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- by Shrajesh thapa 5 months ago

______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 "

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.

Therefore ,

Work done by gravity(W_{g})=- work done by me (W_{ext})

or, ** W _{g}**

* *

*Note:*

______Definition__

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 , - W_{g = }P_{f - }P_{i }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 .

So ,

-W_{g = }P_{f - }P_{infinity } -W_{g = }P_{f - 0 } -W_{g = }P_{f }

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 .

__Derivation__

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