FE Mechanical Practice Problems

Problem 1 · Single-variable calculus

A landscaped area is bounded by the curves y = x² and y = 4x, with x and y in meters. The area enclosed between the two curves is most nearly:

1. A.10.7 m²
2. B.21.3 m²
3. C.32.0 m²
4. D.53.3 m²

Problem 2 · Algorithm and logic development

The array [4, 7, 1, 9, 3] goes through exactly one pass of bubble sort in ascending order. The pass compares each adjacent pair from left to right and swaps the pair when the left value is larger. After this single pass, the array is:

1. A.[1, 3, 4, 7, 9]
2. B.[1, 4, 7, 3, 9]
3. C.[4, 1, 7, 3, 9]
4. D.[1, 4, 3, 7, 9]

Problem 3 · Sample distributions and sizes

The tensile capacity of anchor bolts has a population mean of 120 kN and a standard deviation of 9 kN. A random sample of 9 bolts is tested. For the standard normal distribution, Φ(1.67) = 0.9525. The probability that the sample mean exceeds 125 kN is most nearly:

1. A.0.0475
2. B.0.0950
3. C.0.2877
4. D.0.9525

Problem 4 · Goodness of fit

A linear regression of pavement roughness against age has a negative slope. The error sum of squares is SSE = 14.2 and the total sum of squares is SST = 182.6. The correlation coefficient r is most nearly:

1. A.−0.960
2. B.−0.922
3. C.0.922
4. D.0.960

Problem 5 · Public health, safety, and welfare

While inspecting a parking garage for a client's insurance appraisal, an engineer notices severe spalling and exposed, badly corroded reinforcing bars on the balcony slabs of an occupied apartment building next door, which is outside her assignment. What should she do?

1. A.Mention the observation only in an internal appendix of her client's report
2. B.Notify the neighboring building's owner and, if the hazard is not promptly addressed, the appropriate public authority
3. C.Do nothing, because the neighboring building is outside the scope of her contract
4. D.Give the neighboring owner's contact information to a repair contractor

Problem 6 · Societal impacts

A design team must choose between two circulating pumps for a 20-year continuous duty. Pump A has the lower purchase price; Pump B costs more but uses about 15% less electricity. Which approach best accounts for the economic and environmental impacts of the choice?

1. A.Select the pump with the longer manufacturer's warranty
2. B.Compare life-cycle cost and life-cycle environmental impacts, including energy use over the full 20 years
3. C.Select the more efficient pump regardless of its cost
4. D.Select the pump with the lower purchase price, because first cost dominates total cost

Problem 7 · Time value of money

A packaging machine costs $60,000, has operating and maintenance costs of $8,000 at the end of each year for 6 years, and has a salvage value of $10,000 at the end of year 6. At an interest rate of 8% per year, the present worth of the machine's costs is most nearly:

1. A.$86,983
2. B.$90,681
3. C.$96,983
4. D.$103,285

Problem 8 · Time value of money

An energy-efficiency retrofit costs $10,000 and saves $2,500 at the end of each year for 6 years, with no salvage value. The rate of return on the retrofit is most nearly:

1. A.8.3%
2. B.13.0%
3. C.16.7%
4. D.25.0%

Problem 9 · AC and DC circuits

A 470 μF capacitor in a power-supply filter is charged to 400 V. The energy stored in the capacitor is most nearly:

1. A.0.0940 J
2. B.0.188 J
3. C.37.6 J
4. D.75.2 J

Problem 10 · 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 11 · Static friction

Block A (20 kg) rests on block B (30 kg), which rests on the floor. Block A is tied to the wall by a horizontal cord. The coefficient of static friction is 0.30 at both contact surfaces. Take g = 9.81 m/s². The horizontal force on B needed to start B sliding out from under A is most nearly:

1. A.88.3 N
2. B.147 N
3. C.206 N
4. D.265 N

Problem 12 · Area moments of inertia

For the T-section with a 200 mm × 20 mm flange on top of a 20 mm × 180 mm web (total depth 200 mm, centroid 142.6 mm above the bottom), the moment of inertia about the horizontal centroidal axis is most nearly:

1. A.9.85 × 10⁶ mm⁴
2. B.18.9 × 10⁶ mm⁴
3. C.28.8 × 10⁶ mm⁴
4. D.183 × 10⁶ mm⁴

Problem 13 · Work-energy of particles

A 2.0 kg block slides at 3.0 m/s on a frictionless horizontal surface into a light spring with stiffness 800 N/m. The maximum compression of the spring is most nearly:

1. A.0.0225 m
2. B.0.106 m
3. C.0.150 m
4. D.0.212 m

Problem 14 · Free and forced vibrations

A 10 kg mass on a spring of stiffness 4,000 N/m is connected to a viscous damper with a damping coefficient of 80 N·s/m. The damping ratio is most nearly:

1. A.0.100
2. B.0.200
3. C.0.400
4. D.4.00

Problem 15 · Statically indeterminate systems

A short column is a steel tube (A_s = 3,000 mm², E_s = 200 GPa) completely filled with concrete (A_c = 40,000 mm², E_c = 25 GPa), bonded so both materials shorten equally. A 500 kN axial compressive load is applied through a rigid cap. The compressive stress in the steel is most nearly:

