Law of Conservation of Energy: Meaning, Derivation & Examples

Law of Conservation of Energy

Law of Conservation of Energy: Energy is present everywhere in different forms. We use energy to do our daily work, even when we sit some amount of energy is required. Energy is the universal term that we use in our daily lives. In Physics, energy is stated as the Capacity to do work. This term “Energy” was first propounded by British scientist Thomas Young, in 1802. From tiny micro substances to huge objects energy of some amount is required. Sun is the major source of energy from where we derive energy. There are various forms of energy, such as solar energy, chemical energy, wind energy, thermal energy, chemical energy, electrical energy, etc. It also becomes essential to know how the energy is governed. So in this article, we will discuss the conservation of energy and its principle.  

Principle of Law of Conservation of energy

The principle of the Law of conservation of energy says that “Energy can neither be created nor destroyed. However, it may be converted or transformed from one form to another”. For instance, Solar energy from the sun is transformed into electrical energy by the use of solar panels, Chemical energy is transformed into kinetic energy when a stick of dynamite explodes. So if we take the whole of energy into account then we can say that the energy remains constant in an isolated system. Hence, we can say that energy remains conserved. 

The amount of energy in any system is determined by the following equation below:

Ut = Ui + W + Q

ΔU = W+Q

Where, 

ΔU indicates the change in the internal energy of the system

W indicates the work done in the system

Q indicates the heat added or removed from the system 

Derivation of Law of Conservation of Energy

Let us consider that no potential energy is present at the earth’s surface. For example, Consider an apple falling to the ground. Assume point A where a tree of height ‘H’ is present above the ground. The apple’s potential energy is highest as its velocity is zero.

E = mgH ……………….(1)

The apple’s potential energy starts to decrease, and its kinetic energy rises as it starts to fall. Point B is the point which is close to the bottom of the tree, by the influence of gravity the apples fall quickly. At a height X from the ground, thereby reaching the maximum speed. It approaches point B. Now it will possess both potential and kinetic energy at the same time.

E = K.E + P.E

P.E = mg X  …………………….(2)

As per the third equation of motion,

V2 = 2g (H – X)

½ mv2 = ½ m x 2g (H – X)

K.E = ½ m x 2g (H – X)

K.E = mg (H – X) ……………………(3)

Comparing equations 1, 2 and 3

E = mg (H – X) + mgX

So, E = mgH

At this point kinetic and potential energy becomes equal. 

K.E = P.E

P.E = K.E = E/2 ………………..(4)

The body (that is, apple) is X feet above the ground, Hence

P.E = mgX …………………..(5)

Comparing equations (4) and (5)

mgX = mgH/2

X = H/2

Therefore, the new height is H/2

Application of Law of Conservation of Energy

The application of the law of conservation of Energy is-

• In Torch
• In Hydroelectric Power Plants
• In a Loudspeaker
• In a microphone
• In a Generator