In this article, we will learn what is Potential Energy, its Definition, meaning, formula, equation, examples, diagram, types, unit, etc.

## What is Potential Energy? Definition, Meaning, Examples

### Potential Energy Definition

“Potential Energy” was first coined by William Rankine, a Scottish Physicist in the 19^{th} century. Potential energy or PE is the stored energy capable of doing work due to the position or state of the object under consideration.

The entities that we call “objects” may be tiny particles, and even solar system components have stored energy (potential energy) that is transformed into kinetic energy during motion. Educalingo’s definition of potential energy states that “a form of energy associated with forces acting on a body in a way that depends on body position in space.”

### Potential Energy Meaning & Examples

Potential energy (P.E) is that form of energy having the ability or potential to do work but at present time it cannot do work or apply force on anybody. Hence, we say it’s the energy objects possess in virtue of their position and not motion. P.E comes from a matter and is an inherent property of anything having mass.

- It sometimes gets hard to grasp the concept of PE. If bodies move, they possess kinetic energy, which is relatively straightforward to understand. It’s because we observe the objects moving, and hence we know that they have some energy.
- As far as potential energy is concerned, it’s a form that is stored energy in stationary objects. Since the objects are at rest, therefore it’s a bit trickier to understand the concept.
- Even though potential energy is stored in objects, a force needs to be applied so that the body can store it. These forces may be elastic or gravitational. P.E won’t exist without these forces. The unbalancing of equilibrium of an object results in the conversion of potential energy into kinetic energy.

## What are the Units of Potential Energy?

Potential energy is measured with the following units:

- Calorie,
- Joule,
- BTU (British thermal unit)

Let’s see the relationship between potential energy units, Calorie, Joule, BTU,

- 1 BTU = 252.16 Calorie
- 1 kcal = 4.2 kJ
- 1 kcal = 4200 J
- 1000 cal = 4200 J
- 1 cal = 4.2 J

The quantity only has magnitude and no direction. Therefore, it’s a scalar quantity.

## Potential Energy Formula or Equation & Derivation

### Potential Energy Formula or Equation

The equation for potential energy is given as:

P. E= mgh

- M= mass of the body
- g= acceleration (9.8 m/s
^{2}at earth’s surface) - h= height of body

### Potential Energy Derivation

Potential energy is the work done on a body to take it to a specific height. A body has mass “m.” It is raised to a height “h,” and gravitational force is “g,” which acts on the body. the equation for work done is as under:

- W= Fd

It becomes:

- W= mgh

Work done equals mgh, which the body has gained. Hence potential energy is given as:

- P. E= mgh

## Types of Potential Energy

The types of potential energy are discussed in depth below.

### Gravitation Potential Energy

#### What is Gravitational Potential Energy?

The energy stored in the body due to its vertical position or height is called gravitational potential energy. Due to the gravitational attraction of Earth for the object, the energy is stored. Hence, we can say it’s acquired energy due to a change in the body’s position when it is present in the gravitational field. It may also be defined as the work done by the gravitational force is termed gravitational potential energy.

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

The gravitational potential energy equation is stated below:

Gravitational P. E= mgh

Where “m” is the mass in kg, “g” is acceleration (on the earth’s surface, it is 9.8 ms^{-2}), and “h” is the height to which the body is raised.

#### Gravitational Potential Energy Near Earth’s Surface

Consider a system consisting of our Planet Earth and an object on the surface of the earth. The object is taken as a particle because it is too small compared to Earth’s size. The force acting on the body is equal to its weight “mg” and is acting vertically downwards.

According to Newton’s third law, the body exerts a force on earth of the same magnitude but in the opposite direction. According to Newton’s second law, each of these forces produces acceleration on earth whose magnitude equals mg divided by the mass of earth.

The ratio of the mass of an object to the earth’s mass is minimal; therefore, the earth’s motion is ignored. This way, the system is considered a group of single-particle systems with a constant gravitational force of earth acting upon it.

