Two equally long inclines both make 45° with the horizontal. One is frictionless; the other has kinetic friction. A block, released from rest, takes twice as long on the rough incline. Find the coefficient of kinetic friction.
Options

Question

Two equally long inclines both make 45° with the horizontal. One is frictionless; the other has kinetic friction. A block, released from rest, takes twice as long on the rough incline. Find the coefficient of kinetic friction.

Options

G1 Physics · Accepted Answer

Step 1: For equal displacement L from rest, L = (1/2)at²; hence t ∝ 1/√a. Step 2: Given tᵣ = 2tₛ, we have aᵣ = aₛ/4. Step 3: Smooth acceleration aₛ = g sin45°. Rough acceleration aᵣ = g(sin45° − μₖ cos45°). Step 4: Divide by g sin45°: 1/4 = 1 − μₖ cot45° = 1 − μₖ. Step 5: μₖ = 1 − 1/4 = 3/4. Final answer: μₖ = 0.75, Option D.