A hopper starts dropping gravel at a rate of $75 kg / s$ onto a large conveyor belt moving at an initial speed of $v = 2.2 m / s$ . An external force $m$ immediately starts acting on the belt keeping the conveyor belt moving with constant velocity. Also, the motor driving the conveyer belt starts running with a power output of $n$ as the conveyor belt keeps running at constant speed. All values are in SI unit. Ignore all sources of friction in your analysis.

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Detailed Solution

$\begin{array}{l} {\vec{v}}_{rel} = {\vec{v}}_{gravel} - {\vec{v}}_{belt} = - {vF}_{ext} = M \frac{dV}{dt} - v_{rel} \frac{dM}{dt} \\ F_{ext} = v (\frac{dM}{dt}) = 165 N \end{array}$

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