science 9

ii. What is the average speed in segment OA, AB and BC.

iii. Why does the segment CD represent rest?

l. From the following velocity-time graph,

i.Name the type of motions Velocity (m/s) 10 A B
shown by OA, AB, BC

ii. What is the velocity at point 0 4 10 C
A, B and C? Time 14

iii.What are the accelerations
at portions OA, AB and BC.

iv.Calculate the distance travelled in the portions BC?

Answers 8. a. 2.5 m/s2 b. 4.16 m/s2, 18.75 m c. 36 m/s, 112 m

d. 2m/s2, 500 m, 1000 N e. 1.25 m/s2, 15.62 m, 62.5 m

f. Distance travelled 50 m, accident occurred g. 4s, 40 m

h.2.81m/s2, 1407.13 N i. 1710 N j. 11.25 m/s2, 675 N

k. OA= uniform speed, AB=rest, BC=uniform speed, CD=rest

Average speed in OA is 2m /s, BC = 2 m/s.

l. i. OA= uniform acceleration, AB = uniform velocity BC = uniform

ratardation. ii. At A, 10 m/s; at B, 10 m/s; at C, 0 m/s.

iii. 2.5 m/s2, 0 m/s2 −2.5 m/s2 iv. 20 m

Project Work

Use kinetic trolley and spring balance to test and verify newton’s 2nd law of
motion. Perform this experiment taking help from your teacher.

Glossary
Cover: travel
Magnitude: amount, quantity or relative size
Retardation: decreasing acceleration
Proportional: having a constant ratio
Jerk: pull or move with a sudden movement
Displacement: change in position

47 Times' Crucial Science Book - 9

Chapter

3 Simple

Machine
Archimedes

He is known for Archimedes' principle,
Archimedes' screw, Hydrostatics, Levers,
Infinitesimals, Neuseis constructions.

Estimated Periods :6

ObjAetctthiveeesnd of the lesson, students will be able to:

• introduce simple machine and explain its types,

• explain the principle of lever,

• classify lever and introduce MA, VR and efficiency involved in its working,

• solve simple numerical problems involving MA, VR and efficiency.

Mind Openers

• Do you know what simple machine means?

• How do simple machines make work easier?

• How many types of simple machine do you know? What are they? Discuss.

Introduction

We use a number of devices in our daily life. These devices are
useful to us in many ways. For instance, we use a pulley to draw
water from well, we use a nail-cutter to trim our nails, we use a
broom to sweep dust and dirt from the floor, we use scissors to cut
clothes and paper, etc. These devices are simple in structure and
they make our work easier and faster. Due to their simple structure,
they are called simple machines. Thus, the devices which are simple
in structure and make our work easier and faster are called simple
machines. Nail-cutter, broom, scissors, firetongs, beam balance,
crowbar, wheel barrow, etc are some examples of simple machines.

There are some other machines which are complex in structure. They
are formed by the combination of large number of simple machines.
Such machines are called complex machines. For example, sewing
machine, motor engine, water mill, windmill, etc.

Advantages of simple machines

The simple machines are useful to us in the following ways:

Times' Crucial Science Book - 9 48

1. Simple machines multiply force, i.e. a bigger load is lifted
by applying a smaller effort.

2. It transfers force from one point to another.

3. It accelerates the rate of doing work.

4. A simple machine changes the direction of the applied force.

Terms related to simple machine

Effort and effort distance

The force applied in the simple machine to do useful work is called
effort. It is represented by E and its SI unit is Newton (N). The
distance travelled by the effort while moving the load is called effort
distance. It is denoted by (Ed) and its SI unit is metre (m).

Load and load distance

The force or resistance which is to be overcome by the effort applied
is called load. It is represented by L and its SI unit is newton (N).

For example, when we lift a heavy piece of iron with our hands, the
force that we apply is effort and the weight of iron piece is the load.
The distance travelled by the load is called load distance.

Mechanical Advantage (MA)

Mechanical advantage of a machine is defined as the ratio of load
overcome by the machine to the effort applied.

Mathematically,

Load L
Mechanical advantage = ∴ MA = Ε

Effort

Mechanical advantage has no unit because it is the ratio of two

similar physical quantities (i.e. two forces).

Mechanical advantage is the measure of number of times by which
a simple machine multiplies the applied force. For example, if the
mechanical advantage of a machine is 2, it means that the machine
can lift a load two times heavier than the effort applied.

If the mechanical advantage of a machine is 1, it means that the
machine cannot multiply the applied effort. Such machine can lift a
load that is as heavy as the effort applied.

49 Times' Crucial Science Book - 9

Velocity Ratio (VR)

The velocity ratio of a machine is defined as the ratio of distance
travelled by the effort applied in a machine to the distance travelled
by the load.

Mathematically,

Distance travelled by effort Ed
Velocity Ratio = Distance travelled by load ∴ VR = Ld

Velocity ratio has no unit as it is the ratio of similar physical
quantities (i.e, two distances). If the velocity ratio of a machine is 2,
it means that the effort has to move twice the load distance to lift a
load up to a particular height.

Efficiency (η)

When an effort is applied in a machine, some work is done. The
work done in the machine is called input work.

The input work is the product of effort applied and the effort
distance, i.e.

Input work (Wi) = Effort × Effort distance.

∴ Wi = E × Ed

On the other hand, the machine performs some work due to the
input work. The work performed by the machine is called output
work.

The output work is the product of load and load distance, i.e.

Output work (Wo) = Load × Load distance.

∴ Wo = L × Ld

The ratio of output work to the input work in a machine expressed in
percentage is called efficiency.

