EIT Statics, Dynamics & Mechanics of Materials 4 — Questions and Answers
Question 1: A projectile is launched at 45° with an initial speed of 20 m/s. Neglecting air resistance, what is the maximum height? (g = 9.81 m/s²)
- 5.1 m
- 10.2 m (Correct answer)
- 20.4 m
- 14.4 m
Correct answer: 10.2 m
H = (v₀sin45°)²/(2g) = (20×0.707)²/(19.62) = 200×0.5/19.62 ≈ 10.2 m.
Question 2: Shear stress in a circular shaft under torque T is maximum at the:
- Neutral axis
- Centroid
- Outer surface (Correct answer)
- Mid-radius
Correct answer: Outer surface
Torsional shear stress τ = Tc/J is maximum at the outermost fiber where c is maximum.
Question 3: The principle of transmissibility states that a force on a rigid body can be moved along its:
- Any line parallel to the original force
- Line of action without changing equilibrium (Correct answer)
- Perpendicular direction without effect
- Centroid without changing moments
Correct answer: Line of action without changing equilibrium
Transmissibility: a force may be applied at any point along its line of action and produce the same external effect on a rigid body.
Question 4: Euler's buckling load for a pin-pin column of length L, modulus E, and moment of inertia I is:
- π²EI/L² (Correct answer)
- π²EI/(2L)²
- 2π²EI/L²
- EI/L²
Correct answer: π²EI/L²
Euler's critical load Pcr = π²EI/L² for a pin-pin column (K=1), the fundamental column buckling formula.
Question 5: A material has E = 200 GPa and ν = 0.3. What is its shear modulus G?
- 76.9 GPa (Correct answer)
- 86.9 GPa
- 100 GPa
- 130 GPa
Correct answer: 76.9 GPa
G = E/[2(1+ν)] = 200/[2(1.3)] = 200/2.6 ≈ 76.9 GPa.
Question 6: A 10 kg block slides down a frictionless incline of 30°. What is its acceleration along the incline? (g = 9.81 m/s²)
- 4.91 m/s² (Correct answer)
- 8.50 m/s²
- 9.81 m/s²
- 5.66 m/s²
Correct answer: 4.91 m/s²
Along the incline, net force = mg·sin30° = 10×9.81×0.5 = 49.05 N, so a = F/m = 49.05/10 = 4.91 m/s².
Question 7: In impulse-momentum analysis, the linear impulse of a force F applied over time Δt equals:
- F·Δt = m·Δv (Correct answer)
- F·Δt = ½mv²
- F = m·a·Δt²
- F·Δt = mv₁
Correct answer: F·Δt = m·Δv
Linear impulse-momentum: F·Δt = Δ(mv), meaning the impulse equals the change in linear momentum.
EIT Statics, Dynamics & Mechanics of Materials 4
A projectile is launched at 45° with an initial speed of 20 m/s.
Neglecting air resistance, what is the maximum height? (g = 9.81 m/s²)