## Law of Conservation of Energy?

According to the rules of energy conservation, energy can neither be generated nor destroyed. But energy can be converted from one form to another. Therefore, the magnitude of the total energy of the world remains constant.

In other words, we can say that the sum total of all the energies of a deferred body is fixed. Energy can be converted from one form to another. When energy is converted from one form to another, there is some loss of energy. This is called loss of energy. Most of the energy lost in transformation is converted into heat and some part into sound and light.

### Examples of Transformation of Energy

The process of converting energy from one form to another is called conversion of energy.

- The burning of electric bulbs in this process transforms the electrical energy into thermal energy and light energy.
- In the use of electrical appliances in the houses, the electrical energy in the electric fans, fridges, coolers, AC, etc. is converted into kinetic energy and thermal energy.
- Generating electricity from dynamo In this process, kinetic energy is converted into electrical energy.
- Heat Engine It transforms thermal energy into mechanical energy.
- The burning of lanterns converts chemical energy into thermal energy and optical energy.
- The loud sound produced by the loudspeaker transforms the electrical energy into sound energy.

## Conservation of Mechanical Energy

The mechanical energy of any body i.e. the sum of its kinetic and potential energy is always constant. In many bodies, kinetic energy, potential energy, and potential energy are converted into kinetic energy, but their sum remains fixed at every moment. This is the law of conservation of mechanical energy.

Conservation of mechanical energy can be understood by the following examples.

### 1. Conservation of Energy in Falling Body under Gravity

Suppose an object of mass m starts to fall from a point A located at h height above the earth plane.

The kinetic energy of the object at point A, K = 0 (The object is constant.)

The position energy of the object at point A, U = mgh (The object is at h height above the earth plane.)

The total energy of the object at point A,

E_{A} = Kinetic Energy + Potential Energy

E_{A} = 0 + mgh

E_{A} = mgh ...1

Suppose the object has traveled x distance to point B. If the velocity at point B of the object is v, then from the third equation of motion

v^{2} = u^{2} + 2gx

(Since the object starts falling from a steady state, u = 0)

v^{2} = 0 + 2gx

v^{2} = 2gx

The kinetic energy of the object at point B,

K_{B} = ½ mv^{2}

K_{B} = ½ m×2gx

K_{B} = mgx

The potential energy of the object at point B,

U_{B} = mg (h-x)

(Now the height of the object from the earth plane is h-x.)

Total energy at point B,

E_{B} = K_{B} + U_{B}

E_{B} = mgx + mg(h-x)

E_{B} = mgx + mgh – mgx

E_{B} = mgh ...2

When the object is at point C near the surface of the falling earth. If the velocity at point C is v_{c}, then

v_{c}^{2} = u^{2} + 2gh

v_{c}^{2} = 0 + 2gh

v_{c}^{2} = 2gh

Kinetic Energy, K_{c} = ½ mv_{c}^{2}

K_{c} = ½ m × 2gh

K_{c} = mgh

Potential energy, U = 0

Total energy at point C,

E_{c} = K_{c} + U_{c}

E_{c} = mgh + 0

E_{c} = mgh ...3

From equations 1, 2, and 3,

E_{A} = E_{B} = E_{C}

Therefore, the total energy is conserved at each point.

### 2. Conservation of Energy in Simple Pendulum

When the pendulum is slightly removed from its stop position O (called the mean position), it oscillates between positions A and B at maximum displacement around position O.

When the pendulum is brought to the maximum displacement position A, its potential energy increases. When it is released, its kinetic energy increases, and its kinetic energy is maximized at the mean position O. Then as the pendulum moves from the mean position to another maximum displacement point B, the pendulum's kinetic energy is converted to the potential energy. The total energy at point B is potential energy.

The pendulum returns to the mean position O again. In this way, the pendulum oscillates. The position between points A and B is potential and partly kinetic energy. It can be seen by calculation that in each case the total mechanical energy of the pendulum remains the same i.e. the sum of both pendulum energies remains fixed. Due to the suspension and friction resistance of suspended point S, the heat energy stored in the pendulum is converted to other forms of heat energy and the pendulum finally breaks into rest.

## Mass Energy Equivalence

Albert Einstein based on his researches in 1905 that mass and energy are equal or equal to each other, which is represented by the following equation

E = mc^{2} ...1

Where, m = mass

c = Speed of light in vacuum = 3×10^{8} m/s

The above equation is called the equivalence relation of mass energy.

If the mass of an object is 1 kg, then from equation 1

Energy (E) = 1×c^{2} = (3×10^{8})^{2}^{}

E = 9×10^{16} Jule

Therefore, we can say that energy can also be converted into mass. E Joule energy can be converted (E/c^{2}) to become a mass of kilograms.

Hence energy and mass are interchangeable. Therefore, in this view, the laws of conservation of energy and mass become the same and by combining these two, a general rule is obtained.

In the entire universe, the value of [(total mass × c^{2}) = total energy] is always fixed. Nuclear fission is called mass loss (∆m) mass loss in the fusion process. Therefore

∆E = ∆m × c^{2}

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