Question

In the adjoining figure, the coefficient of friction between wedge ( of mass M) and block ( of mass m) is `mu`.
Find the minimum horizontal force F rquired to keep the block stationary with respect to wedge

Answer 1

Such problems can be solved with or without using the concepte of pseudo force. Let us, solve the problem by both the methods.
a= Acceleration of ( wedge+ block ) in horizontal direction `= (F)/(M+m).`
(i) Inertial frame of reference ( ground) FBD of block with respect to ground ( only real forces have to be applied) with respect to ground block is moving with an acceleration a.

Therefore,
` sumF_(y)=0 " and " sum F_(x)=ma`
`mg= muN " and " N=ma`
`therefore a=(g)/(mu)`
`therefore F= (M+m)a=(M+m)(g)/(mu)`
(ii) Non- inertial frame of reference ( wedge ) FBD of m with respect to wedge ( real + one pseudo force ) with respect to wedge block is stationary.

`therefore sumF_(x)=0=sumF_(y)`
`therefore mg=muN`
and N= ma
`therefore a=(g)/(mu)` and `F=(M+m)a=(M+m)(g)/(mu)`
From the above discussion, we can see that from both the methods results are same.