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A block of mass $m$ is attached to a string and suspended inside a hollow box of mass $M$. The box rests on a scale that measures the system's weight.

If the string breaks, does the reading on the scale change?

Could someone explain this to me in terms of the center of mass and how the force changes on one because I do not really understand how to apply the center of mass principles to this question

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  • $\begingroup$ What do you think, and what is your reasoning? Why do you think center of mass affects the reading of the scale or is important? $\endgroup$ – Bill N Oct 25 '17 at 1:35
  • $\begingroup$ Because the center of mass is accelerating downwards which means that the normal force upwards must increase to counteract that but I am not too sure $\endgroup$ – Jeffrey Chiu Oct 25 '17 at 1:39
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When the string is intact and therefore the CM is at rest, the normal reaction of the balance equals the total weight of the box plus the block.

When the string breaks, the black falls freely and during this the CM is accelerated downwards. So the normal reaction should be smaller than the total weight. In fact it equals $Mg$ only.

When the block hits the floor of the box, the CM is accelerating upwards upwards, and at this moment the normal reaction should be very large, larger than the total weight.

Finally when the block rests on the floor, the normal reaction returns to is normal value, viz., $(M+m)g$.

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