Unit-4 | WORK, ENERGY AND POWER | Class-09

Overview: Work is the scalar product of Force and Displacement. Energy is the capacity of doing work. Power is the rate of doing work. No work can be done without energy. Similarly, power cannot be measured if no work has been done. Here, we will discuss work, nature of work done, energy and its forms, and work.




Work: 

Work is the scalar product of Force and displacement. So, mathematically, Work (W) = Force(F) x Displacement covered (s) 
i.e. W = F x s

The SI unit of Work is Joule (J).

Also, W= Fxs
Where the SI unit of Force is Newton(N) and displacement covered is metre(m). The SI unit of Work is also Newton metre (Nm). 
The CGS unit of Work is erg. 
[1 J = 10^7 erg ]

Work done: 

Work is said to be done if a body covers some displacement in the direction of force applied.

The two factors on which the work done by a body depends are:
i,. magnitude of force applied (F)
ii. displacement produced by the body (s)

One Joule Work:

We know,
W = F x s
when, F = 1 N and s = 1 m
W = 1 Nm

Therefore,
One joule work can be defined as
the work done when 1N force displaces a body through 1m distance in the direction of force applied.
 

 Types of work:

1. Work done against gravity:

Gravity is the force of attraction that attracts every objects towards the centre of the Earth. The work done against this force is called work done against gravity. For example: lifting weights by a bodybuilder.
In this condition,
Work (W) = Force (F) x displacement (s)
= Mass(m) x acceleration due to gravity (g) x height (h)
So, W = mgh

2. Work done against friction:

The force produced when one object slides over another and creates a opposing force is called friction. The work done against this force is called work done against friction . For example: sliding ruler on a table. 
Work (W) = Force (F) x displacement (s)



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Energy:

Energy is the capacity of a body to do work. Its SI unit is Joule (J) and CGS unit is erg. 

Different forms of energy:

1. Mechanical energy:

The energy possessed by a body by the virtue of its motion, position or configuration is called mechanical energy. Mechanical energy can be divided into two types:

a. Kinetic energy (KE):

The energy possessed by a body due to the virtue of its motion is called Kinetic Energy. For example: a moving ball, flying bird, rolling stone, etc.
KE = 1/2 mv^2

Therefore, KE depends on the following factors:
(i) mass of the body (m)
(ii) velocity of the moving body (v)

Derivation of the formula of KE:

Let us consider that a body of mass 'm' starts to move from rest with initial velocity 'u' and gains an acceleration'a' and finally reaches its final velocity 'v' moving a distance 's'.

According to the equation of motion,
We have,
v^2 = u^2 +2as
or, v^2 = 0^2 + 2 as [ Since, u = 0 ]
or, s = v^2 / 2a .......... (i)
Again,
KE = Work Done
= F x s
= m. a . v^2 / 2 a  [ F = ma, s = v^2/2a ]
= 1/2 m. v^2

b. Potential energy (PE):

The energy possessed by a body due to the virtue of its position or configuration is called potential energy. For example: water stored in a dam, etc.

Derivation of the formula of PE:
Let us consider a body of mass 'm' is raised to a height 'h'. Then,
PE = Word Done (W)
= F x s [W = F x s]
= m.g x h [F = mg and s = h]
= mgh.

Potential energy is also called gravitational potential energy.

2. Heat Energy:

The energy produced by a body due to the vibration of molecules in the body is called heat energy. For example: burning firewood, burning coal, etc.

3. Light Energy:

Light is a form of energy which produces sensation of vision. For example: energy possessed by a glowing lamp, bulb, etc.

4. Sound Energy:

Sound is a form of energy produced due to the vibration of a body. For example: earphones, speaker, guitar are the sources of sound energy.

5. Electrical Energy:

The energy produced either due to the flow of electrons through the conductor or due to the change in number of electrons in a body is called electrical energy. For example: Dynamo, cell, etc are the sources of energy.

6. Chemical Energy:

The energy stored in substances is called chemical Energy. These energies get released when a chemical change takes place.

7. Magnetic Energy:

The energy possessed by a magnet is called magnetic energy. 

8. Nuclear Energy:

The energy produced from the nucleus of an atom is called nuclear energy. It is also called atomic energy. It can be produced either due to fission or fusion.

Transformation of Energy:

The process by which energy is converted from one form to another is called transformation of energy. 

Here is the transformation of energy in speaker:
Cell (Electrical energy ) -> Music (Sound energy)


Principle of Conservation of Energy:

The principle of Conservation of Energy states that, 
Energy can neither be created nor destroyed but it can be changed from one form to another.
 
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Power:

Power is the rate of doing work. It is a scalar quantity. It is measured in watt (W) or J/s or horsepower (h.p.). 
Mathematically,
Power (P) = Work done (W) / time taken (t)
So, P = W/t
Or, P = F x s / t
So, P = F x v [ v = s/t ]

Power of a body depends on these following factors:
(i) amount of work done (W)
(ii) time taken to do the work (t)

One Watt Power:

Power is said to be one watt if one joule work is being done in 1 second. 

The SI unit of Power is Watt(W). 

1 horsepower = 746 watt

Numerical Problems:

1. The velocity of a body of mass 60 kg reaches 15 m/s from 0m/s in 12 seconds. Calculate the kinetic energy and power of the body.
Solution:
Here,
Mass of body (m) =  60 kg
Final velocity (v) = 15 m/s
Time taken (t) = 12 s

Now,
Kinetic Energy (KE) = 1/2 mv^2
= 1/2 x 60 x 15^2
= 6750 Joule

And,
Power of the body (P) = W /t
= KE /t
= 6750/ 12
= 562.5 W

2. A man of mass 70kg climbs the Nautale Durbar of Basantapur. He climbs 15 steps in 1 minute. If the height of 1 step is 15cm, calculate his power. (g= 9.8 m/s^2)
Solution:
Here,
mass of the man (m) = 70 kg
height of the steps (h) = 15 x (15/100) m
= 2.25 m
acceleration due to gravity (g) = 9.8 m/s^2
time (t) = 1 minute = 60 seconds

Now, 
Power of the man (P) = mgh / t
= 70 x 9.8 x 2.25 / 60 
= 25.72 W





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