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Two boxes that are tied together with a string and sitting at rest in the middle

ID: 2107639 • Letter: T

Question

Two boxes that are tied together with a string and sitting at rest in the middle of a large air table ( no friction). Between the two boxes is a compressed spring. The string tying the two boxes together is going to be cut suddenly so the spring will expand pushing the boxes apart. The box on the left has four times the mass of the box on the right. At the instant the boxes lose contact with the spring after the string is cut, will the box on the left have a greater, less, equal, or indeterminate speed compared to the one on the right? Explain.

Explanation / Answer

the box on the left will have an equal speed to the right in the begining but it will decrease with time and the right bow will have greater speed later.
A simple explanation:
When the spring is compressed, F=kx force is being applied by the spring on both the boxes but tension in the string restroes them to same position, as soon as the string is cut, tension disappears and all that is left is the spring force which is equal on both boxes.
Now, F=ma; thus higher mass means less acceleration. So, left bos which has higher mass will have lesser acceleration, but both are starting from rest, so intital speed for both is 0 m/s (equal) but now both will accelerate and right box will accelerate faster and gain a higher speed.

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