3. Work, Energy and Power

Work

If a body gets displaced when a force acts on it, work is said to be done. Work is measured by the product of force and displacement of the body along the direction of force.

If a body gets displaced by S when a force F acts on it, then the work $�=�\times �\cos �$ where $�$ = angle between force and displacement

If both force and displacement are in the same direction, then $�=��$

If force and displacement are perpendicular to each other,

$�=0$ as $\cos �=0$.

For example, in case of uniform circular motion work done by the centripetal force is zero.

Work is a scalar quantity and its SI unit is joule.

Energy: Capacity of doing work by a body is called its energy.

Energy is a scalar quantity and its SI unit is joule.

Energy developed in a body due to work done on it is called mechanical energy.

Mechanical energy is of two types

(i) Potential Energy (ii) Kinetic Energy

Potential Energy(PE): The capacity of doing work developed in a body due to its position or configuration is called its potential energy.

Example :(i) energy of stretched or compressed spring (ii) energy of water collected at a height (iii) energy of spring in a watch. PE of body in the gravitational field of earth is mgh. where m = mass, g = acceleration due to gravity, h = height of the body from surface of the earth.

Kinetic Energy: Energy possess by a body due to its motion is called Kinetic Energy of the body. If a body of mass m is moving with speed v, then kinetic energy of the body is $\frac{1}{2}�{�}^2$

Principle of Conservation of Energy: Energy can neither be created nor can be destroyed. Only energy can be transformed from one form to another form. Whenever energy is utilized in one form, equal amount of energy is produced in other form. Hence total energy of the universe always remains the same. This is called the principle of conservation of energy.

Some Equipments used to Transform Energy

S.No.	Equipment	Energy Transformed
1.	Dynamo	Mechanical energy into electrical energy
2.	Candle	Chemical energy into light and heat energy
3.	Microphone	Sound energy into electrical energy
4.	Loud Speaker	Electrical energy into sound energy
5.	Solar Cell	Solar energy into electrical energy
6.	Tube light	Electrical energy into light energy
7.	Electric Bulb	Electrical energy into light and heat energy
8.	Battery	Chemical energy into electrical energy
9.	Electric motor	Electrical energy into mechanical energy
10.	Sitar	Mechanical energy into sound energy

Relation between Momentum and Kinetic Energy:

$��=�$

$��=\frac{{�}^2}{2�}$, where p= momentum = mv

Clearly when momentum is doubled, kinetic energy becomes four times.

Power: Rate of doing work is called power.

If an agent does $�$ work in time $�$, then power of agent = $\frac{�}{�}$.

The unit of power is watt named as a respect to the scientist James Watt.

1 watt (W) = 1 joule per second (joule/sec).

1 kilowatt (kW) = $10^3$ watt (W).

1 megawatt (MW) = $10^6$ watt (W).

Horsepower (HP) is a practical unit of power. $1$ HP = $746$ watt (W).

Units of Work and Energy:

1 watt second (Ws) = $1$ watt (W) × $1$ second = $1$ joule (J).

1 watt hour (Wh) = $3600$ joules (J).

1 kilowatt hour (kWh) = $3.6\times 10^6$ joules (J).

$�$, $��$, $��$, and $��$ are units of power.

$��$, $�ℎ$, and $��ℎ$ are units of work and energy.

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