state and prove law of conservation machenical energy for a freely falling body
Answers
Answer:
Law of conservation of energy - Energy can neither be created nor be destroyed; it can only be transformed from one form to another.
Explanation:
Consider a body of mass m placed at A.
h = AB is the height of the body above the ground
u = 0 is initial velocity at A
v1 = velocity of body at C
v = velocity of body at B, i.e., just above the ground
(i) At point A
PEA = mgh
KEA = 0
Total mechanical energy at A, EA = PEA + KEA = mgh + 0 = mgh
(ii) At point C
v12-0 = 2gs
v12 = 2gs
KEC = 1/2 m(v1)²=1/2m(2gs)=mgs
PEC = mg(h-s)
Total mechanical energy at C, EC = PEC + KEC = mg(h-s) + mgs = mgh
(iii) At point B
v2-02 = 2gh
v2 = 2gh
KEB = 1/2mv²=1/2m(2gh)=mgh
PEB = 0
Total mechanical energy at B, EB = PEB + KEB = 0 + mgh = mgh
The total mechanical energy of the body at A, B and C (also at any other point in the path AB) is the same. So, the total mechanical energy of the body throughout the free fall is conserved.
Refer the attachment ❤️
