Gravitational Potential Energy

# Gravitational Potential Energy

Gravitational potential energy is the energy moved by an item because of an adjustment of its position when it is available in a gravitational field. In basic terms, one might say that gravitational potential energy is an energy that is connected with gravitational power or to gravity.

You can understand gravitational potential energy most easily if you assume you take two pencils. Place one on top of the other. At present, we can state that the pencil on top will have more gravitational potential than the pencil on the table.

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Based on its location in the gravitational field, the pencil, or any other article, can possibly accomplish its task. We will find out with regards to the point exhaustively beneath.

Gravitational energy is the potential energy associated with gravitational force, which is required to lift objects against the Earth’s gravity. The gravitational potential energy due to elevated positions can be observed in water in a reservoir or behind a dam. When an object falls from one point to another inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy decreases by the same amount.

## What is Gravitational Potential Energy?

If a body of mass (m) is displaced into the gravitational influence of a source mass (M), but without accelerating it, the amount of work done in displacing it into the field of the source is stored as potential energy. This is called gravitational potential energy. It is represented with the symbol Ug.

### Explanation:

In general, the potential energy of a body at a given position is defined as the energy stored in the body at that position. The change in potential energy is equal to the amount of work done on the body by external forces.

Since the gravitational force is independent of the path taken for a change in position, it is a conservative force. In addition, all such forces have some potential.

The gravitational influence on a body at infinity is zero, therefore, potential energy is also zero. This point is called the reference point

### Gravitational Potential Energy Formula:

The equation for gravitational potential energy is:

⇒ GPE = m x g x h

Where,

• m is the mass in kilograms
• There is an acceleration of 9.8 g on Earth due to gravity
• h is the height above the ground in metres

Because the potential energy U of the work done is stored, gravitational potential energy at a point at a distance r from the source mass has the formula:

U = – GMm/r

As a test mass moves from one point to another within the gravitational field of a source mass, its potential energy will change as follows:

ΔU = GMm (1/ri – 1/rf)

If ri > rf then ΔU is negative.

### Formula Derivation:

Assuming a body is taken from the surface of the earth up to a height ‘h’ above the ground, then ri = R and rf = R + h then,

ΔU = GMm [1 / R-1 (R+h)]

ΔU = GMmh /R(R+h)

When, h<<R, then, R + h = R and g = GM/R2.

On substituting this in the above equation we get,

Gravitational Potential Energy is

ΔU = mgh

### Points to be remembered:

1. At the center of the earth, the mass of a body is zero because the value of g is zero.
2. If the gravitational field is zero at a point in the gravitational field, the gravitational field is zero as well.

## What is Gravitational Potential?

A point in a gravitational field has a gravitational potential that is the work done per unit mass that an external force would have to do to bring a massive object to that point from some defined position of zero potential, usually infinity. It is the difference in gravitational potential between a chosen point and the zero position.

The gravitational potential is often represented by the symbol V. If the field results from an isolated large object (or any object of finite size), it is conventional to define its magnitude to be zero at an infinite distance from the object; the magnitude is negative everywhere else since the gravitational force is always attractive. Gravitational potential is also defined as the gravitational potential energy per unit mass relative to a zero potential energy position. The two definitions are equivalent.

Simply, it is the gravitational potential energy possessed by a unit test mass

V = U / M

V = – GM / r

### Points to be remembered:

1. A point’s gravitational potential is always negative, and V reaches its maximum at infinity.
2. J/Kg is the SI unit of the gravitational potential.
3. The dimensional formula is M0L2T-2.

In the case of lifting gravity vertically, what happens to potential energy?

Gravitational potential energy is acquired by lifting a weight vertically. Vertical lifting is necessary to obtain gravitational potential energy. Upon the removal of the force, the object would fall back down to the ground, where the gravitational potential energy will be converted to kinetic energy.

Also read: NEET Exam Pattern 2022

## Frequently Asked Questions:

##### What are 3 examples of gravitational potential energy?

A raised weight, water that is behind a dam, a car that is parked at the top of a hill.

##### What are the main types of gravitational potential energy?

Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field.

##### Which factors affect the gravitational potential energy?

Gravitational Potential Energy is determined by three factors: mass, gravity, and height. All three factors are directly proportional to the energy.

##### What is the difference between gravitational potential energy and gravitational potential?

The gravitational potential at a point is defined as the amount of work done on a unit mass when bringing it from infinity to the given point. . The gravitational potential energy of an object is defined as the work done on the object when the object is taken from infinity to the said point.

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