Question

derivation of potential energy​

Answer 1

Derivation:::::----

Potential energy is possessed by an object by virtue of its motion.

Let the mass of the body is m and it is raised to a height of h meters above the ground.

It will do some work. We know that work done is given in terms of force and displacement.

In this case distance of the body is h such that work done is given by : W=F\times h\ ......(1)

W=F×h ......(1)

As the body is moving upwards under the action of gravity.

The force acting on the object is force of gravity i.e. F = mg

Equation (1) becomes :W=mg\times hW=mg×h

We know that, work done is stored in the form of energy. So,E=mghE=mghHence, proved.

Answer 2

$\frak{Derivation \: of \: Potential \: Energy}$

$\mathsf{Things \: to \: know \: before\: Derivation}$

$\mathsf{\implies Work \: done = Fs = F × height = \: Fh}$

$\mathsf{\implies Work = Energy}$

$\mathsf{\implies Force = mass \: × \: acceleration \: = ma}$

$\sf{\implies Acceleration \:due \:to \:gravity =\: 'g'}$

$\mathsf{\implies Potential \: Energy \: is \: also \: written \: as \: E_p}$

$\mathsf{Derivation}$

$\mathsf{\hookrightarrow E_p = Work done = Fs = Fh }$

$\mathsf{\hookrightarrow E_p \: = \: Fh \: = ma × h }$

$\mathsf{\hookrightarrow E_p\: = \: Fs \: = mg × h }$

$\mathsf{\hookrightarrow E_p\: = \:mgh }$