Mathematically,
Output work

Efficiency = Input work × 100%
If the efficiency of a simple machine is 75%. It means that 75%
of applied energy (i.e, input work) is converted into useful work
(i.e, output work). Rest 25% of our energy is wasted to overcome
frictional and gravitational force.

Times' Crucial Science Book - 9 50

In a simple machine, some amount of input work is always wasted
in the form of heat to overcome friction. Hence, the value of output
work is always less than the input work because no machine can be
made frictionless. Due to this reason, a simple machine cannot have
100% or more efficiency.

Relation among MA, VR and efficiency

From the definition of efficiency, we have

Output work

η = Input work × 100%
Here, Output work = Load × Load distance

Input work = Effort × Effort distance ∴ MA =L ,
L × Ld E

∴ η = E × Ed × 100% VR = Ed

[ [It can be rearranged as Ld
L/E MA
η = Ed/ Ld × 100% ∴ η = × 100%
VR

Thus, efficiency of a machine can also be defined as the ratio of
mechanical advantage to the velocity ratio expressed in percentage.
Due to friction, the value of mechanical advantage is always less
than the value of velocity ratio. Hence, the efficiency of a machine
is never 100% or more.

Principle of simple machines

A simple machine does not perform work by itself. Hence, we have
to apply force on a machine to do a particular work.

The force applied in a machine is called effort or input force whereas
the force which is to be overcome by the effort is called load or output
force.

All simple machines work on a basic principle which can be stated
as: in a balanced condition, the work done on a machine (input work)
is equal to the work done by the machine (output work)

i.e. in a balanced condition,

Input work = Output work

or, E × Ed = L × Ld

51 Times' Crucial Science Book - 9

Ideal machine and practical machine
According to the principle of a simple machine, the output work
should be equal to input work. Thus, its efficiency should be 100%.
A simple machine which has 100% efficiency is called an ideal
machine or perfect machine. In other words, a machine which can
convert the whole input work into output work with the no wastage
of energy is called an ideal machine.
However, in practice, no machine can convert whole input work
into output work. So, the output work is always less than the input
work and the efficiency is always less than 100%. It is due to the fact
that a machine is always affected by friction. The friction wastes
the kinetic energy of the machine in the form of heat energy and
hence the output work is less than input work. Thus, the efficiency
of a simple machine can never be 100% or more.
If the efficiency of a simple machine is 90%, it means that 90% of
the input work is converted into useful work and remaining 10%
energy is converted into heat energy while overcoming the friction.
The friction in the moving parts of a machine can be decreased by
applying grease or lubricating oil. This increases the efficiency of
the machine.

Types of simple machines

On the basis of structure and function, simple machines are divided

into six types :

1. Lever 2. Pulley 3. Wheel and Axle

4. Inclined plane 5. Screw 6. Wedge

1. Lever

A lever is a long rigid bar that is capable of rotating about a fixed
point. The fixed point about which a lever rotates is called fulcrum.
A lever consists of three main parts - load, effort and fulcrum. The
load is the object that has to be lifted by the lever whereas the effort
is the force applied to the lever to lift the load.

FL E L
E F
F
EL

Scissors Bottle opener Fire tongs

Times' Crucial Science Book - 9 52

The advantages of the lever depends upon the load distance and
effort distance.

In a lever, MA = Load Effort distance MA
or, η = × 100%
Effort or, VR = Load distance
VR

The lever can be classified into three types on the basis of position
of load, effort and fulcrum. They are:

a. First class lever

The lever in which the fulcrum lies at any point in the middle of
load and effort is called first class lever. Crowbar, scissors, see-saw,
beam balance, dhiki, pliers, cutting shears, etc are some examples
of first class lever.

E

L EL E L
F F

F See-saw Scissors
Crowbar

The first class lever shows all the advantages of lever, i.e. it changes
the direction of applied force, multiplies force and accelerates the
rate of doing work. When the fulcrum is close to the load, the effort
distance increases and it multiplies the applied force. Similarly,
when the fulcrum is close to the effort, the load distance increases
and it accelerates the work. In the use of a crowbar, if we apply the
effort in downward direction, the load is lifted up. Hence, it changes
the direction of applied force.

b. Second class lever

The lever in which the load lies at any point in the middle of effort
and fulcrum is called second class lever. In the second class lever,
the effort distance is always greater than the load distance. Hence,
the second class lever multiplies effort more than any other class of
lever.

Wheel-barrow, nut-cracker, bottle opener, paper cutter, etc are
some examples of second class lever.

53 Times' Crucial Science Book - 9

LE FL
EE
FL
F Bottle opener

Wheel-barrow Onion cutter

c. Third class lever

The lever in which effort lies at any point in the middle of load and
fulcrum is called third class lever. Such lever makes the work safer
and easier. But it cannot multiply effort because the load distance
is always greater than the effort distance.

E F EL
Fire tongs
L E
Broom
FF L

Fishing rod

Fire tongs, sugar tongs, stapler, broom, shovel, fishing rod, spoon,
etc are the examples of third class lever.

Solved Numerical Problem 3.1

Calculate the efficiency of the lever from the data given in the figure.

Solution :

Given,

Load (L) =1600N 400N
Effort (E) =400N
1600N

Load distance(Ld)=20cm

Effortdistance(Ed)=100cm 20cm 100cm

Here,

Mechanical advantage,

Velocity ratio, MA = Load = 1600N = 4

Effort 400N

Effort distance 100 =5
200
VR = Load distance =
Again, efficiency of lever is given by:

MA = 4 × 100% = 80%
η = × 100% 5

VR

∴Hence, the efficiency of the lever is 80%

Times' Crucial Science Book - 9 54

2. Pulley

A pulley is a hard metallic or wooden disc with a grooved rim. A
rope moves around the groove of the disc. The load is tied to one end
of the rope and it is pulled from another end of the rope by applying
effort.

