A question on Newtonian dynamics

Question

Imagine a trolley moving at constant velocity thus, no external force and momentum are conserved. Then at x kg/s sand is falling on that trolley and the velocity of the trolley will decrease as momentum is conserved. So what external force is required to keep the trolley moving at constant velocity i.e. the same velocity before sand dropped on the trolley?

justin hew · Accepted Answer

The answer is in $$F= ma$$
since we want $dot v=0$, then because force is the rate of change of momentum
$$ F= dot p=dot mv=xv $$
We have the required result.

John Hunter · Answer

You need to use the impulse equation
$Force times time = mv-mu$
where $v$ and $u$ are the final and initial velocity of the sand.
Hint:  in this question it's easy to think about the sand falling vertically, but it's the horizontal component of momentum that you should concentrate on.

Yejus · Answer

This is simple Newton's law. If $p$ is the momentum of the trolley at any time $t$, then a change in momentum $$dp = d(mv) = m ,dv + v ,dm.$$
Since you are saying $dv = 0$, this means
$$dp = v, dm.$$ Force is the rate of change of momentum, so
$$frac{dp}{dt} = mathrm{Force} = v , frac{dm}{dt}.$$

A question on Newtonian dynamics

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