**Introduction**

One of the two major forms of energy is potential energy. Potential energy is the amount of energy that an object can hold. It is the power that an item has while it is not in motion. The potential energy of a moving object increases as it slows down.

The object’s capacity strength reduces as it accelerates. Potential energy is the electricity that occurs as a result of the relative locations (configurations) of the components in a physical machine.

This energy shape has the capacity to affect the nation of other items in its vicinity. The energy held in an object due to its height above the ground is referred to as gravitational potential energy.

The attractive gravitational pull between the object and the earth causes this energy to be released. The more an object’s gravitational potential energy, the higher it is positioned. When the object hits the ground, this energy is converted to kinetic energy.

**Definition**

Nuclear-Power states that

“In classical mechanics, the **gravitational potential energy** (P.E) is the energy an object possesses because of its position in a **gravitational field”**.

Gravitational energy is the potential energy associated with gravitational force, as labour is necessary to lift objects against the gravitational pull of the Earth.

Water in a raised reservoir or maintained behind a dam exhibits gravitational potential energy, which is proven by water in an elevated reservoir or kept behind a dam.

When an object descends from one point to another inside a gravitational field, the force of gravity does positive work upon that, as well as the gravitational attraction decreases by the same amount.

The energy held in an object due to its height above the ground is referred to as gravitational potential energy.

The attractive gravitational pull between the object and the earth causes this energy to be released. The more an object’s gravitational potential energy, the higher it is positioned. When the object hits the ground, this energy is converted to kinetic energy.

**SI unit**

The SI unit of gravitational potential energy is Joule. The amount of work done by a force with one newton (N) operating over a one-meter distance (m).

**Formula**

The formula to calculate gravitational potential energy is given as

P.E = mgh

Where,

- m is referred to as the mass of the body
- g is known as gravitational acceleration
- h is the height of the body above the earth’s surface

Above mentioned formula can also be reformed to find mass, gravitational acceleration and height of a body as

- Mass = m = P.E/gh
- Gravitational acceleration = g = P.E/mh
- Height of body = h = P.E/mg

**Derivation**

It is necessary to have clear concepts of work done in order to derive a relation for gravitational potential energy. A force acting on an item can only accomplish work if the object is shifted at the same time that the force is operating.

Because forces and displacements are both vector values with magnitude and direction, there is no reason why the vector force must be constant in size or direction, nor must it be in the direction of the displacement.

By definition work done is equal to dot product of force and displacement

Work done = W = **F.d**

Work done = W = Fdcosθ

Now assume that if the direction of force and displacement are parallel then the angle will be θ=0.

Hence,

Work done = W = Fdcos (0)

Since cos (0) = 1 so

**Work done = W = Fd**

Work is defined by this sentence. It’s more of a hypothesis that’s been empirically proven. However, given the intuitive assumption that a force’s work must be tied to the total change in the system, we can try to establish a quantity that characterizes work. That is precisely what the following sentence does.

In the above equation, displacement d can also be replaced by the height of body h.

W = Fh

Since work done on a body is equal to gain in potential energy so

Work done = P.E = Fh

Or

P.E = Fh

Now as newton’s second law states that force is equal to product of mass and acceleration so

P.E = mah

Since we are talking about the gravitational field so acceleration can be replaced by gravitational acceleration g.

**P.E = mgh**

The above relation shows that potential energy is directly proportional to mass, height and gravitational acceleration.

**How to calculate the problems of Gravitational potential energy?**

**Example 1:**

Roger Federer’s tennis ball weighs 0.3 kg. What is the gravitational potential energy (GPE) of the ball if he serves it at a height of 2.0 m above the ground?

**Solution: Manual method**

**Step 1:** write given data values

Gravitational acceleration = g =10ms^{-2}

Mass = m = 0.3kg

Height = h = 2.0m

Gravitational potential energy = P.E =?

**Step 2:** Write general formula for net force

P.E = mgh

**Step 3:** Put the given data values

P.E = (0.3) (10) (2.0)

P.E = 6.0J

Hence Gravitational potential energy of ball is **6.0J.**

A gravitational potential energy calculator can also be used to solve the above example. This calculator can solve the problems according to the formula of gravitational potential energy PE=m*g*h. To use this calculator follow the below steps.

**Step 1: **Choose the phrase you wish to compute from the drop-down menu.

**Step 2: **Place the given data values or required information into the calculator and press the calculate button.

As a result, the issue is calculated.

**Summary:**

The gravitational potential energy of an item indicates how much energy may be obtained by changing its height. This is used, for example, to determine where and how to build hydroelectric power plants, as well as how to design irrigation and sewage systems. The “object” in a hydro-plant is the body of water behind the dam. But, more importantly, you want to know an object’s gravitational potential energy in proportion to the gravitational potential energy it would have in another location. That is, the distribution of potential energy is critical. In this regard, the gravitational potential energy calculator helps to make more precise observations.

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