What is potential energy ? Explain gravitational potential energy .

Explanation

Potential energy is the stored energy by virtue of the position or configuration of the body .If configuration of the system changes , then its potential energy changes .
Gravitational potential energy : Multiplication of weight of the body and its height from the surface of earth is called the gravitational potential energy relative to the surface of earth .
Suppose a ball of mass is lie down of earth surface the gravitational force acting on it is mg .
If this ball lifted upto height h from the surface of earth , then external force of mg exerted on it in upward direction .
Work done by external force `W = Fd cos theta `
but F = mg, d = h and `theta =0^(0)` (External force and displacement are in upward direction hence `theta = 0^(@)`)
` :. W = mgh cos 0^(@)`
` :. W = mgh `
This type of amount of work is stored as gravitational potential energy .
Work done by gravitational force `W = - mgh`
` :. ` Magnitude of gravitational potential energy is equal to the negative value of work done by gravitational force .
` :. V(h) = 0 mgh` where V(h) = gravitational potential energy
` :, (dV(h))/(dh) = - mg `
`= - F ` where F is the gravitational force and it is in downward direction and so it is negative .
When a ball fall freely then its speed increases . Its speed is obtained when it touches the earth by equation of motion , `v^(2) - u^(2) = 2gh `
For free fall , u = 0
` : v^(2) =2gh`
Multiplying `m/2` on both sides .
` 1/2 mv^(2) = mgh`
It indicates that gravitational potential energy of free fall body converted into kinetic energy .
Dimensional formula of potential energy `[M^(1)L^(2)T^(-2)]` and its SI unit is Joule .