Question

Prove the Conservation of K.E. and P.E. of a freely falling body​

Answer 1

Law of conservation of energy states that:−
Energy can neither be created nor be destroyed.
Energy transforms from one form to another form and, potential energy+ kinetic energy= constant
Proof:−
At point A
K.E=0m/s
P.E=mgh
P.E=mgh
At point B,
K.E.,
2gh=V
2
−O
2

V
2
=2gx
K.E=
2
1
​
mV
2

K.E=
2
1
​
m.2gx
K.E=mgx-----------------------------(1)
P.E=mgh
P.E=m.g.(h−x)
P.E=mgh−mgx---------------------(2)
from(1) and (2)
K.E+P.E constant
mgx+mgh−mgx=mgh
mgh=mgh
At point C,
P.E=0
2gh=v
2
−u
2
( initial velocity =0 m/s)
2gh=v
2

K.E=
2
1
​
.m.v
K.E=
2
1
​
.m.2gh
K.E=mgh
Thus, in all the points the energy is same.


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