Question

A block of mass m is attached to a fixed position 'O' on a smooth inclined wedge of mass M. The block oscillates along the incline with amplitude A and angular frequency $\omega$. The wedge is located on a rough horizontal surface of friction coefficient $\mu$. Find the force of friction acting on the wedge if it always remains at rest.

• A. $\mu (M+m)g$
• B. $\frac{1}{2}m{\omega }^{2}A\sin (\omega t+\varphi )$
• C. $\mu (M+m){\omega }^{2}A\sin (\omega t+\varphi )$
• D. None of these

Answer 1

Answer: (B)

$\frac{1}{2}m{\omega }^{2}A\sin (\omega t+\varphi )$

Force exerted by block along Incline plane
$F=ma=m{\omega }^{2}x=m{\omega }^{2}A\sin (\omega t+\varphi )$
Horizontal component of this force, so
$f=F\cos {60}^{\circ }\Rightarrow f=\frac{1}{2}m{\omega }^{2}A\sin (\omega t+\varphi )$
This force should be equal to friction force.