Theory question 108
StaticsA body of mass 12 kg rests on a rough plane inclined at an angle of 30° to the horizontal. The coefficient of friction between the body and the plane is 2/3.
A force of magnitude P Newtons acts on the body along the inclined plane. Find the value of P if the body is at the point of moving: (a) down the plane
(b) up the plane [Take g = 10 ms−2]
Show the model answer
Model answer
R = mg cos 30° = 120 × 0.866 = 103.9 N; limiting friction F = μR = ⅔ × 103.9 = 69.3 N.
Component of weight down the plane = 120 sin 30° = 60 N.
(a) Moving down: friction acts up the plane: P + 60 = 69.3, so P ≈ 9.3 N.
(b) Moving up: friction acts down the plane: P = 60 + 69.3 ≈ 129.3 N.
Explanation
Friction always opposes the motion that is about to happen.