A 5.0-kg crate is resting on a horizontal plank.The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40.After one end of the plank is raised so the plank makes an angle of 30° with the horizontal, the force of friction is:
A)0 N
B)17 N
C)20 N
D)25 N
E)49 N

Question

Quizplus · Accepted Answer

The force of static friction is calculated using the formula: f_s = μ_s * N, where N is the normal force. When the plank is inclined at 30°, N = mg * cos(30°). The maximum static friction is μ_s * N = 0.50 * 5.0 * 9.8 * cos(30°) ≈ 21.2 N. Since the component of gravitational force parallel to the plank (mg * sin(30°) = 5.0 * 9.8 * 0.5 = 24.5 N) exceeds this, the crate will start to slide, and kinetic friction applies. The kinetic friction is f_k = μ_k * N = 0.40 * 5.0 * 9.8 * cos(30°) ≈ 17 N.

A 50-Kg Crate Is Resting on a Horizontal Plank