Law of Conservation of Energy states the total energy of an isolated system always remains constant. The energy may change its form. It can be converted from one form to other. But the total energy of the system remains unchanged.
In an isolated system, if there is any loss of energy of one form, there is a gain of an equal amount of another form of energy. Thus, energy is neither created nor destroyed. The universe is also an isolated system as there is nothing beyond this. It is therefore said that the total energy of the universe always remains constant in spite of the fact that variety of changes are taking place in the universe every moment.
Conservation of mechanical energy during the free fall of a body
Suppose that an object of mass m lying on the ground is lifted to a height h. The work done is mgh, which is stored in the object as potential energy. This object is now allowed to fall freely. The energy of this object is calculated when it has fallen through a distance h1. The height of the object now above the earth surface is
h2 = h – h1
At this point P, the potential energy = mgh2
When the object falls freely, it gets accelerated and gains in speed. Using the equation,
v² = u² + 2gs
where u is the initial speed at the height h1, i.e. u = 0 and s = h1. Then,
v² = 2gh1
The kinetic energy at point P is given by
K.E = ½mv² = ½m × 2gh1 = mgh1
The total energy at the point P is Kinetic Energy + Potential Energy = mgh1 + mgh2 = mgh
This is same as the potential energy at the highest point. Thus, the total Energy is conserved.