Find the acceleration and if the block slides down

Question

A 4-kg block rests on a 45-degree inclined plane. The coefficient of static friction between the plane and bock is 0.2; that of kinetic friction is 0.1  

a) Does the block begin to slide down the plane?

b) If so, what is its acceleration?

Answer 1

(a)

Compare the component of weight (parallel to the plane) to the static friction.

W_|| = mg sinθ = (4)(9.8)sin45º N = 27.7 N

f_s = μ_smg cosθ = (0.2)(4)(9.8)cos45º N = 5.54 N

f_s < W_|| ⇒ the block slides down the plane

(b)

In the direction down the plane and parallel to the plane,

a = (W_|| - f_k)/m = g sinθ - μ_kg cosθ

Plug in the numbers and finish from here. Be sure to use the coefficient of kinetic friction in this part of the problem.