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The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is 16.0 N when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.

I don't understand what the question is asking. Whose Gravitational potential energy is mentioned- 1st block or 2nd block?

When lighter block goes up it's gravitational Potential energy increases while that of heavier one decreases(since string is inextensible. So both will move same heights in same time.) so how can the system lose its Gravitational Potential energy?

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    $\begingroup$ The decrease in GPE of the heavier block is larger than the increase of GPE of the lighter block, because it is heavier. So the total GPE of the two goes down. $\endgroup$ – knzhou Mar 14 at 17:21
  • $\begingroup$ I would suggest just calculating the total potential energy (sum of potential energy of both objects) at the initial point and at some later time point. You will clearly see that the total potential energy decreases $\endgroup$ – Aaron Stevens Mar 14 at 17:41
  • $\begingroup$ Yes I got that. The masses are unequal. How can I miss that!!!!!!!!!!!!!!!!!!!!!!!!😢 $\endgroup$ – Hritwik Raj Mar 15 at 18:10
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That is simple , take the surface of Earth as your reference frame , the string being inextensible is pulled from both sides by unequal forces (the loads have different masses). Now $\Delta U=mg\Delta H$ ,the terms involved have their usual meanings.Its evident that the change with be unequal due to the two unequal masses ,Done ! , the system thus loses Potential energy.
Again , you can also replace the two masses system with a single mass , situated instantaneously at the center of mass of the system, there is a net force acting on it so it has to lose potential energy on the course of its going down.
Yet another way to view this is , the conservative force , the gravitational force is doing positive work here , so the potential energy has to reduce , $\Delta U=-W_{conservative}$

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Whose Gravitational potential energy is mentioned- 1st block or 2nd block?

Neither! Gravitational potential energy belongs to the system because it is due to the interaction of all the masses, block-1, block-2, and the Earth.

In a problem like this, the gravitational potential energy of the system can change (and usually does) when the positions of the masses change relative to each other. As block-1 moves downward, the GPE of the block-1/Earth interaction decreases; as block-2 moves up, the GPE of the block2/Earth increases. The block-1/block-2 interaction also contributes to the GPE, but it is negligible by a factor of $10^{-12}$ or so. Sum the changes for each pair and that's the total change.

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