The constant gravitational force of earth does work on the body, near the earth’s surface, which depends upon the body’s mass, the difference in height the body transverses, and acceleration because of gravity. So, the work is negative of difference in gravitational potential energy, and the difference is given by:

- ΔU
_{grav}= -W_{grav,AB }=mg (y_{B}– y_{A})

The gravitational P.E function near Earth’s surface is:

- U (y)= mgy+const

The convenient constant to choose is zero for when y=0, which is the lowest vertical position.

#### Gravitational Potential Energy Beyond Earth’s Surface

The gravitational potential energy near the earth’s surface is discussed above, where the force of gravity is constant (mg).

For larger distances, another expression is taken into account. Newton’s universal force of gravitation inversely varies as the square of the distance from Earth’s surface (-GM_{E}m/ r^{2}).

When the object of mass “m” moves distance r_{1} to r_{2} away from the center of Earth, changing P.E is given by:

- ΔU= GM
_{E}m (1/r_{1}– 1/r_{2}) - ΔU= U
_{2}– U_{1}

Hence a simple expression can be written that is:

- U= – GM
_{E}m/r

Would you like to know about Thermal Energy

### Elastic Potential Energy

#### What is Elastic Potential Energy?

The objects that can be stretched or extended, for instance, rubber bands, possess elastic potential energy. The more an object can expand, the greater it will possess elastic potential energy.

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

The formula for elastic potential energy is given as:

U= ½ kx^{2}^{}

Where “x” is the string stretch length in m, “U” is the elastic potential energy and “k” is the spring force constant.

### Electric Potential Energy

#### What is Electric Potential Energy?

The energy required to move a charge against an electric field is known as electric potential energy. More energy would be needed while moving a charge further in an electric field and moving it through a stronger electric field. It is also defined as work done by Coulomb’s force is referred to as electric potential energy.

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

The equation for electric potential energy is given by:

U_{E}= k q_{1}q_{2}/r

Where “UE” is the electric P.E, “k” is Coulomb’s constant, q_{1 }and q_{2 }are for charges, and “r” is the distance of separation.

### Nuclear Potential Energy

Another type of P.E is nuclear potential energy. The energy particles inside atomic nuclei are known as nuclear potential energy. Strong nuclear forces hold the particles together. Weak forces provide P.E for radioactive decay, for instance, beta decay.

### Chemical Potential Energy

Chemical potential energy is another type concerned with the structural arrangement of atoms or molecules. The arrangement is the result of chemical bonds between molecules.

## Calculation of Potential Energy for Electrostatic Forces Between Two Bodies

In the light of Coulomb’s law, the force exerted by charge “Q” on another charge “q” separated by distance “r” is given as:

- F= 1/ 4
*πε*_{0}* Qq/r^{2}. r^{^}

Here r^{^ }is a vector of length 1 directing from Q to q. “*ε*_{0}” is the vacuum permittivity which can also be written as *k*_{e} = 1 ⁄ 4*πε*_{0} called coulomb’s constant.

The potential function for work “W” to move a charge Q from point A to B in the electrostatic force field is hereunder:

- U(r)= 1 ⁄ 4
*πε*_{0}* Qq/r

## Potential Energy Diagram

According to the first law of thermodynamics, energy is neither created nor destroyed; it just changes its forms. Potential energy is a form of energy that is contained by an object in itself.

In simple words, the potential of any object to do work. We can illustrate the concept of potential energy through some examples from our everyday life.

- Have you seen the simple pendulum?
- Do you know how it works?

We will dissect these questions to know the rope of potential energy in our everyday life. A simple pendulum consists of a mass attached with a string that rotates around a pivot, as shown in the above picture.

When the pendulum is resting, there is no work done, but it has gravitational potential energy. When we displace its mass from the O position to the B position, it has the highest gravitational potential energy.

When we release the mass, it starts back and forth motion. Now the question is from where the mass of the pendulum got the energy to move?

The gravitational potential energy, which was contained by mass, forced it to move along the rope. This potential energy converts into kinetic energy and vice versa. The total sum of kinetic and potential energy is called mechanical energy.

## Potential Energy Examples with Solved Problems

### Potential Energy Solved Problem#1

Calculate the current P.E of a ball weighing 0.5 kg which is about to roll off the edge of a 1.5m tall table.

**Solution**

The equation for Potential energy is given by:

P.E = mgh

The ball travels a distance in a downward direction, making it negative.

