Question

A small block of mass m is kept on a rough inclined surface of inclination θ fixed in an elevator. the elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in time t will be
(a) zero
(b) mgvt cos²θ
(c) mgvt sin²θ
(d) mgvt sin 2θ

Answer 1

(c) mgvt sin²θ

Distance (d) travelled by the elevator in time t = vt
The block is not sliding on the wedge.
Then friction force (f) = mg sin$\theta$

Work done by the friction force on the block in time t is given by
$$\begin{gathered} W=Fd\cos (90-\theta ) \\ \Rightarrow W=mg\sin \theta \times d\times \cos (90-\theta ) \\ \Rightarrow W=mgd{\sin }^2\theta \\ \therefore W=mgvt{\sin }^2\theta \end{gathered}$$