Physics, asked by lakshivasu884, 1 year ago

derivation for potential and kinetic energy.(with diagram)
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Answers

Answered by suhasranganna
4

derivation 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

Derivation for the equation of Kinetic Energy:

The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is  

                            v2 - u2 = 2aS

This gives  

                            S = v 2 - u 2 2a  

We know F = ma. Thus using above equations, we can write the workdone by the force, F as

                           W = ma × v 2 - u 2 2a  

                                 or

                     W = 1 2 m( v 2 - u 2 )

If object is starting from its stationary position, that is, u = 0, then

                           W = 1 2 m v 2  

 

It is clear that the work done is equal to the change in the kinetic energy of an object.

If u = 0, the work done will be  W = 1 2 m v 2 .

  1. Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek =  ½  mv2

                                           

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