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This question is from the book Problems in Elementary physics - Bukhovtsev et al. question number 78. It goes like this:

A homogeneous cube is hanging from a line. The line is then cut. Which parts of the cube will have a greater acceleration at the first instant: the bottom parts or the top parts?

The book answers this question simply by stating that the upper part will have an acceleration greater than $g$ while the bottom will accelerate with $g$. It just doesn't provide any further details.

I wish to understand why will the top part fall faster than the bottom at this moment.

Qmechanic
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hellofriends
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1 Answers1

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If the cube is supported at the top, there will be some tension within the cube due to the weight of the cube. This will mean the cube is slightly stretched vertically. When the line is cut this tension will be available to accelerate the top part of the cube. All of the cube will respond to gravity which causes an acceleration of g to it. The cube has additional acceleration as the internal tension within the cube causes it to revert to its original dimensions. This is greatest at the top.

Actually in this scenario, the bottom may have an acceleration slightly less than g as it is experiencing an upward force due to this same tension. (Although instantaneously, the acceleration at the bottom due to this stress will be zero.)

All this assumes that g is constant across the height of the cube, which in reality it is not. However the tension will be much greater than the difference in g.

Rich
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