Saturday, 6 October 2018

newtonian mechanics - Net work done on the body when we lift it and put it on the table is zero?


I'm little confused here. Work done on the body when we lift it and put it on the table is zero, because according to work energy theorem, change in kinetic energy of the body is zero. So, the net work done is zero.


Fine, but now the object has $mgh$ (where $m=$mass of body; $h=$height of body) amount of potential energy stored in it. If the net work done is zero then who has increased its energy?


I'm confused and unable to think it through kindly help.



Answer



You did net work on the body. Gravity did negative net work on the body. The over all work done was zero. The original confusion arose because the work-energy theorem demands we calculate the change in kinetic energy using the net force on the body, but your question considered only the force exerted by you, and ignored that exerted by gravity.



If the body has mass $m$, you were putting a force $mg$ on it to raise it at constant speed. The work-energy theorem says that if you had done this when there were no other forces on the body, the body would have gained kinetic energy $mgh$ as you moved it from the floor to the table.


That analysis ignores gravity, though. Gravity pulled down on the box with force $-mg$. This means the work done by gravity was $-mgh$, and so the total work done on the box was zero. This makes sense because if you lift the box at constant speed, the net force on the box is zero by $F = ma$.


If the box starts by sitting stationary on the floor, there would have to be some small net work done on the box to get it started going up. There would have to be some small negative net work on it to get it to stop.


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