# Energy

## ENERGY

Energy is the ability to perform work. Energy can neither be created nor destroyed, and it can only be transformed from one form to another. The unit of Energy is the same as of Work, i.e. Joules. Energy is found in many things, and thus there are different types of energy.

All forms of energy are either kinetic or potential. The energy in motion is known as Kinetic Energy, whereas Potential Energy is the energy stored in an object and is measured by the amount of work done.

### Types of Energy

Some other types of energy are given below:

• Mechanical energy
• Mechanical wave energy
• Chemical energy
• Electric energy
• Magnetic energy
• Nuclear energy
• Ionization energy
• Elastic energy
• Gravitational energy
• Thermal energy
• Heat Energy

### Unit of Energy

The SI unit of energy is Joules (J), named in honour of James Prescott Joule.

Although there are many forms of energy, it is broadly categorized into:

1.     Kinetic Energy

2.     Potential Energy

## KINETIC ENERGY

Kinetic energy is the energy associated with the object’s motion. Objects in motion are capable of causing a change or are capable of doing work.

To accelerate an object, we have to apply force. To apply force, we need to do work. When work is done on an object, energy is transferred, and the object moves with a new constant speed. We call the energy that is transferred kinetic energy, and it depends on the mass and speed achieved.

·        Kinetic energy of an object is the measure of the work an object can do by virtue of its motion.

·        Kinetic energy is a scalar quantity, and it is entirely described by magnitude alone.

### Units of Kinetic Energy

• The SI unit of kinetic energy is Joule which is equal to 1 kg.m2.s-2.
• The CGS unit of kinetic energy is erg.

### Kinetic Energy Examples

• A truck travelling down the road has more kinetic energy than a car travelling at the same speed because the truck’s mass is much more than the cars.
• A river flowing at a certain speed comprises kinetic energy as water has a certain velocity and mass.
• The kinetic energy of an asteroid falling towards earth is very large.
• The kinetic energy of the aeroplane is more during the flight due to its large mass and speedy velocity.

### Kinetic Energy Transformation

Kinetic energy is transferred between objects and can be transformed into other forms of energy. Yo-Yo is a great example to describe the transformation of kinetic energy. While beginning to play with it, one starts by letting it rest in hand; at this point, all the energy is stored in the ball in the form of potential energy. Once the person drops the yo-yo, the stored energy is transformed into kinetic energy, the energy of movement. Once the ball reaches the bottom of the yo-yo, all the energy is converted to kinetic energy.

## The Formula for Kinetic Energy

The kinetic energy equation is given as:

KE = ½ mv2

Where KE is the kinetic energy, m is the body’s mass, and v is the body’s velocity.

### Deriving Kinetic Energy Equation

Kinetic energy equation can be obtained by the basic process of computing the work (W) that is done by a force (F). If the body of mass m was pushed for a distance of d on a surface by applying a force that’s parallel to it, then the work done would be:

W = F. d = m. a. d

The acceleration in this equation can be substituted by the initial (vi) and final (vf) velocity and the distance. This we get from the kinematic equations of motion.

Simplifying the equation further, we get

KE = ½ mv2

Alternately, one can say that the total work that is done on a system is equivalent to the change in kinetic energy. This statement is equated as follows:

Wnet $∆K$

This equation is known as the work-energy theorem and has large applications even if the forces applied vary in magnitude and direction.

### Is Kinetic Energy a Vector or a Scalar Quantity?

In the expression, we see that velocity (v) is squared. We know that the square of a vector quantity is a scalar, and we also know that mass is a scalar quantity. Therefore, kinetic energy is a scalar quantity.

## Types of Kinetic Energy

There are five types of kinetic energy: radiant, thermal, sound, electrical and mechanical. Let us look at some of the kinetic energy examples and learn more about the different types of kinetic energy.

Radiant energy is a type of kinetic energy that is always in motion travelling through medium or space. Examples of radiant energy are:

• Ultraviolet light
• Gamma rays

### Thermal energy

Thermal energy, known as heat energy, is generated due to the motion of atoms when they collide with each other. Examples of thermal energy are:

• Hot springs
• Heated swimming pools

### Sound energy

The vibration of an object produces sound energy. Sound energy travels through the medium but cannot travel in a vacuum as there are no particles to act as a medium. Examples of sound energy are:

• Tuning fork
• Beating drums

### Electrical energy

Electrical energy is obtained from the free electrons that are of positive and negative charge. Examples of electrical energy are:

• Lightning
• Batteries when in use

### Mechanical energy

The sum of kinetic energy and potential energy is known as mechanical energy, which can neither be created nor be destroyed but converted from one form to another. Examples of mechanical energy are:

• Orbiting of satellites around the earth
• A moving car

## POTENTIAL ENERGY

Potential energy is the energy stored in an object or system of objects. Potential energy can transform into a more obvious form of kinetic energy.

In the case of a bow and an arrow, when the bow is drawn, it stores some amount of energy, which is responsible for the kinetic energy it gains when released.

