## Saturday, April 30, 2016

### Gravitational Potential Energy, Kinetic Energy and Total Energy

Gravitational Potential energy

Gravitational Potential energy of a body on the earth Potential energy is the possessed by the body due to its position on the earth. The potential energy of a body can be measured taking the center of the earth as the reference. It means if the body is at the center of the earth, its potential energy is treated as zero.

Potential energy of the body is also treated as negative and it is a symbolic way of identifying that the body is associated with the system. We need to do some work it getting a body to a particular position on the earth. After the work is done, the energy used in doing the work cannot disappear and it will convert into some other form of energy. This is conservation of energy and energy is neither created and nor created. It just converts from one form to other. Thus the work done by us in putting the body at a certain place is converted into potential energy and it is called gravitational potential energy and it is by default treated as negative.

We can measure the work done in pulling the body to a certain mass by a small distance using the formula that the work done is the product of force and displacement. Force between the body and the mass of the earth can be measured using Newton’s law of gravitation.

In this way, we are going to get the work done in displacing the body only by a small value and we need to know the work done in producing the total displacement. This can be done by integrating the first equation. This total work done is stored in the form of gravitational potential energy.

As we move far away from the surface of the earth, potential energy starts increasing. At infinite height, potential energy becomes zero. Thus potential energy of a body associated with the earth is negative and at the best, at infinity, it will become zero and it cannot turn into a positive value.

Change in Potential Energy

When the body is on the surface of the earth, it will possess some potential energy. When it is moved to a certain height, its potential energy increases. The work done in this process is nothing but the change in the potential energies of final to initial. A sample case is taken and derived the equation for the work done as shown below.

Kinetic energy

Everybody revolving around the earth in a specific orbit will have some velocity and that velocity is called orbital velocity. As the body has orbital velocity, it consists of kinetic energy. We can measure the kinetic energy of the body using he conventional kinetic energy.

It could be noticed that the kinetic energy is positive and its magnitude is double the value of gravitational potential energy.

Total energy

We can find the total mechanical energy of a body as the sum of potential and kinetic energies. By adding both the values, it can be found that the total energy of the body is also has a magnitude of potential energy.

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