← All Free Practice Questions

Free FE Mechanical Practice Questions

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.

Want 600+ more questions? Start your free 7-day trial for full access to all question types including fill-in-blank, multiple-select, and drag-and-drop.

Question 1Mathematics

Using Newton's method with initial guess x₀ = 2 for f(x) = x² - 5, what is the next approximation x₁?

A.2.25
B.2.50
C.2.10
D.1.75
Show Solution

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.

Question 2Probability & Statistics

For a standard normal distribution, approximately what percentage of data falls within ±1 standard deviation of the mean?

A.68%
B.95%
C.99.7%
D.50%
Show Solution

Answer: A

The empirical rule (68-95-99.7): 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ.

Question 3Ethics & Professional Practice

According to the NSPE Code of Ethics, engineers shall hold paramount:

A.Client satisfaction
B.The safety, health, and welfare of the public
C.Cost-effective solutions
D.Employer interests
Show Solution

Answer: B

The fundamental canon of engineering ethics: Engineers shall hold paramount the safety, health, and welfare of the public.

Question 4Engineering Economics

What is the present worth of $10,000 to be received 3 years from now at i = 8%?

A.$7,938
B.$8,000
C.$9,200
D.$7,500
Show Solution

Answer: A

P = F/(1+i)ⁿ = 10,000/(1.08)³ = 10,000/1.2597 = $7,938.

Question 5Electricity & Magnetism

A 12 V battery is connected to a 4 Ω resistor. What is the current flowing through the circuit?

A.3 A
B.48 A
C.0.33 A
D.8 A
Show Solution

Answer: A

Ohm's law: I = V/R = 12/4 = 3 A.

Question 6Statics

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?

A.6.67 kN
B.5.00 kN
C.3.33 kN
D.10.00 kN
Show Solution

Answer: A

Taking moments about the right support: R_L(6) = 10(4). R_L = 40/6 = 6.67 kN.

Question 7Dynamics, Kinematics & Vibrations

A car accelerates from rest at 3 m/s² for 5 seconds. What is the final velocity?

A.15 m/s
B.7.5 m/s
C.37.5 m/s
D.30 m/s
Show Solution

Answer: A

v = v₀ + at = 0 + 3(5) = 15 m/s.

Question 8Mechanics of Materials

A steel rod with diameter 20 mm is subjected to a 50 kN tensile load. What is the normal stress?

A.159.2 MPa
B.250.0 MPa
C.79.6 MPa
D.318.3 MPa
Show Solution

Answer: A

A = π(20)²/4 = 314.16 mm². σ = P/A = 50,000/314.16 = 159.2 MPa.

Question 9Material Properties & Processing

A material has yield strength 250 MPa. Under an applied stress of 125 MPa, the factor of safety against yielding is:

A.2.0
B.1.5
C.0.5
D.125
Show Solution

Answer: A

Factor of safety = Yield strength / Applied stress = 250/125 = 2.0.

Question 10Fluid Mechanics

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?

A.8 m/s
B.4 m/s
C.16 m/s
D.2 m/s
Show Solution

Answer: A

Continuity: A₁V₁ = A₂V₂. V₂ = V₁(D₁/D₂)² = 2(100/50)² = 2(4) = 8 m/s.

Question 11Thermodynamics

A container holds 2 moles of ideal gas at 300 K and 100 kPa. What is the volume? (R = 8.314 J/(mol·K))

A.0.0499 m³
B.0.0831 m³
C.0.0250 m³
D.0.1662 m³
Show Solution

Answer: A

PV = nRT. V = nRT/P = 2(8.314)(300)/100,000 = 4,988.4/100,000 = 0.0499 m³.

Question 12Heat Transfer

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?

A.2,250 W/m²
B.1,500 W/m²
C.3,000 W/m²
D.750 W/m²
Show Solution

Answer: A

Fourier's law: q = k·ΔT/L = 1.5(200-50)/0.10 = 1.5(150)/0.10 = 2,250 W/m².

Question 13Measurements, Instrumentation & Controls

A thermocouple has accuracy ±1.2°C and a data logger has accuracy ±0.5°C. The combined uncertainty (RSS) is:

A.±1.3°C
B.±1.7°C
C.±0.7°C
D.±1.0°C
Show Solution

Answer: A

RSS method: u = √(1.2² + 0.5²) = √(1.44 + 0.25) = √1.69 = 1.3°C.

Question 14Mechanical Design & Analysis

A thin-walled cylindrical pressure vessel has P = 2 MPa, r = 500 mm, t = 10 mm. What is the hoop stress?

A.100 MPa
B.50 MPa
C.200 MPa
D.25 MPa
Show Solution

Answer: A

Hoop stress: σ_h = Pr/t = 2(500)/10 = 100 MPa.

Question 15Statics

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?

A.40 N
B.250 N
C.60 N
D.100 N
Show Solution

Answer: A

Maximum static friction: F = μₛ·N = 0.4(100) = 40 N.

Ready for More?

Access 600+ FE Mechanical questions across all 14 exam domains with timed practice exams, adaptive quizzes, and detailed solutions.

Start Free 7-Day Trial