Question

illustrate the law of conservation of energy by discussing the free fall of the body

Answer 1

LAW OF CONSERVATION OF ENERGY:

Energy can neither be created nor destroyed, but it
is transformed from one form to another. Alternatively,
whenever energy gets transformed, the total energy
remains unchanged.

Proof – In case of a freely falling body

It may be shown that in the absence of external frictional force the total mechanical energy of a body remains constant.
Let a body of mass m falls from a point A, which is at a height h from the ground as shown in fig.

At A,

Kinetic energy kE = 0
Potential energy Ep = mgh
Total energy E = Ep + Ek = mgh + 0= mgh
During the fall, the body is at a position B. The body has moved a distance x from A.At B,velocity v2 = u2 + 2asapplying, v2 = 0 + 2ax = 2axKinetic energy Ek = 1/2 mv2 = 1/2 m x 2gx = mgx
Potential energy Ep = mg (h – x)
Total energy E = Ep + Ek = mg (h-x) + mgx = mgh – mgx + mgx= mgh

If the body reaches the position C.

At C,

Potential energy Ep = 0
Velocity of the body C is
v2 = u2 + 2as
u = 0, a = g, s = h
applying v2 = 0 + 2gh = 2gh

kinetic energy Ek =1/2 mv2=1/2 m x 2gh= mgh

Total energy at C
                      E = Ep + Ek
                     E = 0 + mgh
                     E = mgh
Thus we have seen that sum of potential and kinetic energy of freely falling body at all points remains same. Under the force of gravity, the mechanical energy of a body remains constant.

Answer 2

when an object at it higest position from ground it has maximum amt of kinetic energy .when the object starts falling there is an increase in the kinitic energy and decrease in potential energy as the speed incerases the kinetic energy also increases but the sum of the potential and the kinitic energy remains constant when it is just above the ground the kinetic energy is max and least potential energy. Pe+Ke=constant

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