## Tuesday, December 29, 2015

### Verification of Law of Conservation of Energy for a Freely Falling Body

According to law of conservation of energy, the energy of a system always remains constant. Energy is neither created nor destroyed and it just converts from one form to other. The individual energies of different formats may increase or decrease but the total energy of a system always remains constant.

We can verify law of conservation of energy in the case of any body. When we say energy, we mean mechanical energy. It is the sum of potential and kinetic energy.

It can be verified in the case of a vertically thrown body. To through a body vertically up, we shall give some initial velocity to the body. As the body is thrown vertically up, it is moving against the acceleration due to gravity and hence its velocity will be keep decreasing.

Finally at a certain height, its velocity becomes zero and the body will have only potential energy at that point. The total mechanical energy of the vertically thrown body remains constant.

Here in the video, it is explained how conservation of energy is a valid phenomenon in different phenomenon.

We can verify law of conservation of energy in the case of a freely falling body. Let the body has a specified mass and if its initial velocity is zero then it is called a freely falling body.

Let the body is at a initial height h from the reference point and generally that is ground itself. As it is not having velocity at that point, it wont has any kinetic energy at that point and all of its energy is in the format of potential energy.

Let the body has fallen some height from its initial position. It will acquire some velocity at that point as it has got acceleration due to gravity. As the body has fallen some height, simultaneously its potential energy also decreases. But it is proved in the video presented below that the total energy of the system remains constant.

We can show that by converting the velocity part of the body at the middle position also in terms of height.

When the body reaches the ground, its height becomes zero with respect to reference position and it has no potential energy there. Any way as it came down further with acceleration due to gravity, it acquires more velocity and hence more kinetic energy.

Any way at any point of the journey, the total energy of the  system always remains constant and here it is in the format of potential energy.

This is demonstrated in the video as show below in detail.