__What is called Energy?__

*Energy of a body is defined as the capacity or ability of doing work. Kinetic energy is most important in among all forms of energies.*

- Energy is measured by the amount of
*work*that a body can perform. - Energy and work are mutually interchangeable.
- Hence, all physical quantities like units and dimensions of energy are same as that of work.

There are various forms of energy, such as –

- Kinetic energy. Example – kinetic energy possessed by a moving car, kinetic energy of moving water body etc.
- Potential energy. Example – energy possessed by static water head in dams etc.
- Strain energy. Example – energy possessed by a compressed spring or elongated rubber band etc.
- Light energy. Example – energy of sun light, photoelectric effect etc.
- Electrical energy. Example – electric heater, motor etc.
- Magnetic energy. Example – electromagnets.
- Sound energy. Example – loudspeaker, transducer etc.
- Wind energy. Example – Wind mill etc.
- Pressure energy. Example – bursting of crackers, bombs etc.
- Nuclear energy. Example – nuclear power, atom bomb etc.

Energy in one form can be transformed into another form.

- Kinetic energy.
- Potential energy.

A detail discussion about mechanical energy is done.

__Kinetic Energy__

*The energy possessed by a body due to its motion is called kinetic energy.*

- The amount of work that a moving body can do before coming to rest is the measurement of its kinetic energy.
- Similarly, the amount of work required to bring a body from rest into motion is stored in that body as its kinetic energy.

Consider that a body of mass ( m ) is in rest and a force ( F ) is being applied to put it in motion of *velocity* ( v ) as shown in figure.

- From
*kinematic equations*of motion we have –

( v^2 - u^2 ) = 2as

Since the body was in rest, then initial velocity ( u = 0 ) .

Therefore, \quad ( v^2 - 0 ) = 2as

Or, \quad a = \left ( \frac {v^2}{2s} \right )

- As the
*force*and*displacement*are in the same direction, so the work done will be –

W = F \ s = m \ a \ s = m \left ( \frac {v^2}{2s} \right ) s = \left ( \frac {1}{2} \right ) mv^2

- This amount of work done will remain stored in the moving body as its kinetic energy.

Therefore, kinetic energy of a moving body of mass, ( m ) moving with a velocity ( v ) is given by –

K = \left ( \frac {1}{2} \right ) m v^2

__Relation between Kinetic Energy & Momentum__

- By definition of
*linear momentum*, we have –

p = mv

- And, kinetic energy –

K = \left ( \frac {1}{2} \right ) m v^2

= \left ( \frac {1}{2m} \right ) ( m^2 v^2 )

= \left ( \frac {1}{2m} \right ) ( p^2 )

Therefore, \quad K = \left ( \frac {p^2}{2m} \right )

So, \quad p = \sqrt {2mK}

__Potential Energy__

*Potential energy is the energy stored in a body due to its position or by its configuration. It is **also called mutual energy or energy of configuration.*

- Potential energy is measured by the amount of work that a body or system can do in passing from its present position or configuration to some standard position or configuration called
or**zero position****zero configuration.**

Most common types of potential energies are as follows –

It is the potential energy associated with the state of separation of two bodies, which attract each other by__Gravitational potential energy__*–**gravitational force*.**Elastic potential energy****–**It is the potential energy associated with the state of compression or extension of an elastic object or spring.**Electrostatic potential energy –**It is the potential energy associated with interaction between two*static charges.*

__Power__

*Power is defined as the rate of doing work.*

Therefore, average power is given by –

\text {Average Power} = \text {Work done per unit time}

Or, \quad P_{av} = \left ( \frac {W}{t} \right )

- Power is a ratio of two
*scalar quantities*i.e. work & time, hence it is also a scalar quantity.

### Units of Power

*Power of an agent is one watt if it does work at the rate of one joule per second.*

1 \ \text {watt} = \left [ \frac {1 \ \text {joule}}{1 \ \text {second}} \right ]

Or, \quad 1 \ W = 1 \ \text {J - s}^{-1}

1 \ \text {kW} = 1000 \ \text {W} = 10^3 \ \text {W}

1 \ \text {HP} = 746 \ \text {W} = 0.746 \ \text {kW}

- Commercial unit of electrical power is called
**“**( BOT ) unit of electrical power. It is*Board of trade”***kilowatt hour.**

*One kilowatt hour is the electrical energy consumed by an appliance of 1000 watt for 1 hour.*

- Therefore, \quad 1 \ \text {kWh} = 1 \ \text {kW} \times 1 \ \text {hour}

Or, \quad 1 \ \text {kWh} = 10^3 \ \text {W} \ \times 1 \ \text {hour} = 1000 \ \text {Wh}

Or, \quad 1 \ \text {kWh} = 1000 \ \text {J - s}^{-1} \ \times \ 3600 \ s = 3.6 \times 10^6 \ J

- Therefore, \quad 1 \ \text {BOT} = 3.6 \ \times \ 10^6 \ J

See numerical problems based on this article.