The discussion revolves around the concept of work in the context of a body falling under the influence of gravity. Participants explore the definitions and conventions regarding whether the work is done by the force of gravity on the body or by the body itself. The conversation includes calculations and interpretations of work done during the falling and lifting of a body, examining the implications for energy gain and loss.
Participants express differing views on the interpretation of work done by gravity versus work done by the body. While some agree on the positive nature of work done by gravity, others maintain that the distinction between who is doing the work leads to confusion and disagreement remains on the interpretation of signs in the calculations.
Participants highlight potential limitations in their calculations, including the dependence on coordinate system definitions and the need for clarity on the roles of forces in determining work done. There is also an acknowledgment of unresolved aspects regarding the signs of work in different scenarios.
mpkannan said:When a body falls from a height (h) under gravity,the work involved is mgh. How do you describe this work? Is it 'work done by the force (gravity) on the body' or 'work done by the body'. The confusion is, if work is done on the body the body gains energy; but if work is done by the body the body loses energy. What is the standard convention?
Since gravity acts on the body, we're talking about work done on the body, not by the body. That work happens to be positive as the body falls, since the force and the displacement are in the same direction. (If the body were moving upward, the work done by gravity would be negative.)mpkannan said:When a body falls from a height (h) under gravity,the work involved is mgh. How do you describe this work? Is it 'work done by the force (gravity) on the body' or 'work done by the body'. The confusion is, if work is done on the body the body gains energy; but if work is done by the body the body loses energy. What is the standard convention?
Doc Al said:Since gravity acts on the body, we're talking about work done on the body, not by the body. That work happens to be positive as the body falls, since the force and the displacement are in the same direction. (If the body were moving upward, the work done by gravity would be negative.)
No, it's not the work done by the body. Gravity (-mg) acts on the body.mpkannan said:(1) I consider a Cart coordinate system (drawn as per the right hand thumb rule) with +ve Z axis pointing upwards. Now, consider a body falling from z=h to z=0. The work involved is:
Integral (from h to 0) of [-mg dz] (-mg, because the force is acting downwards). The answer is mgh. Is this not the work done by the body, since it loses this much energy on fall? If so why it is not negative?
Good.(2) If I raise the body from 0 to h, the work done on the the body is:
Integral (from 0 to h) of [mg dz] (here force applied is equal and opposite to gravity; so +mg). The asnwer is mgh. The body gains this much energy and stores it as its potential energy.
Positive work was done in each case. In case 1, gravity did the work; in case 2, you did the work.Why I am not getting opposite signs for the 2 types of work involved?