# Potential Energy

Potential energy is the energy of an object that is stored in it due to its position, state or arrangement. It is one of the two forms of energy, in addition to kinetic energy. It has the potential to do work as when the position, state or arrangement of an object is changed, the energy stored in it is released. For example, when a spring is compressed it stores potential energy due to a change in its position and when we release the spring, the stored potential energy is released in the form of kinetic energy. The energy cannot be created, however, it can be converted from one form into another form. The term potential energy was used for the first time in the 19th century by William Rankine, a Scottish engineer and physicist.

## Types of Potential Energy

The two main types of potential energy as described below:

### 1. Gravitational Potential Energy

It is the stored energy of an object that is held in a vertical position or its position is changed when it is present in a gravitational field. It is the energy stored in an object due to the gravitational attraction of the Earth to the object.

We can say that it is the stored energy due to gravitational force or pull acting on an object. For example, if we take two balls one is placed on the table and another is held above the table, the ball which is higher will have more gravitational potential energy than the ball placed on the table. For example, the gravitational potential energy of the huge ball of a demolition machine depends on two factors: its mass and the height to which it is raised. Both these factors are directly proportional to the gravitational potential energy. The higher an object is from the ground, the greater will be the energy. Likewise, the greater the mass of an object, the greater the energy. So, if more impact is required, the demolition ball will be raised to a greater height or a heavier ball will be used.

### Gravitational Potential Energy Formula

Potential energy is also the ability to do work, so any object has the potential to do work owing to its location in the gravitational field.

The formula for gravitational potential energy is given below:

GPE = mgh

m = mass in kilograms

g = acceleration due to gravity in m/s2 (metres / sec2): 9.8 m/s2

h = height in meters above the ground

### Some Facts

• If the mass is more gravitational potential energy will be more. For example, a 50 kg mass would store twice as much gravitational potential energy as a 25 kg mass, when both are raised to the same height.
• Likewise, the higher an object is from the ground, the greater will be the energy stored by it, an object raised to a height of 10 m will have twice the energy of the object of the same mass raised to a height of 5 m.
• Further, the more is the gravitational pull, the more is energy. For example, an object 10 m above the Earth's surface has more gravitational potential energy than the same object 10 m above the moon's surface as gravity on Earth is more than on the moon.

In hydropower plants where electricity production involves the use of water, the gravitation potential energy of water is used to turn the turbines. The water stored behind a hydroelectric dam is at a higher level than the water of the river, so when it is made to fall, its potential energy changes into kinetic energy, which turns the turbines to produce electricity.

### Solved Examples

1. Find the gravitational potential energy stored by a ball of mass 5 kg, when it is raised to a height of 10m above the ground. (g =9.8 m/s2).

Solution:

We know, GPE = mgh

Here, mass (m) of the object = 5 kg

Displacement (height) = 10 m

Acceleration due to gravity (g) = 9.8 m/s2

So, on putting the values in the given formula, we get:

GPE = m x g x h

= 5 kg x 9.8 m/s-2 x 10 m = 490 J

2. A football weighing 2 kg drops from a building to the ground 40 meters below. Find its gravitational potential energy when it starts falling to the ground

Solution:

Mass of football 'm' = 2 kg

Height of football 'h' = 40 meters

g = 9.8 m/s2

As we know, GPE = mgh

On putting the given values in the above formula, we have;

GPE= 2 x 9.8 x 40

= 784 J

### 2. Elastic Potential Energy

It is the potential energy stored in objects when they are compressed or stretched. We can say that when an object like a rubber band, spring, etc., is compressed or stretched, elastic kinetic energy is stored in it. There are lots of products that are designed to store elastic potential energy such as stretched bow, the bent diver's board just before he dives in, the coil spring of a wind-up clock, and a twister metal coil that powers a toy car, etc. However, every object that stores elastic energy has an elastic limit, if they are compressed, stretched or deformed beyond their elastic limit, they will not return to their original shape.

