15 free practice questions with detailed solutions, covering all 14 NCEES exam domains.
These questions cover the major FE Mechanical exam topics: statics, dynamics, thermodynamics, fluid mechanics, heat transfer, mechanics of materials, and more. Each includes a step-by-step solution.
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Using Newton's method with initial guess x₀ = 2 for f(x) = x² - 5, what is the next approximation x₁?
Answer · A
Newton's method: x₁ = x₀ - f(x₀)/f'(x₀). f(2) = 4-5 = -1. f'(x) = 2x, f'(2) = 4. x₁ = 2 - (-1)/4 = 2.25.
For a standard normal distribution, approximately what percentage of data falls within ±1 standard deviation of the mean?
Answer · A
The empirical rule (68-95-99.7): 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ.
According to the NSPE Code of Ethics, engineers shall hold paramount:
Answer · B
The fundamental canon of engineering ethics: Engineers shall hold paramount the safety, health, and welfare of the public.
What is the present worth of $10,000 to be received 3 years from now at i = 8%?
Answer · A
P = F/(1+i)ⁿ = 10,000/(1.08)³ = 10,000/1.2597 = $7,938.
A 12 V battery is connected to a 4 Ω resistor. What is the current flowing through the circuit?
Answer · A
Ohm's law: I = V/R = 12/4 = 3 A.
A simply supported beam of length 6 m has a 10 kN point load at 2 m from the left support. What is the reaction at the left support?
Answer · A
Taking moments about the right support: R_L(6) = 10(4). R_L = 40/6 = 6.67 kN.
A car accelerates from rest at 3 m/s² for 5 seconds. What is the final velocity?
Answer · A
v = v₀ + at = 0 + 3(5) = 15 m/s.
A steel rod with diameter 20 mm is subjected to a 50 kN tensile load. What is the normal stress?
Answer · A
A = π(20)²/4 = 314.16 mm². σ = P/A = 50,000/314.16 = 159.2 MPa.
A material has yield strength 250 MPa. Under an applied stress of 125 MPa, the factor of safety against yielding is:
Answer · A
Factor of safety = Yield strength / Applied stress = 250/125 = 2.0.
Water flows through a pipe of diameter 100 mm at 2 m/s. The pipe narrows to 50 mm. What is the velocity in the narrow section?
Answer · A
Continuity: A₁V₁ = A₂V₂. V₂ = V₁(D₁/D₂)² = 2(100/50)² = 2(4) = 8 m/s.
A container holds 2 moles of ideal gas at 300 K and 100 kPa. What is the volume? (R = 8.314 J/(mol·K))
Answer · A
PV = nRT. V = nRT/P = 2(8.314)(300)/100,000 = 4,988.4/100,000 = 0.0499 m³.
A 10 cm thick concrete wall (k = 1.5 W/(m·K)) has inner surface at 200°C and outer at 50°C. What is the heat flux?
Answer · A
Fourier's law: q = k·ΔT/L = 1.5(200-50)/0.10 = 1.5(150)/0.10 = 2,250 W/m².
A thermocouple has accuracy ±1.2°C and a data logger has accuracy ±0.5°C. The combined uncertainty (RSS) is:
Answer · A
RSS method: u = √(1.2² + 0.5²) = √(1.44 + 0.25) = √1.69 = 1.3°C.
A thin-walled cylindrical pressure vessel has P = 2 MPa, r = 500 mm, t = 10 mm. What is the hoop stress?
Answer · A
Hoop stress: σ_h = Pr/t = 2(500)/10 = 100 MPa.
A block weighing 100 N rests on a surface with coefficient of static friction μₛ = 0.4. What force is needed to start sliding it?
Answer · A
Maximum static friction: F = μₛ·N = 0.4(100) = 40 N.
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