show that the mechanical energy of a free falling body justifies the law of conservation of mechanical energy
Answers
Law of conservation of energy - Energy can neither be created nor be destroyed; it can only be transformed from one form to another.
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 =
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 =
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.
hope it helps...
hope it helps!
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