Pulleys are used for different purposes. Some of the uses of pulleys
are:

1. It is used to draw water from well.
2. It is used in elevators (lifts).
3. It is used for lifting heavy loads in cranes.

4. It is used is flag stands for hosting the flags.

A pulley can be classified into three types-single fixed pulley, single
movable pulley and compound pulley.

a. Single fixed pulley

A pulley in which the frame is fixed to a rigid Frame
support and the disc rotates along with the rope Wooden disc
is called single fixed pulley. The mechanical
advantage of single fixed pulley is 1, i.e. there Rope
is no gain in mechanical advantage. But we
use such pulley because it helps to change the Load
direction of applied force.

In a single fixed pulley, the distance moved by Single fixed pulley
load is equal to the distance moved by effort.

Effort Rope

b. Single movable pulley

A pulley which moves up and down along Wooden disc
with the load is called single movable pulley. Frame
In such pulley, one end of the rope is tied to
a rigid support and the load is pulled from Load
other end of the rope. The circular disc moves
along with load. In a single movable pulley,

Single movable pulley

VR = No. of rope segments supporting the load =2
Hence, the VR of a single movable pulley is 2.

55 Times' Crucial Science Book - 9

Differences between a single fixed pulley and a single movable pulley

Single fixed pulley Single movable pulley

1. It is fixed to a rigid support and it 1. It moves up and down along with

does not move along with load. load.

2. It cannot multiply applied force. 2. It multiplies the applied force
(effort).

3. It changes the direction of applied 3. It does not change the direction of
force to a more convenient direction. applied force.

4. The value MA and VR of a single 4. The value MA and VR of a single

fixed pulley is always1. movable pulley is 2.

Combined pulley Fixed pulley

A pulley which consists of combination of two Frame Rope

or more pulleys is called combined pulley. Movable pulley

A combined pulley is also called compound Load Effort
pulley or block and tackle system.
Combined pulley
In case of a compound pulley,

VR = No. of rope segments supporting the load.

Or

VR = No. of pulleys used in the pulley system

Solved Numerical Problem 3.2

The mechanical advantage of a pulley system is 4 and its efficiency is 80%.
What is the number of pulley used? What effort will be needed to lift a load of
2000N in such pulley system?

Solution:

Given,

Efficiency(η)=80%

Mechanical advantage(MA)=4

Number of pulley=?

According to formula,

MA MA 4
η = × 100% or, VR = η × 100% or, VR = 80% × 100% = 5
VR

In a combined pulley system the velocity ratio is equal to the number of

pulleys used in the system.

Times' Crucial Science Book - 9 56

Hence,

No. of pulley used=5

Again,

Load(L)=2000N

Effort(E)=?

We know that, or, Effort = Load = 2000N = 500N
4
Mechanical advantage = Load MA

Effort

∴ Effort= 500N

Therefore, the required effort is 500N

3. Wheel and axle

A wheel and axle is a simple machine which consists of two wheels
(cylinder) of different diameters. The larger cylinder or wheel is
fixed rigidly with the small wheel called axie in such a way that
both the wheels spin about the same axis. Generally, load is lifted
by the small wheel and the effort is applied on the big wheel.

Wheel

Axle

Wheel

Axle

String roller reel Screw driver Steering of car

Door knob, wheel of a vehicle, steering wheel of a vehicle, screw
driver, etc are the examples of wheel and axle.

In a wheel and axle, the circumference of larger cylinder (wheel) is
considered as effort distance and that of smaller cylinder (axle) is
considered as load distance. The M A and VR of wheel and axle can
be calculated as:

Load L
∴ MA =
MA =
E
Effort

Similary,

VR = Effort distance Circumfernce of larger cylinder
=
load distance Circumfernce of smaller cylinder

57 Times' Crucial Science Book - 9

[ ](2R)

= (2r)
R= Radius of larger cylinder
r = Radius of smaller cylinder

= R ∴VR= R
rr

Thus, the velocity ratio of a wheel and axle is always greater than

1 because the radius of larger cylinder is always greater than that

of smaller cylinder.

Wheel and Axle : A continuous lever

The wheel and axle is regarded a continuous Fulcrum

lever. It is because wheel and axle move

around a fixed point similar to fulcrum in

the first class lever. The load and effort Effort
lie on the either side of the fixed point

(fulcrum). A lever can move around the Load

fulcrum in less than 90° but the wheel and

axle makes an angle of 360° continuously while working. So it is a

continuous lever.

Solved Numerical Problem 3.3

A wheel of diameter 50cm is connected with an axle of diameter 10cm. If a weight
of 1000N is lifted by applying 250N force, calculate MA, VR and efficiency of
the machine.

Solution:

Given,

Load (L) = 1000N

Effort (E) = 250N

MA =?

According to formula,

MA = L = 1200N =4
E 250N

Again,

Radius of wheel(R)= Diameter (D)
50cm
2

∴ R= 2 =25cm

Similary,

Times' Crucial Science Book - 9 58

10cm
∴ r = 2 = 5cm

Velocity ratio (VR) = ?

Using formula,

Again, R 25cm
VR = = =5

r 5cm

MA 4
Efficiency(η) = × 100% = × 100% = 80%
VR 5

Thus, the MA, V.R and efficiency of the given wheel and axle are 4, 5 and 80%

respectively.

4. Inclined plane Effort Height
Inclined Plane
A slanted surface over which a load Load
can be pulled or pushed is called
inclined plane. In general, it is a
sloping surface. Winding roads on
hills, spiral stair-case, wooden plank
used for loading goods in a truck, etc
are some examples of inclined plane.

