Gravitation-Variations in g-Gravitational Potential Energy

Gravitational potential energy is the energy that an object has due to its position within the field of gravitation. The most popular application of gravitational potential energy is when an object is located near the surface of Earth, at which the acceleration of gravitation is believed to be constant, around 9.8 m/s2.

At a certain position, the value of the gravitational energy is zero. The potential energy at a point higher than the zero point is equivalent to the amount of work required to raise the object to that height without any changes in the kinetic energy. Thus, at this time, the force needed to lift it is the same as the weight. As a result, it is logical that the gravitational potential energy is equal to the weight multiplied by the height to which it is lifted.

The term used to describe gravitational energy comes from the gravity law and is equivalent to the effort that gravity makes to move a mass towards an exact point in space. Due to the inverse square nature of gravity, it is believed that the force will be close to zero at long distances, and it is logical to pick the zero gravitational potential energy in the infinite distance.

The energy from gravitational potentials close to a planet will be negative because gravity does positive work when the mass gets closer. The negative potential is a sign of a “bound state”; once an object is located near an enormous body, it is entrapped until something is able to provide enough energy for it to leave. The basic form of the gravitational potential energy of mass m would be:

U = -GMm/r

Where G is the gravitational constant, and that is, the masses of the attracted body and how far they are from their respective centres.

What is Gravitational Potential Energy?

Potential energy stores the amount of work that was done to move a mass (m) from infinity to a point inside the gravitational force of a source (M) without accelerating. This is called gravitational potential energy. It is represented as the symbol Ug. 

Explanation. The body’s potential energy at any given position can be defined as the energy it stores at that moment. The potential energy changes when the body’s position is affected by external forces. This corresponds to how much work the forces have done to the body.

Because the gravitational force does not depend on the path taken to make a change in location, the work is done independently. The force is, therefore, a conservative force. Furthermore, all of these forces have some potential.

A body’s gravitational influence at infinity is null; therefore, potential energy is null, which is known as a point of reference.

Gravitational Potential Energy Formula

The gravitational potential energy formula is:

⇒ GPE = mgh

where,

• h is measured in metres
• g stands for acceleration due to gravity (9.8 m/s2 on Earth)
• m is the mass measured in kilograms

Gravitational Potential Energy

These examples show two forms of potential electricity, dynamic potential energy, and gravitational potential energy. Gravitational potential energy is energy stored in objects due to their vertical position and height. The object’s gravitational attraction to the Earth stores this energy.

The gravitational potential energy of a massive ball made of some material is dependent on two variables: its mass and the height it is raised to. Gravitational potential energy and the object’s mass are directly related. Higher masses have higher gravitational energy. The gravitational potential of an object’s elevation also has a direct correlation. 

Gravitational potential energy increases with the object’s height. The following equation explains these relationships:

PEgrav = mass × g × height

PEgrav = mgh

In the equation above, m stands for the mass of an object, h stands for its height, and g represents the gravitational field strength (9.8 N/kg Earth-wide), also known as the acceleration of gravity.

In order to determine the gravitational potential energy of an object, it is necessary to arbitrarily assign a zero height location. Usually, the ground is considered to have zero height. However, this is only an arbitrarily determined position that most people agree on.

Because many labs are performed on tabletops, it is customary to set the zero height position for the tabletop. However, this is not a rule. If the tabletop is in the zero position, then an object’s potential energies are determined by its height relative to the tabletop.

If a pendulum swings above the tabletop, it has the potential to produce energy. This can be measured by the height of the ball above the tabletop. You can determine the potential energy of the ball by measuring its mass above the tabletop and its height.

Doubling an object’s height above the zero location will result in doubling its gravitational potential energies. Tripling the height will result in tripling the gravitational potential energy.

Conclusion

Gravitational potential energy refers to the energy generated or possessed by an object as a result of the change in its position when it is within an area of gravitational force. In simpler words, it can be described as – gravitational potential energy is energy that is a result of gravitational force or gravity.

The most typical way to comprehend what is meant by gravitational potential energy can be seen when you have two pencils. One is put on the table, while the other is positioned over the table. We can now say that the pencil that is higher will possess more gravitational potential energy than the one placed at the table.