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?
The work done by a falling body is the product of its weight and the vertical distance it falls. It is a measure of the energy transferred to the body as it falls.
The formula for calculating work done by a falling body is W = mgh, where m is the mass of the body, g is the acceleration due to gravity, and h is the vertical distance the body falls.
Yes, the mass of the falling body does affect the work done. The greater the mass, the more work is done as there is a bigger force acting on the body due to its weight.
The height of the fall directly affects the work done. The higher the fall, the greater the distance the body falls and the more work is done as a result.
Yes, the work done by a falling body can be negative. This occurs when the body is lifted or slowed down during its fall, meaning that energy is being transferred away from the body instead of to it.