In an inclined plane,

l = The distance travelled by the load on the plane surface

h = The actual height through which the load is raised from
the ground.

Now,

Input work = E × l

Output work = L × h

MA = Load L
∴ MA =
Effort
E

But, due to the frictional force between the load and the surface
of inclined plane, the mechanical advantage is less than the value
given by the above relation.

The velocity ratio is given by:

59 Times' Crucial Science Book - 9

Distance travelled by effort on inclined plane
VR= Distance travelled by load through vertical height

Lenght of inclined plane = l
= Height of the plane h

The efficiency of inclined plane is given by
MA

η = × 100%
VR

Solved Numerical Problem 3.4

Calculate the MA, VR and efficiency from the given inclined plane. The length

of inclined plane is 20m and its height is 5m. E=600N
Solution:

Given,

Load(L)=1800N 20m 5m
Effort(E)=600N
Length of inclined plane(l)=20m LLoa=d1800N

Height of inclined plane(h)=5m

Mechanical advantage(MA)=?

Velocity ratio(VR)=?

Efficiency(η)=?

We know that,

L = 1800N =3
MA = 600N

E
Similarly,

l 20m
VR = = =4

h 5m
Again,

MA 3
η = × 100% = × 100% = 75%
VR 4

Hence, the MA, VR and η of the given inclined plane are 3,4 and 75%
respectively.

Times' Crucial Science Book - 9 60

5. Screw

A screw is a simple machine which seems to have

an inclined plane wrapped around a cylindrical
surface.
A screw has spiral ridges called thread of the screw.

The distance between the adjacent threads of screw

is called pitch. In other words, the distance moved

by screw in one complete rotation on being driven
into the wood is called pitch.

In a screw, Distance travelled by effort
Velocity Ratio = Distance travelled by load

Circumference of circle mode by arm of screw diver 2R
∴ VR = p
= Pitch of the screw

Jack screw, screw nail, driller, etc are the examples of screw. A jack

screw is used to lift vehicles while changing their wheels.

6. Wedge Effort

t

A wedge is a simple machine which has

a sharp part at one end and flat part at l
the another end. The effort is generally
load
applied upon the flat part and the sharp load

part performs the work. A wedge is used

to slipt the wooden logs. Axe, knife,

khukuri, nail, chisel, needle, etc are as the examples of wedge.

Let, L be the length of the wedge and t be its thickness. The length

L of the wedge is the distance moved by the effort.

In a wedge, Velocity Ratio = Distance moved by effort
Distance moved by load

Length of wedge L
= Thickness of wedge ∴ VR = t
Moment of force
F

The turning effect of force acting upon

a body about its axis is called moment d

of force. It is given by the product of A B
magnitude of force and the perpendicular

distance between the line of action of force and the fulcrum.

61 Times' Crucial Science Book - 9

Mathematically,

Moment of force = Force × Perpendicular distance

∴S=F×d

Since the SI unit of force is newton (N) and that of distance is metre
(m), the SI unit of moment of force is Newton-metre (Nm).

The larger the distance of the force from the fulcrum, the greater is
the turning effect. It means that a small force can produce a large
turning effect if its distance from the fulcrum is large. Thus, it is
easier to open a tight bolt using a spanner with long handle than
by with a short handle.

When the force is applied in certain angle other than 90°, the
moment of force decreases. If the line of action of force and the
fulcrum are not perpendicular to each other, the moment of force is
given by:

Moment of force = F × d sin B

If a force produces a clockwise rotation

of a body, the moment is called F d
clock wise moment and it is taken

as a positive moment. But, if a force θ
produces anti-clockwise rotation of a A

body, the moment is called anticlockwise moment and is taken as

negative.

Law of moment

The law of moment states that if a body is in equilibrium condition
under the action of a number of forces, the sum of clockwise moments
is equal to the sum of anticlockwise moments”.

Mathematically,

Sum of clock wise moments = Sum of anticlockwise moments

or, Load× Load distance = Effort × Effort distance

∴ L × Ld = E × Ed

Learn and Write
1. VR of a machine is always greater than MA. Why?

VR of a machine is not affected by the friction but MA is affected
by the friction. Therefore, VR is always greater than MA.

Times' Crucial Science Book - 9 62

2. Roads are made winding in hilly regions.

The roads in the hilly region are slanted like inclined planes.
The height of the plane is decreased with respect to length.
Thus, the MA of the plane increases. In this situation, more
load can be rolled by applying small effort. But if the roads are
made steep up in hilly areas, the vehicles cannot move up.

3. The probability of breaking a tall tree is more than a short one
during storms. Why?

When storm applies force to the trees, the distance of the line
of action of force from the fulcrum (root) is more in tall tree
than in the short tree. Due to this, more turning effect of the
force is created in the tall tree than in the short one. Thus,
there is more probability of breaking a tall tree .

4. Lubricants are used in machines. Why?

Efficiency of a machine is reduced by friction between the
movable parts of a machine. When lubricants are used, the
friction will be reduced thereby increasing the efficiency

5. Is it possible to have the same value of mechanical advantage
and velocity ratio for a machine?

It is possible in an ideal case. If there is no friction between
moving parts of the machine, its mechanical advantage is
equal to the velocity ratio.

6. A long spanner (wrench) is used to open a rusted nut or tight
bolt. Why?

It requires larger moment to open a rusted nut or tight bolt.
Since a long spanner has a longer moment arm, it multiplies
the applied force and produces greater turning effect. Hence, it
is easier to open a tight bolt with a long spanner.
Main points to remember

1. The devices which are simple in structure and make our works
easier and faster are called simple machines.

2. The ratio of load overcome by the machine to the effort applied
is called mechanical advantage.

3. The velocity ratio of a machine is defined as the ratio of distance
travelled by effort applied in a machine to the distance travelled
by load.

