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work done in lifting a book from table to shelf

 
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ziaharipur



Joined: 02 Aug 2012
Posts: 2
Location: Pakistan

PostPosted: Thu Aug 02, 2012 11:07 pm    Post subject: work done in lifting a book from table to shelf Reply with quote

A book of mass 5kg is lifted from the table to shelf.

the body was at rest (initial kinetic energy=0), we applied 50 Newton force on it for just a second to produce an acceleration in the body, gravity is exerting 49N force on the body so the net force will be 1N upward this force produced an acceleration of 0.2 m/s/s in the body and after one second this force was reduced to 49 N (equal to the amount of force gravity is exerting on the body) now the body will keep moving in the upward direction with constant velocity that is 0.2 m/s (Newton’s First law of motion). this means that the kinetic energy of the body will be 0.1J and as W= change in Kinetic energy so the net work will be 0.1J during the lift (before coming in rest position on the shelf). When we reach the shelf we decrease our applied force to 48 N for just a second, in this way the net force will be 1N downward now this downward force will decrease the kinetic energy of the body from 0.1J to 0J in one second and the book will come in rest position. During the lift net work was 0.1J and after the lift both kinetic energies (initial and final) are zero so the net work is 0.

This is my understanding about lifting the book from table to shelf Am I right? If not then where I am wrong?
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hepcj
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Joined: 23 Jun 2007
Posts: 125

PostPosted: Sat Aug 04, 2012 8:01 pm    Post subject: Reply with quote

When you raise the book you are doing work against gravity. The work done by you is -mgh. The kinetic energy is zero at the end of the path but the book has gained potential energy.
However, the work energy theorem relates to the net work i.e. a summation of external forces acting on the body. In this case you have the force of gravity and the force lifting the object. Although when the object is moving there is a asymmetry in these forces at the end points the forces are balanced so this is zero.

The work done by you in moving an object such as a book on the shelf is still W = - mgh.

If you were to put the book back to the same vertical point on the table then gravity would do work and it would be W = mgh since gravity is a conservative force.
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