Question

A plank of mass M is placed on a rough horizontal surface and a constant horizontal force F is applied on it. A man of mass m runs on the plank. Find the accelerations of the man so that the plank does not move on the surface. The coefficient of friction between the plank and the surface is $\mu$ Assume that the man does not slip on the plank.

Answer 1

For min a

$ma=F-\mu (M+m)g$

$a_{min}=\frac{F-\mu (M+m)g}{m}$

For max a

$ma=F+\mu (M+m)g$

$a_{min}=\frac{F+\mu (M+m)g}{m}$