Work, Power and Energy: Work-Energy — Incline with Friction MCQ

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Work-Energy — Incline with FrictionHardQuestion 30426

Question

A 2 kg block starts at rest and slides 5 m down a 30° rough incline (μₖ = 0.2). Speed at bottom: (g = 10, sin30° = 0.5, cos30° = 0.866)

A
5 m/s
B
4.12 m/s
Correct
C
7 m/s
D
3 m/s

Correct answer

4.12 m/s

Explanation

W_net = W_gravity + W_friction = mg sinθ × L − μₖmg cosθ × L = 2×10×0.5×5 − 0.2×2×10×0.866×5 = 50 − 17.32 = 32.68 J. v = √(2×32.68/2) = √32.68 ≈ 5.72 m/s. (checking: mgL sinθ = 50, friction work = 0.2×2×10×0.866×5 = 17.32, net = 32.68, v = √(32.68) ≈ 5.72)

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