The discussion centers on the concept of work done by gravity on a falling body, specifically addressing the formula for work, W = mgh. It clarifies that when a body falls, the work is done by the gravitational force on the body, resulting in a gain of kinetic energy. The confusion arises from the interpretation of work as either being done by the body or on the body, with the consensus being that gravity does positive work on the falling body. The calculations presented confirm that the work done by gravity is positive when the body falls, while the work done against gravity when lifting the body is also positive, leading to potential energy gain.
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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?