Potential Energy: Definition, Formula and Examples

Potential Energy: An object can store energy as a result of its position. For example, push/pull doors store potential energy in the form of a spring coil. Even when it is at rest, it is exerting pressure. As soon as someone pushes/pulls it open, the energy charges up and lets the door close automatically back to its resting state.
This stored energy of position is referred to as potential energy. A body possesses potential energy due to its position or configuration. In this article, we will discuss potential energy in Physics and its types.

Potential Energy: Definition

Potential energy is the energy possessed by a body by virtue of its position or configuration. It is also known as stored energy that helps to conduct any work.

For example, we see energy stored in various forms. The energy stored in our food gives us the energy to do our day-to-day activities. The energy stored in a battery provides electrical energy to run the devices connected to it or light a bulb connected in the circuit. Here, we will restrict potential energy stored in the objects due to their position or configuration.

The dams store water which is released to get work done. The energy stored in such a case is the potential energy due to the water’s position or height. When water is released from the height, it helps to rotate the turbine’s blades are utilized to generate electrical energy. Thus, the potential energy is converted into electrical energy.

Definition: Potential Energy is defined as the energy possessed by the body by virtue of its position or configuration in some field.

Formula of Potential Energy

Potential Energy \((E)\) due to the position or height of the object is its gravitational potential energy that can be calculated by using the formula,
\(E=m g h\)
where
\(m\) is the mass of the object
\(h\) is the height of the object
\(g\) is the acceleration due to gravity.

Potential Energy \((E)\) of a spring is the energy associated with the state of compression or expansion of an elastic spring. This potential energy of the spring can do work that is given by the formula,
\(E=W=\frac{1}{2} k x^{2}\)

where

\(W\) is the work done
\(k\) is the constant of the spring and is called spring constant or force constant
\(x\) is the stretch or compression caused in the spring

Unit of Potential Energy

Potential Energy is measured in terms of the capacity to do work, its unit will be the same as that of work. Thus, the SI unit of is joule \(\left( {\rm{J}} \right)\)

The bigger units are
1. kilojoule \(\left( {{\rm{kJ}}} \right)\) where \(1\,{\rm{kJ}} = 1000\;\,{\rm{J}}\)
2. megajoule \(\left( {{\rm{MJ}}} \right)\) where \(1\,{\rm{MJ}} = {10^6}\,{\rm{J}}\)

The \({\rm{CCG}}\) unit of energy is \(1\,{\rm{erg}} = {10^{ – 7}}\,{\rm{J}}.\)

Solved Examples

Q.1. Find the energy possessed by an object of mass \(10 \,{\rm{kg}}\) when it is at a height of \(5 \,{\rm{m}}\) above the ground. Take \({\rm{g}} = 10 \,{\rm{m}}\,{{\rm{s}}^{ – 2}}.\)
Sol: Given that, The mass of the object is \(m = 10\,{\rm{kg}}\)
The height of the object is \(h = 5\,{\rm{m}}\)
The acceleration due to gravity is \(g = 10\,{\rm{m}}\,{{\rm{s}}^{ – 2}}\)
The potential energy possessed by the object is \(E = mgh = 10 \times 10 \times 5 = 500\;\,{\rm{J}}\)
Thus, the potential energy of the object is \(500\,{\rm{J}}\)

Q.2 A spring with constant \({10^4}\,{\rm{N}}\,{{\rm{m}}^{ – 1}}\) is stretched by \(0.5\,{\rm{cm}}.\) Calculate the work done in stretching it.
Sol: Given that,
The spring constant is \(k = {10 ^4}\,{ \rm{N}}\,{{ \rm{m}}^{ – 1}}\)
The spring is stretched by a distance \(x=0.5 \mathrm{~cm}=5 \times 10^{-3} \mathrm{~m}\)
The work done in stretching the spring is \(W=\frac{1}{2} k x^{2}=\frac{1}{2} \times 10^{4} \times\left(5 \times 10^{-3}\right)^{2}=\frac{1}{2} \times 10^{4} \times 25 \times 10^{-6}=0.125 \mathrm{~J}\)
Thus, the work done on the spring is \(0.125 \mathrm{~J}\).

