FE Mechanical practice questions with answers

Answer: B) 1

Write ln(x²) as 2 ln x, or use the chain rule, to get f'(x) = 2/x. At x = 2 the derivative is 1.

• AIncorrect. 0.5 is 1/x at x = 2. It leaves out the factor of 2 that comes from the chain rule: d/dx ln(x²) = (1/x²)(2x) = 2/x.
• BCorrect. ln(x²) = 2 ln x, so f'(x) = 2/x. At x = 2 this gives 1.
• CIncorrect. 4 is the derivative of the inner function, 2x, at x = 2 (it is also the value of x²). The chain rule needs it divided by x², giving 4/4 = 1.
• DIncorrect. 1.39 is the function value, ln 4 ≈ 1.386, not the slope of the function.

Answer: A) 2

• ACorrect. Mean 4; squared deviations sum to 8; 8/(3 − 1) = 4; √4 = 2.
• BIncorrect. That's the population value (divide by n).
• CIncorrect. That's the variance.
• DIncorrect. That's the sum of squared deviations.

Answer: B) Decline to certify it without proper verification

• AIncorrect. That isn't verification.
• BCorrect. Certification must reflect actual knowledge.
• CIncorrect. Schedule doesn't justify false certification.
• DIncorrect. That's still misleading.

Answer: C) $7,582

• AIncorrect. That's the future worth.
• BIncorrect. That ignores interest.
• CCorrect. \(P = 2{,}000(P/A, 10\%, 5) = 2{,}000(3.7908)\).
• DIncorrect. Recheck the series factor.

Answer: D) 1,800 rpm

• AIncorrect. That's a 6-pole motor.
• BIncorrect. That's a 2-pole motor.
• CIncorrect. That's an 8-pole motor.
• DCorrect. \(n_s = 120f/p = 120(60)/4\).

Answer: B) In equilibrium

• AIncorrect. The forces balance.
• BCorrect. Their vector sum is zero.
• CIncorrect. A particle can't rotate; the forces balance.
• DIncorrect. The forces balance.

Answer: D) 13.5 J

• AIncorrect. That's rotational energy alone.
• BIncorrect. Add rotational energy.
• CIncorrect. For a solid disk, \(I = \tfrac{1}{2}mr^2\).
• DCorrect. \(\tfrac{1}{2}mv^2 + \tfrac{1}{2}I\omega^2 = \tfrac{3}{4}mv^2\).

Answer: C) 27°

For a frictionless banked curve, tanθ = v²/(gr) = 400/785 ≈ 0.51, so the bank angle is about 27°.

• AIncorrect. This comes from using sinθ = v²/(gr) = 0.51. The force balance on a frictionless bank gives tanθ = v²/(gr), not sinθ.
• BIncorrect. This comes from adding an extra factor of 2, tanθ = v²/(2gr) ≈ 0.25. Centripetal acceleration is v²/r, with no factor of 2.
• CCorrect. N sinθ = mv²/r and N cosθ = mg, so tanθ = v²/(gr) = 400/(9.81 × 80) ≈ 0.51, which gives θ ≈ 27°.
• DIncorrect. This comes from inverting the ratio, tanθ = gr/v² ≈ 1.96. That gives the complement of the correct angle.

Answer: B) 79.6 MPa

The maximum bending stress in a solid circular shaft is σ = Mc/I = 32M/(πd³). Here that gives about 79.6 MPa.

• AIncorrect. This is 16M/(πd³). It uses the polar section modulus J/c, which applies to torsion. For bending, use S = I/c = πd³/32.
• BCorrect. σ = Mc/I = 32M/(πd³) = 32(500)/[π(0.04)³] = 16,000/2.011×10⁻⁴ ≈ 79.6 MPa.
• CIncorrect. This is twice the correct value. It comes from using the full diameter as c instead of the radius, or from using 64M/(πd³).
• DIncorrect. This is 10 times too small, which points to a unit-conversion slip with the diameter or the result.

Answer: D) Ductile-to-brittle transition temperature

Ferritic (BCC) steels show a ductile-to-brittle transition: Charpy energy drops sharply from the upper shelf to the lower shelf as fracture changes from ductile to cleavage below the transition temperature.

• AIncorrect. The Curie temperature of ferrite is about 770 °C. It marks the loss of ferromagnetism, not a toughness transition near room temperature.
• BIncorrect. The eutectoid temperature (about 727 °C) is where austenite transforms to pearlite. It is far above the test range and does not govern notch toughness.
• CIncorrect. Recrystallization replaces cold-worked grains with new, strain-free grains at elevated temperatures during annealing. It does not explain a sudden low-temperature loss of impact energy.
• DCorrect. BCC ferritic steels show a sigmoidal Charpy curve. Below the transition temperature, fracture becomes brittle cleavage and absorbs little energy.

Answer: B) Relative roughness only

• AIncorrect. That's laminar flow.
• BCorrect. It's independent of Reynolds number there.
• CIncorrect. It depends on relative roughness.
• DIncorrect. It depends on relative roughness.

Answer: D) Saturated liquid properties at the same temperature

• AIncorrect. That isn't the approximation.
• BIncorrect. That isn't appropriate.
• CIncorrect. Liquids aren't ideal gases.
• DCorrect. Liquids are nearly incompressible.

Answer: C) The entire fin were at its base temperature

• AIncorrect. That isn't the definition.
• BIncorrect. That's fin effectiveness.
• CCorrect. Real fins cool along their length.
• DIncorrect. That isn't the definition.

Answer: A) The reading depends on whether the input is rising or falling

• ACorrect. Output paths differ by direction.
• BIncorrect. That's ideal response.
• CIncorrect. That's drift.
• DIncorrect. That isn't hysteresis.

Answer: B) It may buckle laterally unless it is guided or its ends are constrained

Compression springs with a high free-length to coil-diameter ratio can buckle sideways like columns. Designers prevent this by limiting the slenderness, choosing suitable end conditions, or guiding the spring in a bore or over a rod.

• AIncorrect. Surging is a dynamic resonance that happens when the spring is cycled near its natural frequency. A static load does not cause it.
• BCorrect. A slender compression spring acts like a column and can bow sideways under axial load. The critical deflection depends on the end conditions, and guiding the spring in a bore or over a rod helps prevent buckling.
• CIncorrect. The spring rate k = Gd^4/(8D^3 Na) goes down as the number of active coils goes up, so a longer spring with more coils is softer.
• DIncorrect. The wire shear stress, tau = Ks·8FD/(πd^3), depends on load, mean coil diameter, and wire diameter. It does not depend on free length.