**CBSE NOTES CLASS 9 SCIENCE CHAPTER 11**

**WORK AND ENERGY**

**Work**

Work is defined as the product of the force and the displacement in the direction of the force.

Work done = force × displacement

In general if the force and displacement are at an angle θ, with each other, then, the work done is given by

$$\mathrm{W}\mathrm{}=\mathrm{}\stackrel{\u20d7}{\mathrm{F}}.\stackrel{\u20d7}{\mathrm{s}}$$

Or W = F s cos θ

- If F and s are in same direction, work is +ve,
- If F and s are in opposite direction, work is –ve
- If F and s are perpendicular to each other, the work done is 0.
- SI unit of work = Joule (J) = Nm

**Energy**

The energy may be defined as the capacity of a body to do work.

The SI unit of energy is Joule (J) or 1 kJ = 1000 J

**Forms of Energy **

The various forms of energy include mechanical energy (potential energy and kinetic energy), heat energy, chemical energy, and light energy.

**Law of Conservation of Energy **

According to this law, energy can only be converted from one form to another - it can neither be created nor be destroyed. The total energy, before and after the transformation, remains the same. The law of conservation of energy is valid in all situations and for all kinds of transformations.

**Mechanical Energy**

The energy acquired by an object due to work done on it known as Mechanical energy. The sum of Kinetic energy and Potential Energy is referred to as mechanical energy. It is the energy associated with the motion and position of an object.

**Kinetic Energy **

Energy possessed by a body by virtue of its state of motion is called kinetic energy (KE).

Kinetic energy is always positive and is a scalar.

Kinetic Energy, KE = $\frac{1}{2}$ m v^{2 }when m is the mass and v is the velocity of body.

**Proof - **

Using equation,

v^{2} – u^{2} = 2*a* *s*

⇒ *s* = $\frac{{\mathrm{v}}^{2}\mathrm{}\u2013\mathrm{}{\mathrm{u}}^{2}}{2\mathrm{a}}$

Also F = *m* *a*

⇒ W = F . *s* = *m* *a* × $\frac{{\mathrm{v}}^{2}\mathrm{}\u2013\mathrm{}{\mathrm{u}}^{2}}{2\mathrm{a}}$

W = $\frac{1}{2}\mathrm{}$m (v^{2} –u^{2})

If the object had started rest,, that is, u = 0, then

W = $\frac{1}{2}$ m v^{2}

The work done is equal to the change in the kinetic energy of an object.

**Potential Energy **

The energy possessed by an object by virtue of its position or configuration.

There are two common forms of potential energy, gravitational and elastic.

**Gravitational Potential Energy **

The work done on the object against gravity

W = force × displacement

= mgh

Since work done on the object is equal to mgh, energy equal to mgh units is gained by the object. This is the potential energy (E_{P}) of the object.

PE = mgh

**Elastic Potential energy **

The work done to change the shape of a body gets stored in the form of elastic potential energy. Elastic potential energy is never negative whether due to extension or to compression.

**Conservation of Mechanical Energy **

The sum of kinetic energy and potential energy of an object is its total mechanical energy. It would be the same at all points. That is,

Total Energy = Potential Energy + Kinetic Energy = constant

TE = KE + PE = constant

ΔKE = - ΔPE

ΔKE + ΔPE = 0

Or TE = $\frac{1}{2}$ m v^{2} + mgh = constant

**Power **

The time rate of doing work is defined as power (P). More quickly work is done; power will be more.

$$\mathrm{Power\; =}\frac{\mathrm{Work\; done}}{\mathrm{Time\; taken}}$$

**SI Unit of power **

The unit of power is Joule per second which is called Watt (W). When large amounts of power are involved, a more convenient unit is the kilowatt (kW) where,

1 kW = 1000W,

1 Megawatt = 10^{6} Watt

**Commercial Unit of Energy**

The unit Joule is too small and hence is inconvenient to express large quantities of energy. We use a bigger unit of energy called kilowatt hour (kWh).

1 kWh is the energy used in one hour at the rate of 1000 J s^{–1} (or 1 kW).

1 kWh = 1 kW ×1 h

= 1000 W × 3600 s

= 3600000 J

1 kWh = 3.6 × 10^{6 }J.

The electric energy used is expressed in kilowatt hour, which is called 1 unit.