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Question

As shown in the figure, sand is falling from a stationary hopper onto a freight car which is moving with a uniform velocity v0=10 m/s. The sand falls at the rate of μ=5 kg/s. How much force is needed to keep the freight car moving at the speed v0?


A
50 N
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B
0 N
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C
25 N
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D
20 N
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Solution

The correct option is A 50 N
As we know, thrust force acting on the car in the horizontal direction is given by
Fth=μvr=(vrdmdt)
Here, relative velocity of sand loading vr=v0
i.e Fth=μv0=5×10=50 N
(in opposite direction of velocity of car)

and thrust force acting in vertical direction
Ftv=μv (Balanced by Normal force)
where v is the velocity of sand falling into the car.

So we need, F=50 N force in the direction of the car to move it with same speed).


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