P. E= (0.5 kg) (- 9.8 ms^{-2}) (- 1.5 m)

Potential energy= 7.35 J

### Potential Energy Solved Problem#2

A pendulum is dropped from rest. Its string length is 1.2 m. if the mass at the end of the pendulum is 2.03 kg, calculate the initial potential energy.

**Solution**

- P.E=mgh

The height is taken negatively because the ball will travel downwards.

- P.E= (2.03 kg) (-9.8 m/s
^{2}) (-1.2 m)

Potential energy= 23.87 J

### Potential Energy Solved Problem#3

A ball weighing 0.5 kg rolls up the hill. Find how high up the hill it rolls if it was traveling with an initial velocity of 3.12 m/s.

**Solution**

According to conservation of energy equation:

- P.E
_{top}= K.E_{bottom} - mgh= ½ mv
^{2} - (0.5 kg) (9.8 m/s
^{2}) h = ½ (0.5 kg) (3.12 m/s)^{2} - 4.9 kg.m/s
^{2}h= 2.4336 kg.m^{2}/s^{2} - h= 2.4336/ 4.9
- h= 0.497 m
- h= 0.5 m

## Potential Energy & Energy Conservations

There are numerous types of potential energy, and each is associated with a specific kind of force. Specifically talking, every conservative force gives rise to potential energy.

**Principle of Conservation of Energy**

In physics, “conservation” refers to something that is conserved and won’t change. It means that the variable in an equation that represents a conserved quantity is constant over time. Hence, the value doesn’t change before and after the event.

Energy refers to the total energy of a system. As objects move around over time, the energy associated with them, which may be kinetic, gravitational potential, heat, etc., change forms. Still, if energy is conserved, then the total will remain the same. It means it transforms from one form to the other, but the total energy remains constant.

We likely encounter systems (in mechanics) constituting kinetic energy (E_{K}), gravitational P.E (U_{g}), spring or elastic P.E (U_{s}), and heat or thermal energy (E_{h}). The subscripts “i” and “f” are used for initial and final values in the system. The principle of conservation of energy equation is:

E_{Ki}+U_{gi}+ U_{si}= E_{Kf}+U_{gf}+U_{sf}+ E_{Hf}_{}

In expanded form, it is written as:

1/2mv_{i}^{2}+mgh_{i}+1/2kx_{i}^{2}=1/2mv_{f}^{2}+mgh_{f}+1/2kx_{f}^{2}+E_{Hf}

## Potential Enery Uses & Examples

Gravitational potential energy depends upon the weight and height of the body. The more the weight and height, the more gravitational PE.

The P.E of the system of particles is dependent upon initial and final configurations and independent of the path followed by particles. Some examples of potential energy we often observe are discussed below:

**Pendulum**

A pendulum is a structure in which the bob is suspended with a string from a pivot so that it swings. A typical example is a pendulum clock. The potential energy of the pendulum is maximum if it is held at one end (because of its position).

This P.E is then converted to K.E. before coming back on the same path; the bob of the pendulum will reach the other end and stop for some time at the highest point. At this resting point, the K.E is converted to potential energy. The process goes on until the pendulum stops.

**Spring**

The objects that can be stretched and compressed, for instance, spring, possess potential energy known as elastic potential energy, as discussed above in the blog.

When we compress or stretch a spring, it attains elastic potential energy. When compressed spring is released, the stored elastic P.E converts into Kinetic energy.

**Bow and Arrow**

The first law of thermodynamics applies to the working of a bow and an arrow. The law states that energy can neither be created nor destroyed but can be transferred from one form to another. When the archer pulls the bowstring back, the flexible limbs of the bow gain some amount of elastic potential energy.

The more the archer stretches the bowstring, the more elastic PE is stored. When the arrow is released, it travels with great speed. The potential energy gained by the bowstring is transferred to the arrow as kinetic energy, which drives it forward.

**Rocks present on the edge of cliffs**

Rocks are present on the cliffs. Due to their height, they possess gravitational PE. When the rock is pushed, the stored gravitational PE will transform into kinetic energy.

**Food**

We gain energy from the food we eat to perform different everyday tasks. There is a type of potential energy known as chemical kinetic energy present in chemical bonds of substances. Hence, the food has chemical PE.