1. A.1.55 MPa
2. B.7.81 MPa
3. C.11.6 MPa
4. D.62.5 MPa

Problem 16 · Stress and strain caused by bending loads

A W12×40 steel beam (S_x = 51.5 in³) is simply supported over a 24 ft span and carries a single 20 kip concentrated load at midspan. Neglecting self-weight, the maximum bending stress is most nearly:

1. A.2.33 ksi
2. B.14.0 ksi
3. C.28.0 ksi
4. D.55.9 ksi

Problem 17 · Corrosion mechanisms and control

Select all that apply.

A designer must join aluminum panels to a stainless steel frame in a wet outdoor environment. Which of the following measures reduce galvanic corrosion of the joint? Select all that apply.

1. A.Electrically insulate the two metals from each other with nonconductive washers and sleeves
2. B.Choose a pair of metals that lie close together in the galvanic series for this environment
3. C.Make the exposed area of the anodic metal large relative to the cathodic metal
4. D.Paint only the anodic metal and leave the cathodic metal bare
5. E.Fasten the panels with small fasteners made of a metal more anodic than both the panels and the frame

Problem 18 · Stress-strain diagrams

In a tension test, a round steel specimen with a 12.5 mm diameter and a 50.0 mm gauge length elongates 0.040 mm over the gauge length at a load of 20 kN, well within the linear region. The modulus of elasticity is most nearly:

1. A.2.04 GPa
2. B.50.9 GPa
3. C.160 GPa
4. D.204 GPa

Problem 19 · Pumps

A pump delivers 0.060 m³/s of water against a total dynamic head of 45 m. The pump efficiency is 78%. Take γ = 9.81 kN/m³. Enter the required shaft power in kW, to one decimal place.

Fill in the blank: answer in kW.

Problem 20 · 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 21 · Performance of components

In a counterflow heat exchanger, 2.0 kg/s of oil (c_p = 2.1 kJ/(kg·K)) is cooled from 120°C to 60°C by water (c_p = 4.18 kJ/(kg·K)) that warms from 20°C to 45°C. Neglect heat loss to the surroundings. The required water flow rate is most nearly:

1. A.1.34 kg/s
2. B.2.41 kg/s
3. C.4.80 kg/s
4. D.9.55 kg/s

Problem 22 · Power cycles

An ideal air-standard Diesel cycle has a compression ratio of 18 and a cutoff ratio of 2. Take k = 1.4. The thermal efficiency is most nearly:

1. A.48.4%
2. B.58.5%
3. C.63.2%
4. D.68.5%

Problem 23 · Radiation

An uninsulated pipe 0.10 m in diameter and 2.0 m long has a surface temperature of 450 K and an emissivity of 0.80. It sits in a large room whose walls are at 300 K. Take σ = 5.67 × 10⁻⁸ W/(m²·K⁴). The net radiation heat loss from the pipe is most nearly:

1. A.14.4 W
2. B.28.0 W
3. C.938 W
4. D.1,172 W

Problem 24 · Conduction

A long aluminum pin fin (k = 200 W/(m·K)) is 5 mm in diameter. Its base is at 120°C, and it is surrounded by air at 20°C with h = 25 W/(m²·K). Treat the fin as infinitely long. The heat transfer from the fin is most nearly:

1. A.0.154 W
2. B.3.93 W
3. C.7.85 W
4. D.11.1 W

Problem 25 · Control systems

A unity negative-feedback system has the forward-path transfer function G(s) = 40/[s(s + 5)]. The reference input is the ramp r(t) = 2t. The steady-state error is most nearly:

1. A.0
2. B.0.125
3. C.0.222
4. D.0.250

Problem 26 · Sensors and transducers

An NTC thermistor follows R = R₀ exp[β(1/T − 1/T₀)] with T in kelvins, R₀ = 10.0 kΩ at T₀ = 25°C and β = 3,950 K. Its measured resistance is 3.60 kΩ. Enter the temperature in °C to one decimal place.

Fill in the blank: answer in °C.

Problem 27 · Deformation and stiffness

An aluminum bracket acts as a cantilever 150 mm long with a rectangular section 20 mm wide and 6 mm thick, loaded at its free end so it bends about the axis parallel to the 20 mm width. Take E = 70 GPa. The bracket's stiffness at the free end is most nearly:

1. A.22.4 N/mm
2. B.249 N/mm
3. C.358 N/mm
4. D.3,360 N/mm

Problem 28 · Power transmission

A compound gear train is driven by a 5.0 kW motor at 1,800 rpm. Gear A (20 teeth) on the motor shaft drives gear B (60 teeth). Gear C (15 teeth) is on the same shaft as B and drives gear D (45 teeth) on the output shaft. Neglecting losses, the output torque is most nearly:

1. A.2.95 N·m
2. B.26.5 N·m
3. C.79.6 N·m
4. D.239 N·m