# Potential Energy Formula     ## What is the Potential Energy Formula?

When you talk about the potential energy formula, Physics will come up with several definitions. That is because there are different forms of potential energy. In general terms, Potential energy is the energy stored in the body of an object. Some of the different kinds of potential energy include electric potential energy, gravitational potential energy, spring potential energy, elastic potential energy, etc. The potential energy formula depends on the type of potential energy.  Potential energy is an important factor in determining the state of rest or motion of the body.

### What are the Potential Energy Types?

There are different kinds of potential energy. Some of them include:

Gravitational potential energy can be defined as the body’s energy by virtue of the gravitational force acting on them.

Electric potential energy is defined as the energy stored in the body by virtue of its electrons’ arrangements.

Elastic potential energy is known as the energy stored in the body by virtue of its elastic properties.

Spring potential energy is a modified form of elastic potential energy that takes place in the spring.

### What is the Potential Energy Formula?

As stated earlier, the potential energy formula depends on the type of Potential energy. The gravitational potential energy formula is

PE= mgh

Where PE is Potential energy

m is the mass of the body

h is the height at which the body is placed above the ground

g is the acceleration due to gravity.

The elastic potential energy formula or spring potential energy formula is

U= ½ k∆x2

Where U is the elastic potential energy

K is the spring constant

∆x is the change in position.

The electric potential energy formula is

UE= kq1q2/r

Where UE is the electric potential energy

k stands for Coulomb’s constant

whereas q1 and q2 stands for charges of the two separate points present in the circuit

r stands for distance of the separation.

In general, the SI unit of Potential energy is Joule, and the dimensional formula is M1L2T-2.

### Potential Energy Examples

There are several examples of potential energy. When a ball is thrown upward, mechanical energy is converted to kinetic energy by virtue of its motion. As it reaches the highest point, the kinetic energy is converted to potential energy. However, the potential energy is converted to kinetic energy as the ball comes down.

### Potential Energy Formula Derivation

According to the potential energy function for a conservative force, the force acting on an object can be described as,

F = dUdx dU = −Fdx ∫x2x1U = −∫x2x1Fdx

According to the definition of potential energy, the force acting on the object is F= mg

H is the height from the point of reference

Substituting these formulas,

U = −[mg(h1−h2)]

or, U = [mg(h2−h1)]

Where,

U – Potential energy

M- the mass of the object

G – acceleration due to gravity

h1 - the height of the point of reference

h2 - the height at which the object is positioned.

### Applications of Potential Energy

An object’s potential energy is derived from its position when it is stationary rather than from its motion, i.e., movement and potential energy do not have velocity, unlike kinetic energy. Following are some of the applications of potential energy:

• When an elastic band is stretched to tie something, it gains potential energy, and when it is released, it gains kinetic energy, which has velocity. Here, potential energy is converted to kinetic energy without any loss of energy.

• When the river water is dammed and used to generate hydroelectricity, it attains potential energy and is converted to kinetic energy when the river water flows freely.

• When an archer drags back an arrow, the arrow has potential energy converted to kinetic energy to move forward towards the target when released.

• If you hold a ball vertically upwards from the ground, it is subjected to potential energy caused by the gravitational force.

• In chemistry, chemical potential energy stored in the molecules is the reason for chemical reaction and bonding.

• We see a pendulum in a clock. When it is held at an end, it has potential energy which is converted to kinetic energy when it is released.

• Elastic potential energy is present in spring when it is compressed or released freely, but when the spring is in movement, it is subjected to kinetic energy.

• Even the food we eat has some form of chemical potential energy that reaches our stomach. Our body enzymes convert it to kinetic energy and use it to perform different tasks.

• When snow falls on mountains or a surface, it has potential energy. When this energy exceeds the holding capacity of the surface, it is released as an avalanche and gets converted to kinetic energy when it falls.

• A bullet loaded in a gun also works on the same principle similar to the bow and arrow. It has potential energy when it is at rest and gets converted to kinetic energy when it is shot by anyone.

### Conclusion

Potential energy is known as the energy possessed by the body by virtue of its position. There are different forms of potential energy. Different potential energy formulas represent all these forms.

## FAQs on Potential Energy Formula

1. Give one example of potential energy getting converted to electrical energy.

Several dams are converted to harness the potential energy of flowing rivers. The turbines present in the dams convert the potential energy of water to electrical energy.

2. State the changes in energy types when a ball is thrown upward.

When a ball is at ground level, the potential energy is zero. When it is thrown upward, it moves due to kinetic energy present in the ball by virtue of its motion. As it reaches its maximum height, the kinetic energy is converted to potential energy. As the ball comes down, the potential energy is again converted to kinetic energy.

3. What are the different forms of potential energy?

There are different forms of potential energy. Some of them are gravitational potential energy, electrical potential energy, spring potential energy, elastic potential energy, etc. Its own potential energy formulas represent every kind of potential energy.

4. What is potential energy, and how is it different from Kinetic energy?

Energy in general means the ability to do a task. For example, the force applied to an object to move is a kind of energy. It is basically divided into kinetic and potential energy. Potential energy is the energy used to finish a task, but it directly can not act as a source of energy. The potential energy of an object derives from its position rather than its motion, i.e., movement.

When the objects are moved from a state of equilibrium, they have some kind of energy due to gravity, chemical reactions etc., and this is known as the object’s potential energy. For example, when an archer drags back an arrow before shooting it, it gains potential energy to move towards the target when released from the bow. It leads to kinetic energy when the arrow is released from the bow. The release of potential energy triggers kinetic energy.

When an object does work, its acceleration increases and leads to kinetic energy, it is further divided into vibrational energy, translational energy, rotational energy. The major difference between the both is, potential energy is energy in a stationary position and kinetic energy is the energy in motion. On the other hand, kinetic energy has another element called velocity, which is absent in potential energy.

5. What is the relation of potential energy to chemistry?

Potential energy of a body is derived from its position when it is stationary rather than from its motion, i.e. movement. Potential energy lacks the concept of velocity, unlike kinetic energy. We generally think that the concept of potential energy is related to physics, but this concept can be found in any object, including the smallest invisible molecules of chemistry.

In this subject, we study potential chemical energy, the energy stored in the molecules which is the main source for chemical reactions and chemical bonds. This stored potential energy in molecules is released in chemical reactions when two or more elements or com[pounds come together.

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