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# Mechanics: Conservation of momentum on variable mass system

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Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as in the figure. The conveyor belt is supported by frictionless rollers and moves at a constant speed of 0.750 m/s under the action of a constant horizontal external force Fext 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 Fext, (d) the work done by Fext in 1 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 (d) and (e) different?

##### Solution Summary

Sand is poured at a constant rate on a conveyor belt moving with constant velocity. The external force, energy and work done are calculated.

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