Potential Energy

The term potential energy was introduced in the 19th-century by the Scottish Engineer and Physicist William Rankine, and this concept has a relationship with Greek philosopher Aristotle's concept of potentiality. Potential energy definition is given as the energy produced when there is an alteration in the form or state of the object. The energy which is stored by an object by the virtue of its position relative to various parts of the system is known as potential energy. 

When a spring is compressed or stretched, it is displaced from its equilibrium position. So, some amount of energy is gained which is stored in the form of stress and can be felt with our hands when we stretch it. 

In terms of Physics, we define potential energy as the energy protected/stored by an object due to its relative position to other objects, which it stresses/saves within itself, its electric charge, or other factors like energy. 

Potential Energy Examples

Below are some potential energy examples which illustrate the real-life applications of potential energy. Here the relationship between the potential energy and kinetic energy is also explained very well:

• Water at the top of the waterfall stores energy (which is the potential energy) and that energy helps rotate the turbine and convert its kinetic energy into electricity. 

• A rubber band is an application of Newton’s first law of motion or the law of inertia. Now, as you apply force on it, it stretches and enlarges by length. It is because the molecules inside the rubber band had initially stored energy, and when you apply the force, all molecules are set into motion because they gain kinetic energy. Eventually, they set apart and the band stretches. 

• You take a bow and an arrow, and initially, they both have stored energy. Now, as you stretch the bow, and leave it, the arrow leaves the bow and reaches far away according to the magnitude of force applied by us. So, this stored energy or simply the potential energy gets transformed into kinetic energy by the force of our fingers.

Other Potential Energy Examples

• A child sitting at the top of the swing has stored potential energy, which transforms into kinetic energy when he starts sliding down.

• A truck standing at the tip of the mountain has potential energy unless it slides along with the mountain to reach the ground. Now, as the driver starts the truck, the truck utilizes all its stored potential energy to make drag down the ground. 

Potential Energy- Types

Potential energy is classified into different types as follows-

1. Gravitational Potential Energy

2. Elastic Potential Energy

3. Electrostatic Potential Energy

Gravitational Potential Energy

The energy possessed by an object when it is raised to a certain height against the gravity is known as the gravitational potential energy of that object. The gravitational energy is independent of the distance traveled by the object. It depends on the difference between the initial height of the object and its final height, which is the displacement of the object. Therefore, the path taken by the object along which it has reached the height is not taken into consideration. The gravitational potential energy is given by-

W=mgh

Where,

w= work done

m= mass

g= acceleration due to  gravity 

h= height 

Elastic Potential Energy

The energy which is stored in an object which possesses the capability to compress or stretch is known as the elastic potential energy. It is used in trampolines, rubber bands, and bungee cords. The elastic potential energy is greater if the object is more stretched. 

The elastic potential energy of an object in mathematical terms is given by-

\[U = \frac{1}{2} k x^2 \]

Where the elastic potential energy is represented as U, spring force constant is represented as k, and stretch length of the string is represented by x.

The following objects are specifically designed to store elastic potential energy:

• A twisted rubber band that powers a toy plane/bungee cord.

• A stretchable bow.

• A bent diver’s board just before a diver dives in a river.

• Coil spring of a wind-up clock/generator/motor.

Electrostatic Potential Energy 

Electrostatic potential energy is the energy required to move a charge from one point to another through a potential difference. Mathematically, we can say, 

U=Vq,

Where U is the electrostatic potential energy, V is the potential difference and q is the charge.

Potential Energy Units

The potential energy is denoted by U, V, or PE. The SI unit of the potential energy is Joule which is symbolized by an English letter ‘J’. The dimension of potential energy is M1L2T-2.

Relation Between Kinetic Energy and Potential Energy

In the last example, we discussed the scenario of a truck going up the tip of the mountain and then going down the mountain to reach the ground.

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So, initially, it had stored energy that is the potential energy, and then it started moving up the mountain, which is the kinetic energy. So, the total energy utilized by it is given as:

KEi + PEi 

Now, as it is at the tip, and it again has a final stored or potential energy as it starts moving down the mountain, this stored energy transforms to kinetic energy. Now, the total energy used in the final case is as follows:

KEf + PEf

So, whatever total energy was used initially equals the energy used finally. So, the relationship between kinetic and potential energy is:

KEi  + PEi = KEf + PEf