Similarly, in the case of a spring, when it is displaced from its equilibrium position, it gains some amount of energy which we observe in the form of stress we feel in our hands upon stretching it.

## Potential Energy Formula

The formula for potential energy depends on the force acting on the two objects. For the gravitational force, the formula is:

 W = m×g×h = mgh

Where,

• m is the mass in kilograms
• g is the acceleration due to gravity
• h is the height in meters

## Potential Energy Unit

Gravitational potential energy has the same units as kinetic energy: kg m2 / s2
Note: All energy has the same units – kg m2 / s2, and is measured using the unit Joule (J).

## Types of Potential Energy

Potential energy is one of the two main forms of energy. There are two main types of potential energy, and they are:

• Gravitational Potential Energy
• Elastic Potential Energy

### GRAVITATIONAL POTENTIAL ENERGY

The gravitational potential energy of an object is defined as the energy possessed by an object that rose to a certain height against gravity. We shall formulate gravitational energy with the following example.

• Consider an object of mass = m.
• Placed at a height h from the ground, as shown in the figure.

As we know, the force required to raise the object equals m×g, that is, the object’s weight.

As the object is raised against the force of gravity, some amount of work (W) is done on it.

Work done on the object = force × displacement.

So,

 W = m×g×h = mgh

Above is the potential energy formula.

As per the law of conservation of energy, since the work done on the object is equal to m×g×h, the energy gained by the object = m×g×h, which in this case is the potential energy E.

E of an object raised to a height h above the ground = m×g×h

It is important to note that the gravitational energy does not depend upon the distance travelIed by the object, but the displacement, i.e., the difference between the initial and the final height of the object. Hence, the path along which the object has reached the height is not considered. In the example shown above, the gravitational potential energy for both blocks A and B will be the same.

### ELASTIC POTENTIAL ENERGY

Elastic potential energy is stored in objects that can be compressed or stretched, such as rubber bands, trampolines and bungee cords. The more an object can stretch, the more elastic its potential energy is. Many objects are specifically designed to store elastic potential energy, such as the following:

• A twisted rubber band that powers a toy plane
• An archer’s stretched bow
• A bent diver’s board just before a diver dives in
• The coil spring of a wind-up clock

An object that stores elastic potential energy will typically have a high elastic limit. However, all elastic objects have a threshold to the load they can sustain. When deformed beyond the elastic limit, the object will no longer return to its original shape.

Elastic potential energy can be calculated using the following formula:

U = ½ kx2

Where,

• U is the elastic potential energy
• k is the spring force constant
• x is the string stretch length in m

## POTENTIAL ENERGY EXAMPLES

Stones sitting on an edge of a cliff possess potential energy. The potential energy will be converted if the stones fall to kinetic energy.

Tree branches high up the tree have potential energy because they can fall to the ground.

The food that we eat has chemical potential energy. Our body digests this potential energy and provides the necessary energy for bodily functions.

The chemical potential energy of a firecracker is released when the fuse of the firecracker is lit.

WORK-ENERGY THEOREM

According to this theorem, the net work done on a body is equal to the change in kinetic energy of the body. This is known as Work-Energy Theorem. It can be represented as:

Kf – K= W

Where Kf = Final kinetic energy

K= Initial kinetic energy

W = net work done

So the above equation follows the law of conservation of energy, according to which we can only transfer energy from one form to another. Also, here the work done is the work done by all forces acting on the body like gravity, friction, external force etc. For example, consider the following figure.

According to the Work energy theorem,

Work done by all the forces = Change in Kinetic Energy

Wg + WN + Wf  =Kf – Ki

Where Wg = work done by gravity

WN = work done by a normal force

Wf = work done by friction

Kf = final kinetic energy

Ki = initial kinetic energy

### Work done by a constant force

A constant force will produce constant acceleration. Let the acceleration be ‘a’.

From the equation of motion,

v2 = u2 + 2as

2as = v2 – u2

Multiplying both sides with mass ‘m’

Comparing the above equation, we get,

Work done by force (F) = F.s

Where ‘s’ is the displacement of the body.

### Work done by Non-Uniform Force

Now the equation,

W = F.ds

This is only valid when force remains constant throughout the displacement. Suppose we have a force represented below,

For these kinds of forces, we can assume that force remains constant for a very small displacement and then integrate that from the initial position to the final position.

This is work done by a variable force. A graphical approach to this would be finding the area between F(x) and x from xi  to xf.

The shaded portion represents the work done by force F(x).

## Difference between Kinetic Energy and Potential Energy

 S .no Kinetic Energy Potential Energy 1 Kinetic energy is the kind of energy present in a body due to the property of its motion Potential Energy is the type of energy present in a body due to the property of its state 2 It can be easily transferred from one body to another It is not transferable 3 The determining factors for kinetic energy are Speed or velocity and mass Here, the determining factors are Height/ distance and mass 4 Flowing water is one of the examples of kinetic energy Water present at the top of a hill is an example of potential energy 5 It is relative with respect to nature It is non-relative with respect to nature