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I initially hold an object of mass m at a height, say h, above the ground. The potential energy is $mgh.$ Now I slowly bring the object down and stop the motion at a height $h'$ above the ground. Assume there is no air.

Now initially the potential energy of the object was $mgh$. As I bring it down, the object possesses some kinetic energy which would compensate for the decreasing potential energy and conserve the initial energy of $mgh$. But at the point $h'$ above ground, the object comes to rest. So there is no kinetic energy. So how is energy conserved? We need to have $mgh=mgh'+\text{some energy}$. But what is that some energy? Any help is very much appreciated.

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Something has to slow and stop the motion of the body.

If I slow it down with my hand, the object is doing work on my hand, transferring energy from the object to my hand. Some of the energy goes into potential energy in my muscle fibers, and some into heat.

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