- The energy is a conserved quantity. There won’t be any change in the energy of an isolated system.
- The energy can neither be created nor can it be destroyed. It can only be changed from its one form to another form.
- For example: if we throw a stone upward with certain velocity, initially, it has maximum velocity and hence maximum kinetic energy.
- As it moves up, its velocity goes on At a certain height, its velocity becomes zero, and hence its kinetic energy becomes zero.
- At the same time, the stone gains height as it moves up.
- As the stone gains height, its potential energy increases. Hence, it is clear that when a stone is thrown up, there is continuous decrease in kinetic energy and increase in the potential energy.
- However, the total energy of the stone remains the same. This is the principle of conservation of energy.
- According to principle of conservation of energy, the energy can neither be created nor be destroyed but can be changed from one form to another form.
Image Source: nuclearpower Image Source: Braincart
Energy conservation in free fall
Consider a body of mass m is initially at a point A which is at a height h from the ground as in the given figure. Let the body fall freely under gravity so that the acceleration of the body is g– acceleration due to gravity. After a certain time, the body reaches a point B which is at height (h-x) from the ground.
As the body falls down, its velocity increases. Finally, the body strikes the ground C with velocity v.
For the point A
When the body is at A, velocity (u) = 0 and the height from the ground (h) = h.
Hence, the kinetic energy of the body (K.E)a = ½ mu2 = 0
And the potential energy of the body is (PE)a = mgh
The total mechanical energy of body at point A is given by
Ea = (K.E)a + (P.E)a = 0 + mgh = mgh
∴ Ea = mgh …………………………………………………………. (i)
For the point B
When the body is at point B on its way down, we have initial velocity (u) = 0
Final velocity (v) = vb
Distance travelled = AB=AC – BC = h – (h-x) = x
We have, v2 = u2 + 2gh (formula)
Or, vb2 = 0 + 2gx = 2gx
∴ vb2 = 2gx
Now, the kinetic energy of the body at point B is
(K.E)b = ½ mvb2 = ½ m(2gx) = mgx
Also, the potential energy of the body at point B is
(P.E)b = mgh = mg(h-x)
Therefore, the total mechanical energy of the body when it is at the point B is given by
Eb = (K.E)b + (P.E)b = mgx + mg(h-x) = mgx + mgh – mgx = mgh
∴ Eb= mgh…………………………………………………………… (ii)
For the point C
When the body is at point C, we have, for the motion of the body
Initial velocity (u) = 0
Final velocity (v) = vc
Distance travelled = h
We have, v2= u2 + 2gh
or, vc2 = 0 + 2gh =2gh
∴vc2 = 2gh
Hence, when the body is at point C, the kinetic energy is given by,
(K.E)c = ½ mvc2 = ½ m(2gh) = mgh
Similarly, the potential energy of the body at the point C is given by,
(P.E)c = mg(height of point C) = mg × 0 = 0
Hence, the total mechanical energy of the body when it is at the point C is given by,
Ec = (K.E)c + (P.E)c = mgh + 0 = mgh
∴ Ec = mgh………………………………………………………… (iii)
From equation (i), (ii) and (iii), it is seen that the total mechanical energy of a freely falling body when it is at point A is equal to the energy when it is at B or C.
This implies that the total mechanical energy of a freely falling body is conserved.
In other words, the principle of conservation of energy holds true in this case of a freely falling body.
If a graph is plotted between the total mechanical energy of a freely falling body and its height from the ground, a curve is obtained as in figure below.
Principle of Conservation of Energy