A 1.0 kg object begins to slide down a ramp that is inclined to a certain angle.

Question

A 1.0 kg object begins to slide down a ramp that is inclined to a certain angle. The force of friction acting on the object as it slides down the ramp is 2.0 N. If the object travels 1.20 m down the ramp in 1.0 s, determine the angle of the ramp and the coefficient of kinetic friction between the object and the ramp.

Answer 1

Accelaration: s = at²/2; a = 2s/t² = 2·1.2m/1s² = 2.4 m/s².

Friction force F = μmgcosθ and mgsinθ - F = ma; sinθ = (ma + F)/(mg) = (1·2.4 + 2)/(1·9.8) = 0.449.

θ = sin^-1(0.449) = 26.68°; μ = F/(mgcosθ) = 2N/(1kg·9.8m/s²cos26.68°) = 0.2284