In physics, the phrase conservation denotes something that does not change. It indicates that a variable always remains constant in an equation over time. Its value will remain the same before and after an event. In physics, we study numerous conserved quantities. They are remarkably beneficial for making predictions in situations that would otherwise be extremely complex. There are three fundamental quantities, i.e. momentum, energy, and angular momentum, which remain conserved in the machines. In the below notes, we will learn about the definition, principle, and examples of the Conservation Law of Energy.

Law of conservation of energy:

The conservation Law of Energy explains that the energy could neither be created nor be destroyed, and it can only transform from one form to another. It denotes that the energy will remain uniform throughout the system unless some additional energy is added from outside.

To determine the amount of energy in the system, we will use the following equation:-

U_T = U_i + W + Q

Here,

• U_T denotes the complete internal energy of the system
• U_i denotes the initial inner energy of the system
• W denotes total work done by the system
• Q denotes the net heat transfer.

We can also find a change in the system’s internal energy using the first law of thermodynamics.

ΔU = W+Q

Examples of law of conservation of energy:

• The cue ball is thrown at a standing eight-ball while playing pool. The cue ball has a good amount of energy. When it collides with the eight-ball, its energy is transferred to the eight-ball, which causes it to move. The cue ball’s energy gets passed to the eight-ball and thus, it loses energy and slows down.
• When a ball hits the window, the glass gets shattered into pieces. This happens because the ball’s energy is transferred to the window glass.
• Water can generate electricity. Potential energy gets converted into kinetic energy as it falls from the sky. This energy is subsequently used to turn a generator’s turbine, producing electricity. This way, the potential energy of the water in the dam could be transformed into kinetic energy.
• An animal resting on the top branch of a tree possesses potential energy. If that animal falls to the ground for any reason, the potential energy gets transformed into kinetic energy.
• When an electric bulb is switched on, electrical energy is converted into light energy, resulting in a glow.
• Sam needed assistance pushing the large furniture. His brother assists him, and the two push the sofa across the room together. By doing so, the boys transmitted energy to the furniture, which led to it sliding over the wood floor.

Derivation of the law of conservation of energy:

Let us suppose that the potential energy (P.E) of the ground’s surface is zero.

Let us take an example of an object freely falling from a tree.

Consider point A, which is at the height “H” from the earth to the tree. The object’s velocity is zero, and the potential energy is highest at that point.

E = mgH ——— (a)

When an object is falling, its P.E is reducing, and the kinetic energy (K.E) is increasing.

Suppose, at point B, which is around the bottom of the tree, the object is freely falling under gravity and the height of the object is X from the earth. The object has motion as it reaches point B. At a certain point, the object has both potential and kinetic energy.

Energy (E) = Kinetic Energy(K.E) + Potential energy(P.E)

P.E = mgX ——— (b)

Third law of motion states that,

v² =2 g(H–X)

½ mv²=½ m.2 g(H–X)

K.E = mg(H–X)

K.E=mg(H-X)——– (c)

Using (a), (b) and (c)

E = mg(H – X) + mgX

After simplifying the equation, we will get,

E = mgH

Conclusion:

In the above text, we learned about the Law of energy conservation and its derivatives. The law of energy conservation states that energy can neither be created nor be destroyed; it can only transform from one configuration/form to another. We encounter numerous daily life examples of the Conservation Law of Energy like, in the case of the glowing bulb, the electrical energy changes into light energy. In the case of a turbine, the mechanical energy is converted into electrical energy. Similarly, when an athlete kicks a football, the kinetic energy of the athlete transfers to the ball, and the football displaces from its place.