Serway & Jewett — Linear Momentum and Collisions: Problem 52

Sand from a stationary hopper falls onto a moving conveyor belt at the rate of \(5.00 \text{ kg/s}\) as shown in Figure P9.52. The conveyor belt is supported by frictionless rollers and moves at a constant speed of \(v = 0.750 \text{ m/s}\) under the action of a constant horizontal external force \(\vec{F}_{\text{ext}}\) supplied by the motor that drives the belt. Find (a) the sand’s rate of change of momentum in the horizontal direction, (b) the force of friction exerted by the belt on the sand, (c) the external force \(\vec{F}_{\text{ext}}\), (d) the work done by \(\vec{F}_{\text{ext}}\) in \(1 \text{ s}\), and (e) the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion. (f) Why are the answers to parts (d) and (e) different?