Gravitational Potential Energy

Gravitational potential energy is the energy possessed by a body due to a certain gravitational force with which it interacts with another body. In terms of planet Earth, gravitational potential energy is the energy in possession by a body located at a certain height relative to the surface of planet Earth. Gravitational potential energy is often in use with its short name – potential energy.

Gravitational – potential energy

To understand which physical quantities this type of energy depends on, consider the following situations:

• Imagine two identical bodies located at different heights relative to the surface of the planet Earth. Let the first body be at a height of 1m, and the second body at a height of 50m. It is very logical that a body located at a higher height has more energy. A body falling from a greater height can do more damage. This example shows that the gravitational energy depends directly on the height of the body.
• Imagine two bodies of different mass located at the same height relative to the planet Earth. Let the first body have a mass of 1 kg, and the second body of 500 kg. It is clear that a body with more mass has more energy. A body with more mass can do more damage when falling. This example shows that the gravitational potential energy depends directly on the mass of the body.
• Due to the different distance of different locations on the surface of the planet Earth from its center, the action of the gravitational force between the Earth and the body can be different. Therefore, the closer the body is to the center of the Earth, the greater will be the gravitational force between them. Due to this fact, the gravitational energy depends on the earth’s acceleration which is different in different locations on the planet earth.

The examples listed above in the text show that the gravitational potential energy depends on the mass of the body, the height at which it is located (relative to the surface of the planet Earth), and the exact location where it is located.

Gravitational potential energy formula

The formula for calculating gravitational potential energy is:

From the formula itself, it is clear that a body cannot possess this type of energy, if it is on the surface of the planet Earth (h=0, multiplying by 0 gives 0). To calculate this type of energy, it is enough to calculate the product of the mass of the body, the ground acceleration, and the height at which the body is located.

Example number 1. Calculate the gravitational potential energy possessed by a body with a mass of 7 kg, located at a height of 4 m from the surface of the Earth, if it is located in Macedonia. The ground acceleration in Macedonia is 9.81 meters per second per square.

By substituting the given values from the task in the main formula, the expression is:

After calculating the product of the three numbers, it is clear that the potential energy possessed by the body from task 1 is 274.68J.

Transforming the formula

By transforming the formula, the remaining three variants of the formula for gravitational potential energy are in use.

We can calculate mass through energy, height and ground acceleration with the formula:

Earth’s acceleration, through energy, height and mass, can be available with the formula:

We can calculate height through energy, mass and ground acceleration with the formula:

Finally, these variants allow us to calculate mass, ground acceleration or height, if we are given all other values of physical quantities except the required one.

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Tags: Energy, Gravitational, Potential