without having directed the work
4. D.Holds the highest management position in the firm, whether or not licensed

Problem 11 · Hazard communications

An NFPA 704 placard on a storage tank shows the number 4 in the red diamond. This indicates:

1. A.Severe health hazard
2. B.Severe flammability hazard: the material vaporizes readily and burns readily at normal conditions
3. C.Severe instability (reactivity) hazard
4. D.Minimal flammability hazard

Problem 12 · Confined space entry and ventilation rates

Before entry into a permit-required confined space, the atmosphere is tested with a multigas meter. In what order should the hazards be tested?

1. A.Any order, because all readings appear at the same time
2. B.Oxygen first, then flammable gases and vapors, then toxic gases
3. C.Flammable gases first, then toxic gases, then oxygen
4. D.Toxic gases first, then oxygen, then flammable gases

Problem 13 · Project selection

A $120,000 CNC router is depreciated by MACRS as 5-year property. The MACRS rates for years 1 through 6 are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The book value at the end of year 3 is most nearly:

1. A.$20,736
2. B.$23,040
3. C.$34,560
4. D.$48,000

Problem 14 · Time value of money

A supplier charges 1.5% per month on overdue balances, compounded monthly. What is the effective annual interest rate? Enter the rate in percent to two decimal places.

Fill in the blank: answer in %.

Problem 15 · Centroid of area

An area consists of a rectangle 400 mm wide and 200 mm tall with a semicircle of radius 100 mm attached to the middle of its top edge (flat side down, curved side up). The distance from the bottom of the rectangle to the centroid of the composite area is most nearly:

1. A.90.6 mm
2. B.100.0 mm
3. C.123.4 mm
4. D.140.2 mm

Problem 16 · Equivalent force systems

An 800 N force acts at point P, located 1.2 m to the right of and 0.5 m above point O. The force is directed downward and to the right at 60° below the horizontal. The force is replaced by an equivalent force-couple system at O. The magnitude of the couple is most nearly:

1. A.631 N·m
2. B.831 N·m
3. C.960 N·m
4. D.1,031 N·m

Problem 17 · Kinematics of particles

A ball is launched from level ground at 20 m/s and 35° above the horizontal. Neglect air resistance and take g = 9.81 m/s². Its horizontal range on the level ground is most nearly:

1. A.13.9 m
2. B.19.2 m
3. C.23.4 m
4. D.38.3 m

Problem 18 · Kinematics of mechanisms

In a Scotch yoke mechanism, a crank of 0.10 m radius turns at a constant 600 rpm and drives a slotted yoke in simple harmonic motion, x = r cos ωt. The maximum acceleration of the yoke is most nearly:

1. A.6.28 m/s²
2. B.10.0 m/s²
3. C.62.8 m/s²
4. D.395 m/s²

Problem 19 · Stress transformations and Mohr's circle

A point on a machine bracket is in plane stress with σx = 80 MPa (tension), σy = −20 MPa (compression) and τxy = 40 MPa. The maximum principal stress is most nearly:

1. A.30.0 MPa
2. B.64.0 MPa
3. C.80.0 MPa
4. D.94.0 MPa

Problem 20 · Stress and strain caused by axial loads

A stepped bar has a 4 ft steel segment (A = 0.50 in², E = 29,000 ksi) joined end to end with a 3 ft aluminum segment (A = 1.00 in², E = 10,000 ksi). One end is fixed and a 10 kip axial tension is applied at the other end. The total elongation is most nearly:

1. A.0.0331 in.
2. B.0.0360 in.
3. C.0.0455 in.
4. D.0.0691 in.

Problem 21 · Properties (e.g., chemical, electrical, mechanical, physical, thermal)

An aluminum ring with a bore of 50.00 mm at 20°C must be heated so it just slides over a steel shaft that measures 50.05 mm at 20°C; the shaft stays at 20°C. The coefficient of thermal expansion is 23.0 × 10⁻⁶ /°C for the aluminum and 12.0 × 10⁻⁶ /°C for the steel. The minimum temperature rise of the ring is most nearly:

1. A.21.7 °C
2. B.43.5 °C
3. C.83.3 °C
4. D.90.9 °C

Problem 22 · Engineered materials (e.g., composites, polymers)

A glass-fiber/polyester composite contains 40% glass fibers by mass. The glass density is 2.54 g/cm³ and the cured polyester density is 1.38 g/cm³. Assuming no voids, the composite density is most nearly:

1. A.1.69 g/cm³
2. B.1.84 g/cm³
3. C.1.96 g/cm³
4. D.2.08 g/cm³

Problem 23 · Compressible flow

Air at a static temperature of 280 K flows at 500 m/s. Take k = 1.4 and R = 287 J/(kg·K). Enter the stagnation temperature in K, to the nearest kelvin.

Fill in the blank: answer in K.

Problem 24 · Pipe and duct flow and friction losses

Water flows at 0.15 m³/s through 850 m of 300 mm diameter pipe. The Darcy friction factor is 0.018. Take g = 9.81 m/s². Enter the friction head loss in meters, to one decimal place.

Fill in the blank: answer in m.

Problem 25 · DC circuit analysis

Node A connects through a 2 Ω resistor to the positive terminal of a 12 V source, through a 5 Ω resistor to the positive terminal of a 24 V source, and through a 10 Ω resistor to the reference node. The negative terminals of both sources are at the reference node. The voltage of node A relative to the reference is most nearly:

1. A.1.50 V
2. B.13.5 V
3. C.15.4 V
4. D.18.0 V

Problem 26 · AC circuit analysis

A 120 V rms, 60 Hz source supplies a series circuit of a 30 Ω resistor and a 0.10 H inductor. The rms current is most nearly:

1. A.1.77 A
2. B.2.49 A
3. C.3.18 A
4. D.3.92 A

Problem 27 · Conduction

A house wall consists of 13 mm gypsum board (k = 0.17 W/(m·K)), 90 mm of insulation (k = 0.040 W/(m·K)), and 20 mm wood siding (k = 0.12 W/(m·K)). The inside film coefficient is 8 W/(m²·K), and the outside film coefficient is 25 W/(m²·K). The indoor air is at 21°C and the outdoor air at −10°C. The steady heat flux through the wall is most nearly:

1. A.4.14 W/m²
2. B.11.7 W/m²
3. C.12.4 W/m²
4. D.13.8 W/m²

Problem 28 · Processes

Gas in a piston-cylinder device expands polytropically with n = 1.3 from 1.0 MPa and 0.050 m³ to a final volume of 0.20 m³. What is the boundary work done by the gas? Enter the value in kJ to one decimal place.

Fill in the blank: answer in kJ.