63 Times' Crucial Science Book - 9

4. There are six types of simple machines. They are: lever, pulley,
wheel and axle, inclined plane, screw and wedge.

5. A lever is a long rigid bar which is capable of moving about a
fixed point, called fulcrum.

6. A pulley is a round metallic or wooden disc having a grooved
rim along which a rope passes.

7. Basically, there are two types of pulleys: single fixed pulley
and single movable pulley.

8. Wheel and axle is a simple machine which is made of two
coaxial cylinders of different diameters.

9. Inclined plane is a simple machine because it makes our works

easier and faster

Exercise

1. Choose the best alternative in each case.

a. The mechanical advantage of a single fixed pulley is

i. 1 ii. 2 iii. 0 iv. Not fixed

b. A movable pulley

i. Multiplies force ii. Changes the direction of applied force

iii. Multiplies speed iv. All of these

c. Which of the following is not affected by friction?

i. MA ii. VR iii. Efficiency iv. All of these

d. What is the SI unit of moment of force?

i. N/kg ii. N/m2 iii. N/m iv. Nm

e. The velocity ratio of a wheel and axle is given by
iv. l/h
i. r/ R ii. L/E iii. R/r

2. Answer these questions in very short.

a. Define the terms load and effort in a simple machine.

b. What are the factors affecting the mechanical advantage of
a machine?

c. What is velocity ratio? What is its unit?

d. What is an ideal machine?

e. Is it possible to have an ideal machine in our daily life?

f. A machine is labelled with 60% efficiency. What does it
mean?

g. Write down the formula to calculate the velocity ratio of a
wheel and axle.

Times' Crucial Science Book - 9 64

h. What is a wheelbarrow?

i. Derive the relationship between MA, VR and efficiency.

j. What is the advantage of using single fixed pulley although
it does not multiply force?

3. Define:

a. Effort b. Load c. Effort distance d. Load distance

e. Efficiency f.Mechanical advantage g. Input work

h. Output work i. Lever j. Pulley

4. Differentiate between:

a. Pulley and wheel and axle

b. Screw driver and jack screw

5. Give reasons:

a. The efficiency of a simple machine can never be 100%.

b. The velocity ratio of a single movable pulley is 2.

c. The hilly regions have winding roads.

d. Wheel and axle is regarded as a continuous lever.

e. It is easier to open a tight bolt with a spanner having a long
handle.

f. A tall tree has a greater possibility of breaking than a short
one in a storm.

6. Answer these questions:

a. What is a lever ? Give two examples each of three types of
levers.

b. Give examples of any six simple machines used in your
daily life and classify them.

c. Why is an inclined plane considered as a machine?

d. What is wedge? Give examples.

e. How do you calculate MA and VR in a wedge?

f. What is the law of moment?

7. Solve the following numerical problems:
a. In a first class lever of length 1m, a pivot is placed at a

65 Times' Crucial Science Book - 9

distance of 20cm from a load of 400N. If the effort used is
200N, calculate

(i) MA (ii) VR and (iii) Efficiency

b. A block and tackle consisting of 6 pulleys is used to lift a

load of 300N with an effort of 75N. Calculate the MA, VR

and efficiency of the machine.

c. A truck of mass 10,000kg is moving through a sloppy road

of length 20km with the help of 5000N force. If the truck

climbs the vertical height of 200m and its efficiency is 80%,

calculate the additional mass that can be carried by the

truck.

d. A wheel and axle arrangement having the wheel of radius

20cm and the axle with radius 10cm can lift a load of 150N

with an effort of 90N. Calculate MA, VR and η .

e. If a lever lifts a load four times the effort applied and the

effort distance is 5 times the load distance, calculate its

efficiency.

f. Calculate the value of ‘E’ from the diagram.

50 cm 20 cm

E=? 50N

g. Calculate the value of ‘L’ from the following diagram.

50 cm 40 cm

30 cm
L=? 40N 30N

Answers 7. a. 2,4,50% b. 4,6,66.67%c. 30000kg

d.1.67,2,83.5%e. 80% f. 20 N g. 48 N

Project Work

Visit the carpenter’s workshop nearby your home or school. What kinds of
simple machine does he use and for what purpose? Ask him or observe yourself
and complete the given table:

Name of simple machine Type of simple machine Function / Utility

Times' Crucial Science Book - 9 66

Chapter

4 Work,Energy
and Power
James Watt
He is known for the discovery of steam engine,
separate condenser, parallel motion, etc.
Estimated Periods : 6

ObjAetctthiveeesnd of the lesson, students will be able to:

• define work, energy and power with their units;
• define energy and identify various forms of energy;
• interpret relations among work, energy and power;
• distinguish between work, energy and power;
• solve simple numerical problems related to work, energy and power.

Mind Openers

• Why do you feel hungry when you work hard?
• Are you doing any work while reading books?
• How many forms of energy do you know? What are they? Discuss.

Work

Various activities are done in everyday life. Ploughing field, chopping
woods, reading books, playing games, writing, walking, carrying
loads, etc are such activities. These all activities are called works
in general sense. But, all these activities are not work in science. In
science, for any activity to be work, force is to applied to any object
and the object should be displaced in the direction of force.

Thus, work is said to be done when a force is applied on a body and
the body moves in the direction of the force applied. It is calculated
as the product of force applied and the displacement of body in the
direction of the force.

Mathematically,

Work = Force × displacement (in the direction of force)

W=F×d

The SI unit of work is Newton meter (Nm) or Joule (J). In CGS
system, it is measured in erg.

67 Times' Crucial Science Book - 9

From the above formula, it can be said that two conditions are
needed for the work to be done. They are:

i. force must be applied on an object and
ii. the object must be displaced in the direction of force.

