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Question-

Sand is being dropped from a stationary dropper at a rate of 0.5 kg s$^{-1}$ on a conveyor belt moving with a velocity of 5 ms¹. The power needed to keep belt moving with the same velocity will be:

Solution given- enter image description here

My confusion-

Power= energy supplied per second.

It is given that 0.5 kg of mass is added oer second. So for the added mass to gain velocity 5m/s, kinetic energy supplied should be 6.25J. So power is 6.25 watts. Where have I gone wrong?

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2 Answers 2

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Both computations are correct; the sand only gains 6.25W of energy per second despite the belt needing 12.5W to run. This is an inelastic collision; energy is not conserved.

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  • $\begingroup$ Thank you! Momentum will still be conserved right? $\endgroup$
    – Pumpkin_Star
    Commented Dec 7, 2023 at 15:42
  • $\begingroup$ Yes, momentum is conserved. $\endgroup$
    – naturallyInconsistent
    Commented Dec 7, 2023 at 15:44
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Where you've gone wrong – and it's an unusual student who doesn't go wrong – is not to have thought carefully enough about what happens when the sand reaches the belt. Each sand grain reaches the belt with a horizontal velocity component of zero, and yet very soon has acquired the belt's velocity. A frictional force from the belt has done work on the grain to bring it up to speed, that is to give it its KE. But during this process the sand grain has been sliding backwards relative to the belt ('rubbing against it') and energy is transferred from the belt's motor to thermal energy – the belt and the sand get slightly hotter. This is why you have to supply more energy than just the KE acquired by the sand.

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  • $\begingroup$ This answer doesn't contradict naturally inconsistent's answer; the answers are equivalent. $\endgroup$
    – Philip Wood
    Commented Dec 7, 2023 at 15:56

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