Question Detail
Question
For the 3-kg crate sliding down the same 1 m, 30° ramp, but now with a coefficient of kinetic friction μ_k = 0.15, what is its speed at the bottom?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Initial PE = mgh = 3 × 9.8 × 0.5 = 14.7 J. Friction force f_k = μ_k m g cos θ = 0.15 × 3 × 9.8 × cos 30° = 0.15 × 29.4 × 0.866 = 3.82 N. Work done by friction W_f = -f_k × d = -3.82 × 1 = -3.82 J. Final KE = Initial PE + W_f = 14.7 - 3.82 = 10.88 J. So, ½ × 3 × v² = 10.88, v² = 7.25, v = 2.69 m/s.
Hint
The work done by friction (a nonconservative force) reduces the mechanical energy. Use W_nc = ΔKE + ΔPE.