Question

A man of mass $50kg$ is pulled on a plank of mass $100kg$ kept on a smooth with force of $100N$. If both man plank move together, Find force of friction acting on man.

Answer 1

The man is standing on the plank. Then he is pulling the rope towards himself. He pushes the plank forward with the legs so that he can pull the rope backwards.

So the friction f acts in the forward direction for the plank. Also f acts in the opposite direction on the man. The tension T in the rope is 100 N (given). Let the friction force = f Newtons.

Let the common acceleration = a m/s^2

Man: net force = T - f = m a = 50 a

Plank: net force = T + f = m a = 100 a

As T = 100 N, a = 4/3 m/s^2 and f = 100/3 Newtons.