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Question

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s1. What is the speed of the trolley after the entire sand bag is empty ?

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Solution

Since the hole is on the floor , that means sand is falling vertically with respect to trolley. Therefore there is no force in horizontal direction hence in horizontal direction momentum is conserved.
Let M= mass of trolley
m= mass of sandbag
v1= initial velocity
v2= final velocity ( to be found)
Then P1=(M+m)v1 when the sand bag is empty the momentum is
P2=(M+0)v2
Momentum is conserved in horizontal direction so
P1=P2
=v2=(M+m)Mv1=300+25300×27×518=8.215m/s

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