# Law of Conservation of Energy

Energy is required for the evolution of life forms on earth. In Physics, it is defined as the capacity to do work. We know that energy exists in different forms in nature. You have learned about various forms of energy – heat, electrical, chemical, nuclear, etc. In this article, we will learn about the laws and principles which governs energy known as the law of conservation of energy.

## What is the Law of Conservation of Energy?

The law of conservation of energy states that energy can neither be created nor be destroyed. It may be transferred from one of its forms to the other. If you take all forms of energy into account, the total energy of an isolated system always remains constant.

So in an isolated system such as the universe, if there is a loss of energy in some part of it, there must be a gain of an equal amount of energy in some other part of the universe. Although this principle cannot be proved, there is no known example of a violation of the law of conservation of energy.

### Proof for Law of Conservation of Energy:

Considering the potential energy at the surface of the earth to be zero. Let us see an example of a fruit falling from a tree.

Consider a point A, which is at some height ‘H’ from the ground on the tree, the velocity of the fruit is zero hence potential energy is maximum there.

E = mgH ———- (1)

When the fruit is falling, its potential energy is decreasing and kinetic energy is increasing.

At point B, which is near the bottom of the tree, the fruit is falling freely under gravity and is at a height X from the ground, and it has a speed as it reaches point B. So, at this point it will have both kinetic and potential energy.

E = K.E + P.E

P.E = mgX ——— (2)

According to third equation of motion,

$v^{2 }= 2g(H – X)\\ \\ \Rightarrow \frac{1}{2}mv^{2}=\frac{1}{2}m.2g(H – X)\\ \\ \Rightarrow K.E=\frac{1}{2}m.2g(H – X) \\ \Rightarrow K.E=mg(H – X)$

K.E=mg(H-X)——– (3)

Using (1), (2) and (3)

E = mg(H – X) + mgX

E = mg(H – X + X)

E = mgH

Similarly, if we see the energy at point C which is at the bottom of the tree, it will come out to be mgH. We can see as the fruit is falling to the bottom and here, potential energy is getting converted into kinetic energy. So there must be a point where kinetic energy becomes equal to potential energy. Suppose we need to find that height ‘x’ from the ground. We know that at that point,

K.E = P.E

=> P.E = K.E = $\frac {E}{2}$ ——– (4)

E2 is the new energy

Where, E = mgH2

H2 is the new height.

As the body is at height X from the ground,

P.E = mgX ——— (5)

Using (4) and (5) we get,

$mgX=\frac{mgH}{2}\\ \\ \Rightarrow X=\frac{H}{2}$

H2 is referred to the new height

### Energy Conservation:

Energy conservation is not about limiting the use of resources which will finally run out all together. The ideal way of conservation would be reducing demand on a limited supply and enabling that supply to begin to rebuild itself. Many times the best way of doing this is to replace the energy used with an alternate.

### Examples:

In physics, most of the inventions rely on the fact that energy is conserved when it is transferred from one form to another. A number of electrical and mechanical devices operate solely on the law of conservation of energy. We will discuss a few examples here.

• In a torch, the chemical energy of the batteries is converted into electrical energy, which is converted into light and heat energy.
• In hydroelectric power plants, waterfalls on the turbines from a height. This, in turn, rotates the turbines and generates electricity. Hence, the potential energy of water is converted into the kinetic energy of the turbine, which is further converted into electrical energy.
• In a loudspeaker, electrical energy is converted into sound energy.
• In a microphone, sound energy is converted into electrical energy.
• In a generator, mechanical energy is converted into electrical energy.
• When fuels are burnt, chemical energy is converted into heat and light energy.
• Chemical energy from food is converted to thermal energy when it is broken down in the body and is used to keep it warm.

Stay tuned with Byju’s to learn more about the law of conservation of energy, heat energy and much more.

#### Practise This Question

A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity v0. The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of v0 if the particle passes through the point of suspension.