Question

Sand drops at a rate of 2000 kg/min from the bottom of a hopper onto a belt conveyer moving horizontally at 250 m/min. Determine the force needed to drive the conveyer, neglecting friction.

Answer 1

The idea is, the belt should run at that speed even after the sand has fallen on it. When this happens fallen sand also moves at that speed. Then what happens is that the linear momentum of sand is changed. Momentum change generates some force on the sand by the belt & at the same time, the same is generated on the belt by sand (Newton's 3rd)
Then it's about calculating the momentum change of the sand.
Try this.