Analogy to understand G.P.E
The above spring mass system is in equilibrium .
If I apply force of F newton to displace it to x meters away from its initial position then
Work done = F * x
When I stop pulling it further away from x meters from the initial position , and leave it then it goes back to its initial position .
Who applied the force ? How did it get back to its initial position ?
-The work done by me is stored as potential energy . When I left pulling it , the potential energy gets converted into the kinetic energy .
Since , I am not a part of spring mass system the work done by me is termed as "work done by an external agent "
Let us imagine gravity to work just like a spring . As , I lift an object to a greater height the spring gets stretched more and more . The work done by me increases with the increment in the stretching of the spring (or the height). Since work done by me is stored as potential energy , we can say the potential energy increases with the height .
From the above explanation we can create a relationship between work done by me and the potential energy as
Work done by me = Potential energy
If I stop lifting and gently put it down with a constant velocity then the spring gets compressed. With the compression of spring height decreases. As the height decreases potential energy also decreases . Here , the work done by gravity increases with the decrement in the height . The work done by gravity is positive as the displacement is towards the direction of force . Work done by me is negative because the displace is opposite to the direction of force applied by me and it keeps the velocity constant throughout the process.
Work done by gravity(Wg)=- work done by me (Wext)
or, Wg =-P.E
The gravitational potential energy at a point in gravitational field is defined as the amount of work done while bringing a body from infinity to that point with constant velocity .
infinity - We know that , - Wg = Pf - Pi
To find potential at a point we should assume the initial point to have potential energy 0.
It is assumed that the potential energy at infinity be 0 .
-Wg = Pf - Pinfinity
-Wg = Pf - 0
-Wg = Pf
constant velocity - According to work-energy theorem ,
Work done = change in kinetic energy
If we consider velocity to be constant then change in kinetic energy is 0 .
Here , the work done is only stored as potential energy and is not converted into kinetic energy. So velocity is considered to be constant .