### Elastic Energy Formula:

It can be calculated by using the following formula:

U = ½ kx2

Where,

U denotes the elastic potential energy

K: spring force constant

x: the length of string stretch in metres

### Potential Energy Units

Like other types of energy and work, the SI unit of potential energy is 'Joule' which is denoted by the English letter 'J' and 1 J = N m = 1 kg m2/s2

### Potential Energy Examples / Uses in Daily Life

1. Pendulum: A pendulum is a structure wherein weight is suspended from a pivot. The pendulum swings from one end to another end due to potential energy stored in it. For example, when you held it at one end, it has the maximum potential energy due to its position (height above the ground). As you release the ball, the ball starts moving towards another end as its potential energy is converted into kinetic energy. At the other end, it again stores potential energy due to its raised position and again as it moves back and this energy again changes into kinetic energy. This process keeps going on until the pendulum is stopped. The pendulum in pendulum clocks works in a similar way and enables the clock to give the correct time.
2. Spring: Spring is used in lots of objects like toys, clocks, etc. The spring when compressed or stretched stores elastic potential energy. This energy aids the functions of various products like toys, clocks, gas lighters, and various other small instruments.
3. Bow and Arrow: The bow and arrow also make use of potential energy that allows the arrow to move fast. When the archer pulls the bowstring, elastic potential energy is stored in the flexible limbs of the bow. The more the bow is pulled, the greater the energy stored and the arrow moves more quickly. Here, the elastic potential energy stored by the bow is transferred into the kinetic energy of the arrow.
4. Stored water in Dams: The water is held in dams to fulfil various purposes like generation of electricity, irrigation, providing water for drinking purposes and industrial uses. The water held at the dam stores potential energy as it is at a higher level than the level of the river. When the gates of the dam are opened, the water at a higher level starts flowing down, and its potential energy is converted into kinetic energy which can be used to turn turbines to generate electricity. All hydropower plants use water in this manner to produce electricity. This moving water is also used for irrigation of nearby crop fields.
5. Rollercoaster: The wagon of a rollercoaster make use of its potential energy to move at a high speed. The wagon when at the top position has maximum potential energy due to its height as it starts moving down its height from the ground start decreasing which means its potential energy starts converting into kinetic energy.
6. Wrecking Ball: The wrecking ball of crane stores potential energy which is used to perform demolition work. The ball is raised to a certain height so that it gains potential energy and this energy is converted into kinetic energy to crush the buildings or other hard structures.
7. Swimmer: The diving board, which is used by swimmers to dive into the water, also stores elastic potential energy. The diving board when pushed down by swimmers stores elastic potential energy. When the board comes to its original position the stored energy is converted into kinetic energy which is used by the swimmer to get the extra push to perform the diving. The more kinetic energy, the easier will be the dive.
8. Snow-capped mountains: The snow on the snow-capped mountains also possesses potential energy due to its height from the ground. Sometimes, during the snowfall, when the weight of the snow at the top increases it tends to fall or results in a snow avalanche, and when it happens the stored energy of the snow is converted into kinetic energy and the snow starts moving down the mountains quickly.
9. Catapult: The catapult also works by using the potential energy of the stretched band. When we pull the band, it stores the elastic potential energy, which is converted into kinetic energy when it returns to its loose shape, this kinetic energy throws away the object placed in the stretched band.
10. Fruits: The ripened fruits that fall on the ground also possess potential energy due to their position or height from the ground. When they get separated from the branch their stored energy changes into kinetic energy, which causes downward movement towards the ground. Similarly, other parts also tend to fall on the ground like leaves, branches, flowers, etc.

## Difference between Kinetic Energy and Potential Energy

Kinetic Energy Potential Energy
It is the energy possessed by a body due to its motion, such as a moving ball. It is the energy possessed by a body or stored in it due to its position or change in its state, arrangement, etc.
It is directly proportional to the mass and speed or velocity of the object. It is directly proportional to the mass and height of an object to which it is raised from the ground. Further, the more change in arrangement, the more is this energy such as compressed spring.
It can be transferred from one object to another object, for example, when a moving ball collides with another ball, the anther ball also starts moving. It cannot be transferred from one object to another object.
It is influenced by the environment and is relative to the environment. It is not affected by environmental factors.
Its determining factors are velocity and mass. Its determining factors are mass, and height or distance.
The object is always in motion. The object is not moving, it remains at rest.
It can be converted into potential energy, for example, when you throw a ball upwards its kinetic energy starts decreasing and it gains maximum potential energy after reaching maximum height. It can be converted into kinetic energy, for example, a ball at rest on the table when falls to the ground, its potential energy changes into kinetic energy.
Its formula is ½ mv2 Its formula is m.g.h
The term kinetic energy is given by William Thomson. The term potential energy is given by William Rankine.
Examples include moving vehicles, moving balls, and all objects that are in motion. Examples include flower pot on the table, water stored at a dam, stretched or compressed spring, etc.

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