Question

derive an expression for potential energy​

Answer 1

Answer:

Derivation for the equation of Potential Energy:

Let the work done on the object against gravity = W

               Work done, W = force × displacement

               Work done, W  = mg × h

               Work done, W = mgh

Since workdone on the object is equal to mgh, an energy equal  to mgh units is gained by the object . This is the potential energy (Ep) of the object.

                            Ep = mgh

Answer 2

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

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

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

$\mathsf{\implies Work = Energy}$

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

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

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

$\mathsf{Derivation}$

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

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

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

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