A small block of mass m is placed on a rough inclined surface of inclination heta fixed inside an elevator. The elevator ascends 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 a time t evaluates to

Step-by-step solution

Since the elevator ascends with a uniform velocity v , the acceleration of the block is zero. The block is at rest relative to the incline, so it is in equilibrium. The force of friction f acts upwards along the inclined plane to balance the component of gravity. Its magnitude is given by: f = mg The displacement of the block in time t is s = vt in the vertically upward direction. The angle between the upward inclined plane (direction of friction) and the vertical displacement is 90^ - . The work done by the force