Gravitational potential energy

In general observation, humans saw that if an object was kept at a height, it gained some kind of energy in it, by which it was falling on the ground. 

We also know that force is fundamental and helps the object move, stop, or change its direction. This force gets stored as work/energy, according to physicists. This energy was either kinetic energy or potential energy.

So when the object was at the height, the body possessed the energy due to the virtue of gravitational force; this energy was called potential energy.

As the word itself means, the potential energy means that the body gains the potential to do work. 

Why is the concept of gravitational potential energy important?

The conservation of energy theorem is based on potential energy and kinetic energy and for using this theorem in practical use, we must understand the concept of gravitational potential energy.

It also tells the amount of energy possessed by the object.

Definition and concept:

The gravitational potential energy can be defined as the energy that is held by the body due to the virtue of its position. 

The gravitational potential energy is also defined as the amount of work that will have to be done on the body to bring it to a position near another body from infinity.

Gravitational potential energy is a relative term. The gravitational potential energy at a point has no real meaning; scientists generally define the gravitational potential energy for ground. 

The gravitational potential energy of the earth’s surface/ground is assumed to be zero joules. The gravitational potential energy of any other body at any height is taken relative to it. But It does not actually depend on the body’s mass only; it also depends on the body’s height.

The formula of gravitational potential energy: 

The formula that defines the gravitational potential energy between the two bodies, this formula has been derived from the concept that force= work X displacement. 

And dw = (GMm/x2)dx integrating this, we get the formula, 

U= -G Mm/ r2  

The formula for the gravitational potential energy is potential energy at the given height is:

Here one body is considered as earth.

We derive another formula for the gravitational potential energy, 

U(height)- U(Ground) = gravitational potential energy 

Here U(ground)=0.

The gravitational potential energy= mass x acceleration due to gravity x body height from the ground.

U = mgh

Here, g = 9.8 on Earth

Units and dimensions:

The unit of the gravitational potential energy is joules/kilograms and the dimensional formula of this physical quantity is [M0L2T-2]. 

Interpretation of the formula of the gravitational potential energy:

1. Let us assume that we are at the height of 1km above the ground,and we hold a ball of mass 100 gm. The formula for gravitational potential energy is- U = mgh

So, the gravitational potential energy possessed by the ball is 0.98 joules/kg. (0.1 x 9.8 x 1 = 0.98)

Using formulas and the conservation of energy theorem, we can find the kinetic energy and potential energies when the ball is thrown.

Using formulas, you can also find the velocity with which the ball will fall on earth and other physical quantities. 

2. Suppose a ball is at a distance x from the ground, and a similar ball is at a height 2x from the ground. We simply see that the ball’s potential energy at twice the distance possesses twice the energy, and hence we also observe that total energy will also be double. 

Conclusion: 

The gravitational potential energy can be defined as the energy that is held by the body due to the virtue of its position. The gravitational potential energy is also defined as the amount of work that will have to be done on the body to bring it to a position near another body from infinity.

Gravitational potential energy is a relative term; gravitational potential energy at a point has no real meaning. Scientists define the gravitational potential energy generally to ground.  People use various formulas according to the need for a problem statement.