- #1

songoku

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- 325

- Homework Statement
- Please see below

- Relevant Equations
- Momentum

Impulse

Conservation of momentum

1) Since the sand spilling out downwards, it means that there is change in momentum in vertical direction (before the sand spills and after the sand spills) but no change in momentum in horizontal direction so no net force in horizontal direction and no acceleration in horizonal direction, so the speed of the train car will be constant. Is this correct?

2) If I consider the momentum of the system (train car + sand inside train car) in horizontal direction, the momentum will decrease because the speed is constant and the mass of sand decreases. But this means that the there is change in momentum in horizontal direction so the momentum in horizontal direction is not conserved and there will be net force acting on the system so the speed can't be constant, which contradicts to what I thought in part (1)

3) I want to know how the momentum of spilling sand affects the system so I draw free body diagram for the train car. There will be 3 forces acting on it, normal force from ground acting upwards, weight of the train car and also weight of sand (both acting downwards). Initially, normal force = weight of train car + weight of sand (to prevent vertical motion).

When the sand spills out, there will be additional force due to the change in momentum of spilling sand in vertical direction, directed downwards. The weight of sand in the train car decreases so to prevent vertical motion of train car:

Normal force from ground on train car = weight of train car + new weight of sand + downwards force due to change in momentum of spilling sand

Is that correct?

And if I want to compare normal force before and after the sand spills, can I say they will be the same? Maybe because the decrease in weight of sand in the train car will be the same as the downwards force due to change in momentum (I don't really know the reason behind this, just guessing)

Thanks