Question

What force should be applied on the wedge so that the block over it does not move?

Answer 1

Answer:

Hey i didn't get your question but this might be your answer.

Explanation:

Let a block of mass m is placed on smooth wedge of inclination angle theta.

The whole system is accelerated horizontally.

Since system is accelerated horizontally  such that the box does not slip on the wedge.

We know, F=ma

Hence component resolved into 2 ma cos theta and ma sin theta.

we have:

ma cos theta=mg sin theta

that implies, a=g tan theta------------(i)

N=mg cos theta+ma sin theta---------(ii)

Substituting (i) into (ii):

N=mg cos theta+m(g tan theta)sin theta

N=mg cos theta+mg(sin theta/cos theta)sin theta

N=(mg cos^2 theta+mg sin^2 theta)/(cos theta)

=mg/cos theta(cos^2 theta+sin^2 theta)

N=mg/cos theta

(as sin ^2 theta +cos ^2 theta=1)