A body slides down a smooth 30° incline in time T. Over the same distance on a rough 30° incline it takes αT. If μ = (1/√x)[(α²-1)/α²], find x.

Question

G1 Physics · Accepted Answer

Smooth acceleration is a₀ = g sin30°. Rough acceleration is a = g(sin30°-μcos30°). Since time from rest over the same distance is proportional to 1/√a, α² = a₀/a. Solving gives μ = tan30°(α²-1)/α² = (1/√3)(α²-1)/α², so x = 3.