Question

Find the minimum force P required to avoid sliding of the block of weight W on the incline plane

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

If there was no friction block would have slided down as P along with friction is just able to avoid sliding.

So friction has to be up the incline on the block.

Now,

Psin$\alpha +N=mgcos\lambda$

N = $mgcos\lambda -Psin\alpha$

$Pcos\alpha +\mu N=mgsin\lambda$

$Pcos\alpha +\mu (mgcos\lambda -Psin\alpha )=mgsin\lambda$

$P(cos\alpha -\mu sin\alpha )=mg(sin\lambda -\mu cos\lambda )$

$P=mg\frac{(sin\lambda -\mu cos\lambda )}{(cos\alpha -\mu sin\alpha )}$