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# Gravitational Potential Energy – Definition, Formulas and Examples

Jul 16, 2022

## What is Gravitational Potential Energy?

The potential energy produced by height and gravity is known as Gravitational Potential Energy. There are some forms of energy that are simple to conceptualise. An object that moves quickly has more kinetic energy than an object that moves slowly. A child with a lot of “energy” is rushing around a playroom.

However, as per physics, energy is neither created nor destroyed. This concept is called conservation of energy. Where does the energy go when a speeding vehicle travels uphill and slows down to a stop due to how steep it is? What happens to the energy in the forearms when a person moves a box off the floor?

The answer to all these questions is transformed into gravitational potential energy.  (GPE) is similar to height energy. The more GPE an article has, the higher it is put. Although it may appear unusual, there is a logical reason why this should exist.

### Why should Gravitational Potential Energy exist?

How can a person tell something is energetic just by looking at its height? Let’s consider the following procedure:

Start by raising a ball beyond the body from the ground. Then throw it. It then goes quickly to the ground. Energy is considered to be conserved, indicating that it can only be transformed from one type into another and can neither be created nor destroyed. Therefore, whatever energy an individual expends must be put to use.

As seen in the first step, an individual has exerted their entire effort by lifting the ball with the help of their hands. The food, which initially came from the sunlight through the food supply chain, provided this strength or energy to the individual to lift the ball from the ground. This energy must be utilised somewhere because it was expended when the person lifted the ball. Therefore, one can ascertain that the energy is kept as (GPE) inside the ball.

Step 2 lets the ball reach its maximum height and then fall to the ground. The fact that the ball started moving right away after being released demonstrates that, indeed, stored energy inside it! The ball falls faster and faster while acquiring kinetic energy (KE). Kinetic energy is created from (GPE).

The ball will nearly touch the ground in step 3 but has not quite done so. The ball is roughly the height it began before you raised it just before it struck the ground. It has reached its maximum acceleration and KE as a result. It indicates that the (GPE) it had before its dropping is equivalent to the kinetic energy it has now.

Once the ball strikes the ground, the earth absorbs this kinetic energy in two ways: through heat that evaporates in the ground and through the motions of the earth (since earth is a huge planet, the motions are small and rarely impossible to be seen).

## Gravitational Potential Energy Definition

The most important force is the gravitational force, commonly known as gravity. When an object with mass is uplifted in a gravitational field, energy is absorbed into the storage due to the gravitational force. This force is called weight. This storage of energy is called gravitational potential energy.

Simply put, what is (GPE)? It is the amount of work required to displace a body of mass (m) from infinite to a position within the gravitational field of a source mass (M) without propelling it is collected in the form of potential energy. The stored or collected energy is called “gravitational potential energy”. The gravitational potential energy is symbolised as “Ug”. It is the energy an item has or acquires as a result of a change in motion when it is in a gravitational field.

Elaboration: Now, everyone is aware that the energy held within a body at a specific position is termed as “potential energy” of a body. The change in potential energy is equivalent to the amount of work performed on the body by the forces if the body’s motion changes due to the influence of external forces.

The work performed under the influence of gravitational force is irrespective of the path used for the displacement, making it a conservative force. Additionally, all of these forces have some potential.

A reference point is where potential energy is zero because the gravitational force on a body (object) at infinity is zero.

The (GPE) formula combines mass (m), the earth’s gravitational momentum (g), and height above the surface of the earth (h) to the energy stored by gravity. It can be symbolised as:

Gravitational potential energy (GPE) = Mass (m) X gravitational field strength (g) X height above the earth surface (h)

GPE = mgh

## Gravitational Potential Energy Formula

Imagine lifting a material of mass (m) to a height (h) while resisting gravity. A winch and cable lift the material vertically, creating a parallel force between lifting the material and gravity. Suppose g is the gravitational acceleration, the gravitational force, Fg, multiplied by h. In that case, the vertical distance that the material has travelled will calculate the work performed by force on the mass.

Thus, the (GPE) formula can be stated as follows:

GPE = m X g X h

The material would return to the ground if the force were withdrawn, and the gravitational potential energy transforms itself into kinetic energy as the material drops or falls towards the ground.

Gravitational potential energy = mass X gravitational strength X-height

• The gravitational potential energy is expressed in Joules (J).
• The mass, m, is expressed in kilograms (kg).
• The height, h, is expressed in metres (m).
• The gravitational field strength, g, is expressed in newtons per kilogram.

Everywhere on the earth’s crust, the acceleration caused by gravity has a (nearly) constant value and is directed at the planet’s centre of mass: g = 9.81 m/s2. Therefore, the object’s mass and height above the surface are the only information needed to calculate gravitational potential energy.

 Test Your Understandings  Q. Consider a 10 kg load suspended five metres above the earth’s surface by a system of ropes. How much gravitational potential energy does it possess? Solution: The gravitational potential energy for the given information would be as follows: GPE = mgh =10 kg × 9.81 m/s2 × 5m = 490.5 Joules

### Gravitational Potential Energy Examples

The gravitational potential energy is directly related to the height energy. Thus, the higher the gravitational energy, the higher the object’s position. For instance, a textbook on a higher shelf has more potential energy than a textbook on the bottom shelf because it has a longer distance to fall. The following are the gravitational potential energy examples:

• Lifting heavy weights.
• Water retentive to a dam.
• An automobile is parked on a hilltop.
• A yo-yo game before it is deployed.
• Stream water at the top of the waterfall.
• A book before it tumbles over on a table.
• A kid at the summit of a park slide.
• A ripened fruit before falling on the ground.

### Conclusion

What is gravitational potential energy? It is the energy an item has or acquires when its location changes due to being in a gravitational field. Gravitational potential energy definition can be explained as an energy that has a connection to gravitational force or gravity. Students must comprehend this topic well to grasp higher-level concepts easily.

### 1. How is gravitational potential energy measured?

Ans. Like all other types of energy, gravitational potential energy is measured in units called Joules (J). Gravitational potential energy can change in various forms of energy during the energy transitions, such as mechanical or kinetic energy. When students know the object’s mass and height in the discussion, they can easily calculate the gravitational potential energy using the gravitational potential energy formula.

### 2. What is the gravity law?

Ans. According to the law of gravity, all objects are affected by each other’s gravitational pull. Determining the origin of gravitational potential energy is based on the law of gravity. According to the law of gravity, effort against gravity must be equivalent to the object’s gravitational potential energy to move an object to a specific position. It is the reason that the gravitational potential energy is dependent on both height and the gravitational acceleration, g.

### 3. What is gravitational potential energy?

Ans. An object’s energy due to its height or vertical position relative to a reference point—typically the earth’s surface—is known as gravitational potential energy. GPE is a shorthand for the definition of gravitational potential energy. The acceleration caused by gravity, g, the object’s mass, measured in kilograms, m, and height, measured in metres, h, all affect the gravitational potential energy. These three factors multiplied together to give us the gravitational potential energy:

GPE = mgh

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