If an object is levitated above the surface of the earth with constant velocity so the net work done is equal to zero then the object must possess no potential energy =0 at a certain height $h$ because work of weight downwards is equal to external force work upwards. What is wrong with my explanation and how an object possess potential energy even if net work is zero.
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$\begingroup$ I don't understand how zero PE at some height follows from the fact that the forces are balanced. We might be better able to help if we understood your reasoning. $\endgroup$– garypCommented Nov 14, 2021 at 15:31
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2 Answers
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Assume that for the potential energy ($U$) we choose by convention that it is zero at the Earth's surface. $U$ at any other height $h$ above the Earth is then:
$$U=mgh$$
Now since as that height and the object's velocity is constant there's no work done on the object and it's potential and kinetic energy remain unchanging.
But:
$$U=mgh > 0$$
still holds.
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If the external force is acting vertically then the work done by the external force is equal to the magnitude of the force times the vertical distance that it acts through. The fact that the magnitude of the force happens to be equal to the weight of the object (if we assume the velocity of the object is constant) is irrelevant.
So we have
Work done = force x increase in height = weight x increase in height = increase in potential energy of object
You can either think of this as work done by the force on the object or as work done by the force against gravity.
answered Nov 14, 2021 at 10:29