Question

prove that potential energy by work energy therom​

Answer 1

Hlew,

Here's your answer...

Work energy theorem states that- Work is a result of force and the resulting displacement. Now, we already know that all moving objects have kinetic energy. So, there must be a relation between Work and kinetic energy. This relation between the kinetic energy of an object and workdone is called “Work-Energy Theorem”. It is expressed as:

                                       W = ΔK

Work done Under a Constant Force

We have already learnt about the equations of motion earlier and know that,

                          v² + u² = 2as

Here, v is the final velocity of the object; u is the initial velocity of the object; a is the constant acceleration and s is the distance traversed by the object. We can also write this equation as,

                         v² - u² = 2as

We can substitute the values in the equation with the vector quantities, therefore:  

                         v² - u² = 2a.d

If we multiply both sides with m/2, we get:

                        1/2 mv² - 1/2 mu² = ma.d

From Newton’s second law, we know that F=ma, hence:

                             1/2 mv² - 1/2 mu² = F.d

Now, we already know that W= F.d and, K.E. = (mv²)/2,

So, the above equation may be rewritten as:

                             Kf - Ki = W

Hence, we have:

                       ΔK = W

Therefore, we have proved the Work-Energy Theorem. The Work done on an object is equal to the change in its kinetic energy.

Thanks.

Sorry baby 'wink'