Question

How to prove that totalmechanical energy is conserved?

Answer 1

Heya......!!!!

Mechanical Energy ( ME ) = PE + KE .

We know that Total mechanical Energy is
conserved .

Let us proove it by the Case of Freely falling body .

♣Proof :

A ball is dropped from height " s "

Let the total height be " s " .

3 cases would be in the situation of freely falling body .

♦♦ when the body is at its highest point :

At highest point KE = 0
PE + KE = PE + 0 => (( mgh ))

♦♦ when the body is in between the highest point and the ground at a height 's'.

=> taking out the velocity ( v )

=> v^2 - 0 = 2g(h - s) = 2g( h - s ) .

Now ,, E = PE + KE = mgs + (1/2)mv^2 .

putting the value of v ,, we get :-

mgs + (1/2)m[2g(h-s)] = (( mgh ))

♦♦ Last case :when the body just touches the ground , it has PE = 0 ,, KE = max.

velocity ( v' ) = v'^2 = 2gh

Now ,, E = 1/2mv'^2

putting value of v' we get => (( mgh. ))

In All three cases we observe that Total Energy is Conserved.
Thus . We Total Mechanical energy is Conserved.

Hope It Helps You ^_^

Answer 2

Hope helps you
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