Theory question 108
StaticsA body of mass 40 kg is placed on a rough inclined plane which makes an angle of 30° with the horizontal. If a force of 420 N is applied upwards paralell to the plane, find the: (a) maximum frictional force that will keep the body in equilibrium; (b) coefficient of friction. [Take g = 10 ms−2]
Show the model answer
Model answer
Weight component down the plane = 400 sin 30° = 200 N; normal reaction R = 400 cos 30° ≈ 346.4 N.
(a) 420 N up is more than 200 N, so the body tends to move up and friction acts down the plane: F = 420 − 200 = 220 N.
(b) μ = F/R = 220/346.4 ≈ 0.635.
Explanation
Decide which way the body tends to move; friction acts the other way.