Question

A block of mass $m$ is stationary with respect to a wedge of mass $M$ moving with uniform speed $v$ on a horizontal surface. Find the work done by friction force on the block in $t$ second.

• A. zero
• B. $-\frac{m g v t}{2}sin 2\theta $
• C. $-\frac{m g v t}{2}$
• D. $-\frac{m g v t}{2}sin^{2} \theta $

Answer 1

Answer: (B)

As the block is at rest with respect to wedge,
$f_{r}=mgsin \theta $
Work done by friction
$W=FScos \theta $
$W=-\left(m g sin \theta \right)\left(v t\right)cos⁡\theta $
$W=-\frac{m g sin 2 \theta }{2}\left(v t\right)$