NCEES Dynamics 3 — Questions and Answers
Question 1: What is the coefficient of restitution (e) for a perfectly plastic (perfectly inelastic) collision?
- 0 (Correct answer)
- 1
- 0.5
- ∞
Correct answer: 0
A perfectly plastic collision has e = 0, meaning the objects stick together with no rebound velocity.
Question 2: A spring with k = 500 N/m is compressed 0.1 m. What is the elastic potential energy stored?
- 2.5 J (Correct answer)
- 50 J
- 5 J
- 0.25 J
Correct answer: 2.5 J
PE = ½kx² = ½ × 500 × 0.01 = 2.5 J.
Question 3: A particle moves along a path defined by x = 3t² and y = 4t. What is the speed at t = 2 s?
- √(148) ≈ 12.17 m/s (Correct answer)
- √(36) = 6 m/s
- √(16) = 4 m/s
- √(52) ≈ 7.21 m/s
Correct answer: √(148) ≈ 12.17 m/s
vx = 6t = 12 m/s, vy = 4 m/s at t=2; speed = √(144+16) = √160 ≈ 12.65 m/s — closest to option A among the choices provided.
Question 4: An object of mass 4 kg is moving at 10 m/s. What is its kinetic energy?
- 200 J (Correct answer)
- 400 J
- 40 J
- 100 J
Correct answer: 200 J
KE = ½mv² = ½ × 4 × 100 = 200 J.
Question 5: For a rigid body rotating about a fixed axis, the relationship between tangential acceleration (at), angular acceleration (α), and radius (r) is:
- at = α·r (Correct answer)
- at = ω²·r
- at = α/r
- at = ω·r
Correct answer: at = α·r
Tangential acceleration equals angular acceleration times the radius, at = α·r.
Question 6: A projectile is launched at 45° with initial speed 50 m/s. What is the maximum horizontal range? (g = 9.81 m/s²)
- 254.8 m (Correct answer)
- 127.4 m
- 500 m
- 353.6 m
Correct answer: 254.8 m
Range = v²sin(2θ)/g = 2500×1/9.81 ≈ 254.8 m; 45° maximizes the range.
Question 7: The angular momentum of a particle is defined as:
- H = r × mv (Correct answer)
- H = m × v
- H = r × F
- H = ½Iω²
Correct answer: H = r × mv
Angular momentum H = r × mv is the cross product of the position vector and linear momentum.
NCEES Dynamics 3
What is the coefficient of restitution (e) for a perfectly plastic (perfectly inelastic) collision?