A plank of mass `M` is placed on a rough horizontal surface and a contant horizontal force `F` is applied on it . A man of mass `m` runs on the plank find the range of acceleration of the man that the plank does not move on the surface is `mu` .Assume that the does not slip on the plank

Explanation

Here `f_(1) =` force of friction between man and plank `f_(2) =` force of friction between man and plank and surface

for the plank not to move
`F- (f_(2))_(max) le f_(1) le F + (f_(2))_(max)`
or `F - mu (M + m) g le ma le F + mu (M + m) g`
or a should lie between `(F)/(m) - (mu (M + m) g)/(m)`
and `(F)/(m) + (mu (M + m) g)/(m)`