If any one of the above conditions is not fulfilled, no work will be
done. If a porter carries a heavy load on his head and stands for one
hour, the work done will be zero Joule. This is because there is no
displacement.

One Joule work

We have,

W=F×d

If F = 1 N and d = 1 m then W = F × d = 1 × 1 = 1 Joule

Thus, One Joule work is defined as the amount of work done when 1
Newton force displaces a body through 1 meter in its own direction.

Types of work

It is of two types. They are:
i. Work against friction
ii. Work against gravity

Work against friction

When a body moves over another

body, a type of force is created Effort

between surfaces of these two

bodies in contacts which opposes the

motion. Such opposing force is called

friction. When force is applied to a

body and the body moves opposite

to the direction of the friction, the

work done is called work against

friction. For example, when we push

a body, friction opposes the motion Friction
of the body, i.e. direction of friction

is opposite to the direction of our

force. When our force is sufficient to overcome friction, the body

moves against the direction of friction. Here, work done is the work

against friction.

Times' Crucial Science Book - 9 68

Solved Numerical Problem 4.1

A man pushes a load of 500 N through a distance of 15 m. Calculate the
amount of the work done. Mention the type of work done in this case.

Solution,

Force (F) = 500 N

Displacement (d) = 15 m

Work (W) =?

We have,

W = F × d = 500 × 15 = 7500 Joule

∴ The amount of work done is 7500 Joule. The work done in this case is
work against friction.

Work against gravity
Gravity is the force by which everybody is
pulled by the earth towards its centre. When
force is applied to a body against the gravity,
the work done is called work against gravity.
For example, when you lift a load from the
ground, the force is applied against the gravity
and the load is lifted against gravity.

Solved Numerical Problem 4.2

A man lifts a load of 50 kg to a height of 20 m. Calculate the amount of
work done. Mention the type of work done in this case. [g = 10m/s ].
Solution:

Force (F) = mg = 50 × 10 = 500 N
Displacement (d) = 20m
Work (W) = ?
We have,
W =F×d

= 500 × 20
= 10,000 Joule
The amount of work done is 10,000 Joule and the type of work is work
against gravity.

69 Times' Crucial Science Book - 9

When a body moves in an inclined plane, C
B
work done is both work against friction

and work against gravity. It is because, F
d

the body is neither moving horizontally Load
Aθ
nor vertically only.

In this situation,

Work against friction is calculated by using a formula,

Work against friction

Wf = Force × horizontal displacement
= F × AB

= F × dcosq

∴Wf = Fdcosq
Work against gravity is calculated by using a formula:

Work against gravity

Wg = Force × vertical displacement
= F × BC

= F × dsinq

∴ Wg = Fdsinq
Here,

Total work done = work against friction + work against gravity

= Fdcosq + Fdsinq

∴ WT = Fd (Cosq + Sinq)

Solved Numerical Problem 4.3 C

Calculate the:

i. work done against friction 50kg 20m
ii. work done against gravity

iii. total work done when a body of A 30° B

mass 50 kg is pulled through

an inclined plane of length 20 m which is inclined to an angle

of 30° with horizontal plane.

Solution: Length of the plane (d)=20m

Angle of inclination (q)=30°

Force(F)= 50 × 10=500N

We have,

Work against fricition(Wf ) = Fdcosq

Times' Crucial Science Book - 9 70

Again, = 500 × 20 × Cos30°
Work against gravity(Wg ) √3

Total work done (WT )= Wf + Wg = 500 × 20 ×
2

= 5000√3 Joule

= Fdsinq
= 500 × 20 × Sin30°

1
= 500 × 20 ×

2
= 5000Joule
= 5000√3 + 5000Joule
= 5000(√3 + 1) Joule

Energy

All living things need food to survive. Food is the source of energy.
Energy is used by them for carrying out various activities. Similarly,
vehicles, machines, engines, etc also need energy to run. They get
energy from fuels such as petrol, diesel, coal, etc. The appliances
like lamp, radio, television, telephone, etc also work with the help
of energy. No work can be done without energy.

Thus, energy can be defined as the capacity of doing energy. Its SI
unit is Joule. It is also measured in calorie. (4.2 J = 1 calorie)

Forms of energy

There are various forms of energy. They are:

i. Chemical energy ii. Mechanical energy

iii. Electrical energy iv. Magnetic energy

v. Heat energy vi. Sound energy

vii. Light energy viii. Nuclear energy

i. Chemical energy

Different substances like foods, coal, petrol, diesel, firewood, etc
store energy. When those substances undergo chemical change, such
energy is released. This form of energy is called chemical energy.

The energy stored in a body which is released during chemical
change occurring in it is chemical energy. Chemical energy of petrol,

71 Times' Crucial Science Book - 9

diesel, coal, firewood, etc is released in the form of heat, light or
sound when they are burnt.

ii. Mechanical energy

The energy possessed by a body by virtue of its position, configuration

or motion is called mechanical energy. It is of two types:

a. Kinetic energy b. Potential energy

a. Kinetic energy (KE)

The energy possessed by a body due to its motion is called kinetic
energy. A flying bird, a moving car, running vehicle, flowing water,
a bullet fired from a gun, a rolling stone, etc contain kinetic energy.
Kinetic energy of a body is calculated by using a formula

∴ KE = 1 mv2
Where, m = ma2ss of the body and v = speed of the body

Activity 4 .1 To study the factors affecting kinetic energy of an object

Materials required:

A cricket ball, a tennis ball, etc.

Procedure:
1. Tell your friend to take a cricket ball and throw it towards you.

Catch the ball.
2. Tell him to repeat the same activity with more speed of the ball.
3. Now, tell him to take a tennis ball and throw it towards you.

