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Power to keep a conveyor belt moving while sand falls on it

This type of question, asked 2 times: 27 Jul 2022, 29 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    3
    Sand is being dropped from a stationary dropper at a rate of 0.5kgs−10.5kgs^{- 1} on a conveyor belt moving with a velocity of 5 ms−15{\text{ }ms}^{- 1}. The power needed to keep belt moving with the same velocity will be:

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  2. Question 2

    29 Jan 2025

    87
    A sand dropper drops sand of mass m(t)m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e. dmdt∝v\frac{dm}{dt}\propto\sqrt{v}. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

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