When it reaches the stomach, the energy is used by our body. In other words, we can say that anything made of atoms possesses potential energy.

**Water**

Water held in reservoirs or dams is present there for different purposes like generating electricity in hydropower plants, flood prevention, irrigation, industrial use, human consumption, and PE.

Water present in reservoirs is stationary because it’s prevented from flowing. Hence it possesses P.E due to its state. When gates at the dam are opened, the water at rest starts flowing, so the stored P.E is transformed into K.E.

**Firing bullet from a gun**

Before firing, the bullet is at rest. Anything at rest possesses PE. When the bullet is at rest, it has stored P.E, which is converted to kinetic energy when it is fired.

**Roller Coasters**

A Roller coaster is another example. Before the free fall, when the wagon is held at the top of the rollercoaster, it has P.E. The energy cart possesses due to the height and weight of people is known as gravitational PE.

The greater the number of people, the greater will be the gravitational P.E of the cart. As the wagon slides on track further, the stored P.E converts into K.E.

**Rubber bands**

A typical example of PE is a rubber band. The stretching of a rubber band results in storing of P.E inside the band. Hence, we say the stretched band has elastic potential energy in it.

When the rubber band is released, it attains its original shape, resulting in the conversion of P.E into K.E.

**Swimmers**

The swimmers stand on the diving board and stretch their bodies. This stretching results in the storage of gravitational P.E in the bodies. When they dive, this energy transformed into kinetic energy.

That is why the swimmers jump during diving to attain maximum gravitation P.E. This results in a more significant amount of kinetic energy. It is necessary because cutting the viscosity of water is easier if kinetic energy is greater.

**Wrecking Ball**

The wrecking ball is used in crushing the buildings. It is the same as a pendulum. The crane swings the wrecking ball to a specific height which makes it gain potential energy, which is further converted to K.E for crushing the buildings.

**Snow**

Snow covers the peaks of high mountains. This snow is at rest and possesses gravitational PE. When snowfall occurs, the new snow falls on the mountains.

The already present packed cover of snow breaks resulting in avalanches. The stored P.E has converted to K.E; hence snow swiftly rolls down the mountains.

## Facts about Potential Energy

- The energy is concerned with forces acting on a body that depends only on the body’s position in space.
- The energy is transformed instantly.
- There are several types of potential energy, each associated with a specific force.
- P.E is a function of the system’s state in which it is defined relative to that for a specific state.
- Gravity is a form of potential energy.
- Potential energy is an inherent property of everything that has mass.

## Advatages of Potential Energy

Some of the advantages of potential energy are stated below.

- P.E can be used to generate pumped-storage hydroelectricity.
- The liquid stays in the glass due to P.E.
- It is easy when you are cycling down a hill.
- There would be no gravitational force. Without it, nothing would stay on the earth.
- Potential differences are utilized in water wheels and water turbines.
- Ripe fruits fall off the trees.
- Toilets don’t overflow and can be used again and again.
- Nuclear power is a highly reliable form of energy.
- Due to low fuel costs, large amounts of nuclear energy can be produced from fission reactions.
- Gravitational potential energy is produced and transformed easily.
- It helps in the reduction of global warming.

## Disadvatages of Potential Energy

Following are some of the disadvantages resulting due to potential energy.

- The stored potential energy in rocks at cliffs can cause them to slide, which results in serious accidents.
- Snow avalanches are another natural disaster that can be caused because of potential energy.
- It is hard while you are cycling up a slope or hill.
- Hiking up a mountain or hill is pretty hard.
- Extraction of fossil fuels.
- A greater amount of waste is produced.
- Energy exists in limited supply, and therefore I categorized it as a nonrenewable source of energy.

## Conclusion

Potential energy is possessed by bodies at rest. It doesn’t have direction and only possesses magnitude; therefore, P.E is a scalar quantity. Mathematically P.E= mgh. The SI unit is joules “J”.

There are various types of potential energy, such as gravitational, elastic, electric, nuclear, and chemical potential energy. The blog intends to explain the examples, advantages, disadvantages, derivation, and other related laws such as the principle of conservation of energy.