*Work:*

Work done by a constant force to move an object = displacement × force parallel to direction

Work is a **scalar** quantity

*W = Fs*** **

Where:

*W* = work [J]

*F* = force creating the work [N]

*S* = displacement [m]

*Energy:*

Energy is the potential or ability of a system to do work.

Energy is a scalar quantity

*Power:*

Is the rate of work done

*Or*** **

Rate of energy transfer

*F = W / t = E / t*** **

Where:

*P* = power [J s-1]

*W* = work [J]

*E* = energy [J]

*t *= time [s]

*Potential Energy** *

Potential energy is the energy within an object because of its position or state.

Gravitational potential energy:

*E = mgh*

Where:

*E* = potential energy [J]

*m *= mass [kg]

*g* = gravitational acceleration [m s-2]

*h* = height of the location of the object [m]

Elastic potential energy: *F* / N

*W = ½ Fs*

Where:

*W* = work done [J]

*F* = force exerted [N]

*s *= extension or compression of the spring [m]

*Kinetic Energy*

Kinetic energy is energy acquired by an object during movement.

**E = ½ mv2**

Where:

*E* = kinetic energy [J]

*m *= mass [kg]

*v* = velocity of the object [m s-1]

## Law of Conservation of Energy

*Statement**:*

The law of conservation of energy states that:

**“Energy may neither be created nor**** destroyed; it can only change shape”.**

**Explanation**:

Consider a body of mass **m**at height **h** above the ground. Its kinetic energy at that point A is:

K.E = 1/2(mv2)

K.E = 1/2 m * (0)

K.E = 0 …….. (i)

**The potential Energy at point A is : **

P.E = mgh …………(ii)

**So the total energy at point A will be : **

T.E = K.E + P.E

E(A) = 0 + mgh

**E(A) = mgh**

Suppose the body is released from this height and falls through a distance **x**. Its new height will be **(h-x)**. The velocity with which it reaches point **B** is calculated by using the third equation of motion:

2gs = Vf2 – Vi2

As we know:

- Vi = 0
- S = x

Therefore,

2gx = Vf2 – 0

2gx = v2

The kinetic energy at point B is:

K.E. = 1/2 mv2

Substituting the value of v2:

K.E. = 1/2 * m * 2gx

K.E = mgx

The Potential Energy at point B is:

P.E = mgh

The height of the body is (h-x):

P.E. = mg(h-x)

The total energy at point B is :

E(B) = P.E + K.E.

E(B) = mgx + mg(h-x)

E(B) = mgx + mgh – mgx

**E(B) = mgh**

Hence, the total energy at point A and B are same. It means that the total value of energy remains constant.

*Power:*

Power is the rate at which energy is used.

*P *= *E/* *t*

## Need to Conserve Energy:

The fuel that burns in running factories, transport and other activities is mainly obtained from underground deposits in the form of coal, oil, gas and other similar raw forms. These deposits are rapidly decreasing and one day all these resources of energy will be consumed. It is therefore highly important for us to avoid wastage of energy.

the consumption of two much energy is also having adverse effect on our environment. The air in big cities is heavy because of pollution caused by industrial wastes and smoke produced by automobiles. To ensure comfortable living with a neat environment, it is the responsibility of all of us as individuals to conserve energy.

*Efficiency:*

Efficiency is the ratio at which the output power is compared to the input power.

Efficiency = Output power

___________ x 100%

Input power

*Elasticity:*

Elasticity is the ability of an object to return to its original shape and size after the applied external force applied onto it has been removed.

*Hooke’s Law:*

Hooke’s Law states that the extension or compression of a spring is **directly** **proportional** to the force acting on it provided the **elastic limit** of the spring has not been exceeded.

## Definitions:

## 1. Joule:

It is the work done by a force of one Newton when the body is displaced one meter.

## 2. Erg:

It is the work done by a force of one Dyne when the body is displaced one centimeter.

## 3. Foot Pound (ft-lb):

It is the work done by a force of one pound when the body is displaced one foot.

## 4. Force:

It is an agent that moves or tends to move or stops or tends to stop a body.

## 5. Watt:

Watt is the unit of power that is equal to the quantity of 1 Joule work done in 1 second.

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CHAPTER 9- MACHINES