Catch the ball
4. Tell him to repeat the activity of step ’iii’ with more speed. What

do you observe?

Observation:
When the speed of the cricket ball is increased, it becomes more
difficult to catch. It is due to more kinetic energy of the ball which
is caused due to increased speed. To catch the cricket ball is more
difficult than to catch the tennis ball even though both balls have
equal speed. It is due to more kinetic energy of the cricket ball due
to its more mass.

Conclusion:

The kinetic energy possessed by a body depends upon mass and
speed of the body. The more the mass and speed of the body, the
more the kinetic energy.

Times' Crucial Science Book - 9 72

Derivation of formula of Kinetic Energy

u=0 a v
F m m

s

Suppose a body of mass m is at rest state ( u = 0). When a force F is
applied to it, it moves with an acceleration a. It travels a distance s
when its final velocity becomes v.

The work done on the body by the force ’F’ is calculated as:

Work done = Force × displacement

or, W = F × S

or, W = m × a × s …………… (i)

According to equation of motion,

v2=u2+2as

or, v2=0+2as

s= v2 …………… (ii)
2a

Substituting the value of 's' from equation (ii) in equation(i)

W = m × a × v2
2a

∴W= 1 mv2
2

The kinetic energy gained by the body is due to the force applied.
Thus, the kinetic energy of the body is equal to the work done by
the applied force.

∴KE of the body = Work done

1 Times' Crucial Science Book - 9
∴ KE = mv2

2
73

Solved Numerical Problem 4.4

If a bicycle of weight 20kg is moving with a speed of 10m/s, what is its
kinetic energy?
Solution: Given,

Mass of bicycle(m)=20kg
Speed(v)=10m/s
Kinetic energy(KE)=?
Using the relationship,
11
KE = mv2 = × 20 × (10)2 = 1000J
22
Thus, the kinetic energy of the bicycle is 1000 Joule.

b. Potential energy (PE)

Energy possessed by a body by virtue of its position or configuration

is called potential energy. Stretched rubber, stretched bow,

compressed spring, leg lifted to kick a ball, water stored in a dam,

a body at a height, etc have potential energy. Stretched rubber,

compressed spring, etc have PE due to change in configuration

whereas water stored in a dam, a body at a height, etc have PE due

to height. Potential energy of a body at a certain height from the

ground is calculated by using a formula

PE = mgh m

Where h
m = mass of the body

g = acceleration due to gravity (g = 9.8 m/s2) m
h = height from the ground

Derivation of formula of potential energy

Suppose, a body having mass m is lying on the ground. Let the body
is lifted to a height h in vertically upward direction. To lift it, force
mg is required.

Now, the work done is given by

Work done = Force × displacement

W = F × d or, W = mg × h ∴ W = mgh

Times' Crucial Science Book - 9 74

This work done is stored in the body in the form of potential energy.
This potential energy is called gravitational potential energy.

∴Gravitational potential energy = mgh

∴PE = m × g × h
Solved Numerical Problem 4.5

If a rice sack of weight 50kg is lifted above ground through a height of
15m, What is the potential energy stoned in the sack? (Given, g=10m/s2)

Solution: Given,

Mass of sack(m)=50kg

Height(h)=15m

Acceleration due to gravity(g)=10m/s2 15m
Potential energy(PE)=?

We know that,

PE= m×g×h = 50×10×15 = 7500J. 50kg
Hence, the potential energy stoned in the sack is 7500J

iii. Electrical energy

The energy which is produced due to the flow of electrons through a
conductor is called electrical energy.

Electrical energy is the most essential energy in modern days.
Devices like computer, television, radio, fridge, fax, telephone,
calculators, etc use electrical energy. Electrical energy can be easily
converted into other forms of energy. Dry cell, dynamo, hydro-power
station, solar cell, etc are the sources of electrical energy.

iv. Magnetic energy

The energy possessed by a magnet is called magnetic energy. A
conductor carrying electricity also has magnetic energy. Magnetic
energy is used in dynamo or generator to produce electricity. It is
used in electrical and electronic devices such as radio, television,
loudspeaker, microphone, motor, electric bell, etc.

v. Heat energy

Every substance is composed of tiny particles called molecules.
These molecules are always vibrating. Thus, every molecule has
kinetic energy. The sum of kinetic energy of all the molecules of a
substance is heat energy.

75 Times' Crucial Science Book - 9

The more the speed of vibration of molecules, the more is the heat
energy contained by the body. Heat energy is used to cook food, run
vehicles, dry clothes, etc.

vi. Sound energy

Sound is a form of energy which is produced due to vibration of
an object. Sound transmits in the form of longitudinal wave. An
electric bell, temple bell, a radio, a television, etc produce sound.

vii. Light energy

Light is a form of energy which produces sensation of vision. When
a body is extremely hot, it emits radiation. Light is also a radiation.
Light energy is used by plants during photosynthesis and stored
in food in the form of chemical energy. Light energy is also used to
produce electricity in photo cells. The sun, electric bulbs, burning
candle, etc are the sources of light.

viii. Nuclear energy (Atomic energy)

The energy contained in the nucleus of an atom is called nuclear
energy. Nuclear energy is released when a larger nucleus splits into
smaller nuclei or smaller nuclei fuse to form a large nucleus. The
process in which a larger nucleus splits into smaller nuclei along
with the release of large amount of energy is called nuclear fission
and the process in which smaller nuclei fuse to form a large nucleus
is called nuclear fusion.

Nuclear energy is used to make atom bomb, produce electricity, etc.
Energy is produced in the sun due to fusion of hydrogen nuclei into
a helium nucleus.

