Question

proof of conservation law of energy with help of motion of freely falling body.

Answer 1

hey genius
here is your answer

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the law of conservation of energy state that energy can neither be created nor be destroy. it can only be translated in one form to another form

A. Top

Let us consider a ball of mass m falling from rest down from a wall of height h.

Since the ball is in rest the KE = ½mv2 = 0, PE = mgh

Total energy = PE + KE = mgh + 0 = mgh.

B. In between.

Let us consider an intermediate position of the falling ball at a height x from the ground

PE of the ball at height x from ground = mgx

Now velocity of the ball at that point, applying

v2 = u2 + 2gs

u = 0, here displacement s = h - x

Thus v2 = 2g(h-x)

Now KE = ½mv2

=> KE = ½m×2g(h-x) = mg(h-x)

E = KE + PE = mgx + mg(h-x) = mgh  

C. At bottom just before hitting the ground

Here PE = mg×0 = 0

Velocity of the ball v2 = 2gh

KE = ½mv2 = ½m×2gh = mgh. 

Neglecting air resistance we have seen that in the above cases the total energy remains the same = mgh.

Thus the total energy is unchanged and initial energy = mgh = final energy.  Hence, total energy remains constant or conserved.

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Answer 2

Refer the attachment ❤️