Types of Potential Energy

Potential Energy is of two types in mechanics which are discussed in detail below:

1. Gravitational potential energy: The gravitational potential energy is the energy possessed by an object due to its position with respect to the ground.

2. Elastic potential energy: Elastic potential energy is the energy associated with the state of compression or expansion of an elastic spring.

Factors

Potential Energy due to an object’s position, which is its gravitational potential energy, is determined by the following factors:

1. Mass of the object: The more the mass of the object, the more will be the potential energy possessed by it and vice versa.
2. The height of the object with respect to the ground: The more the height of the object from the ground, the more will be the potential energy possessed by it and vice versa. Here, the path taken by the object to reach the height does not make any difference to the potential energy gained by the object rather it only depends on the height of the object with respect to the ground. So, the potential energy possessed by an object is path-independent. This finds many applications in real-life scenarios.
3. The acceleration due to gravity at the position of the object: The potential energy of an object is directly proportional to the value of the acceleration due to gravity at that position of the object.

Potential Energy due to the configuration of the object which is its elastic potential energy depends on the following factors:

1. The force constant of the object: The potential energy possessed by the object will be higher with a higher force constant of the object and vice versa.
2. The stretch or compression caused in the object: Within the elastic limits, the more the object is stretched or compressed, the more will be its potential energy and vice versa.

Applications of Potential Energy

Potential energy is the energy possessed by an object due to its position or configuration. So, any object at some position or with a definite configuration has some potential energy. Some of the applications of the potential energy in our day-to-day life are listed below.

1. The potential energy concept also underpins the thrilling roller coaster ride that we enjoy. The ride is allowed to fall from a height where it possesses potential energy, converted into kinetic energy. In the course of the ride, it is converted back into potential energy for further motion of the ride until it wears off completely and comes to a halt at the desired point.

2. While using a bow, the bow’s string is stretched to provide sufficient energy to the arrow aimed at a point. While pulling the string, we are storing the potential energy in it, which can push the arrow to hit the aimed point.

3. In some toys, we need to rotate the key placed in them. We are winding the spring in the toy and storing the potential energy in it. This stored potential energy in the toys is used to make some movement or get some work done.

4. The water flowing in the river possesses energy utilized to run the turbine and produce electricity. For this purpose, dams are constructed to store this water and use the potential energy stored in it as per our requirement. Here, the potential energy stored in the water is converted into electrical energy.

5. Trampolines bounce due to the stored potential energy in the spring attached to them. When we jump on a trampoline, the springs connected at its ends will get stretched thus storing potential energy in it, which is released to achieve the desired bounce.

Conclusion

We hope that this article would have helped you understand the concept of potential energy in detail, along with its formula and units. We are also optimistic that this article would have helped you gain some insights on the types of potential energy, the factors affecting it as well as its applications in real-life situations.

Topics Related to Potential Energy

FAQs about Potential Energy

Let’s look at some of the commonly asked questions about potential energy:

Q.1. What is potential energy in short answer?
Ans: Potential energy is defined as the energy possessed by a body by virtue of its position or state.

Q.2. What is the potential energy formula?
Ans: The gravitational potential energy can be calculated using the formula, \(E=m g h\).

Q.3. How is potential energy different from kinetic energy?
Ans: Potential energy is the energy possessed by an object due to the virtue of its position whereas kinetic energy is the energy possessed by an object due to the virtue of its motion.

Q.4. What is the SI unit of potential energy?
Ans: The SI unit of potential energy is joule.

Q.5. What is the best example of potential energy?
Ans: The water stored in dams possesses potential energy that is used to run the turbine and produce electricity.

We hope you were able to get some assistance in comprehending the concept of potential energy. The various topics covered here should have given you a good understanding of the definition, formula, and unit of potential energy, as well as its applications. If you have any questions about the concept of Potential energy or in general about this page, reach us through the comment box below and we will get back to you as soon as possible.