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Question
A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system?
Solution 1
The speed of the centre of mass (CM) of a trolley and child system remains unchanged when the child runs around on a moving trolley with uniform speed V on a smooth floor. This is because the child's movements are internal actions within the trolley-child system, and internal forces do not affect the system's total momentum. With no external forces acting on the system, the CM's velocity remains constant at V.
Solution 2
The trolley is moving on a smooth horizontal floor, the smoothness of the floor means that no external horizontal forces are acting on the system. When the child runs on the trolley, the forces exerted by the child on the trolley and by the trolley on the child are both internal forces.
`vec"F"_"ext" = vec0`
According to the law of conservation of momentum,
`"M" vec"v"_"cm" = "constant"`;
`vec"v"_"cm" = "constant"`
This implies that the velocity of the center of mass will remain constant.
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