Transformation of energy

Energy exists in various forms. One form of energy can be converted
into other forms. The process of conversion of energy from one form
to another form is called transformation of energy. The process of
transformation of energy is very common in daily life. Some of the
common examples are as follows:
i. Electric bulb operates with electrical energy. Electrical energy

is converted into light and heat energy by the electric bulb.
ii. Electric heater produces heat by converting electrical energy

into heat energy.
iii. Loudspeaker converts electrical energy into sound energy.
iv. The chemical energy of a battery is converted into electrical

Times' Crucial Science Book - 9 76

energy when a radio is turned on. The electrical energy is again
converted into sound energy which we hear.
v. The chemical energy of food is used by humans for carrying
various activities. This chemical energy is converted into
muscular energy. The muscular energy converts into kinetic
energy while moving, sound energy while speaking, potential
energy while climbing trees, etc.

Chemical energy Muscular energy Kinetic energy
in food in human body while running

vi. Potential energy contained in water stored in a reservoir gets
converted into kinetic energy when it falls to rotate turbine in
hydropower stations. The rotating turbine operates generator
which converts kinetic energy into electrical energy.

Water collected in dam Rotation of turbine Generator
Potential energy Kinetic energy Electrical energy

vii. Electric fan converts electrical energy into mechanical energy.

Law of conservation of energy

When energy changes from one form to another, the energy of the
former form disappears and the energy in equal amount of later
form reappears. Thus, energy does not get lost. But, it changes its
forms only. Therefore, the total sum of all forms of energy in the
universe remains constant. This is called conservation of energy.
The law of conservation of energy states that energy can neither be
created nor be destroyed but can only be changed from one form into
another.

For example, when a kerosene lamp burns, the amount of kerosene
in the lamp decreases. Here, the chemical energy of the kerosene
is converted into heat and light energy. The sum of heat and light
energy produced is equal to the amount of chemical energy used.

Relation between work and energy

Work and energy are very much related. A body can do work if it
has energy. When work is done by a body, it loses energy. The
amount of work done is equal to the amount of energy it lost.
Similarly, when work is done on a body, it gains energy. The work

77 Times' Crucial Science Book - 9

done is equal to the amount of energy gained. For example, when a
person lifts a body of mass m from the ground to a
height h , he does work against gravity. The work done
is calculated as,

Work done = F × displacement h
Work done = mg × h

∴ W = mgh

m

The work done on the body is mgh Joule. Here, mgh
Joule energy of the person is used. Thus, mgh Joule
of energy is decreased in the person’s body. But mgh Joule energy
is increased to that lifted body. When that body is on the ground,
total gravitational potential energy is 0 Joule. When it is lifted, the
gravitation potential is mgh Joule.

Thus, work done = Energy gained or lost.

Power
Suppose, Ram carries a load of 200 N to a distance 30 m in 50
seconds and Shyam carries the same load to the distance of 30 m in
30 seconds. Here, both Ram and Shyam do equal amount of work.
Each of them do 6000 Joule work. But the time taken by them is
different. Ram takes more time than Shyam to do equal amount of
work. In other words, Shyam does more work in each second than
Ram. Ram does 120 Joule work in each second whereas Shyam does
200 J work in each second. Hence, the power of Shyam is more than
that of Ram.
The rate of doing work is called power. In other words, the rate of
change of energy is called power. Its SI unit is Joule per second or
Watt.

Mathematically,

Power(P) = Work done W
∴P=
One watt power Time taken
t

W
P=

t

If W=1J, and t=1s,then P=1Watt ∴P=1Watt
1J

i.e.P =
1s

Times' Crucial Science Book - 9 78

Thus, a body is said to have One Watt power if it can do 1 Joule work
in 1 second. Horse power (HP), Kilowatt (KW), Megawatt (MW), etc
are bigger units of power.

746 Watt = 1 HP

1000 Watt = 1 Kilowatt

1000000 Watt = 1 Megawatt

If 100 Watt is written on an electric bulb, what does it mean?

100 Watt written on an electric bulb means that the bulb consumes
100 Joule electrical energy in 1 second and converts it into heat and
light energy.

Solved Numerical Problem 4.6

Deepta weighs 40 kg. He climbs a staircase of height 3 meter in 6 seconds.
Find his power.

Solution:

Mass (m) = 40 kg

Force (F) = mg = 40 × 10 = 400 N

Displacement (d) = 3 m

Time (t) = 6 s

Power = ?

We have,

W F×d = 400 × 3 = 200Watt
P= =
tt 6

∴Power of Deepta is 200Watt

Comparison of work, energy and power

Work Energy Power

1. It is the product 1. It is the capacity of 1. It is the rate of doing

of force applied and doing work. work.

displacement in the

direction of force.

2. Its SI unit is Joule. 2. Its SI unit is Joule. 2. Its SI unit is Watt.

79 Times' Crucial Science Book - 9

3. Its value does not 3. Its value does not 3. Its value depends

depend upon time. depend upon time. upon time taken to do

work.

4. Work is of two types. 4. Energy has several 4. It does not have any

They are work against forms. types.

friction and work against

gravity.

Learn and Write

1. A person standing for long time feels tired even though
he seems not doing work. Why?

When a person stands for long time, he is using his energy for
holding his body upright. Moreover, various internal works like
flow of blood, pumping of blood by heart, movement of lungs
and other organs, etc are taking place continuously. For all
these activities, energy is being used. Due to the use of energy,
the person feels tired even though he is standing only.

2. What will be the change in kinetic energy of a body
when its speed is increased 2 times?

Kinetic energy of a body having mass ’m’ and speed ’v’ is
calculated by using a formula

KE1 = 1 mv2..........................................(i)
2
When speed is increased two times, the kinetic energy will be

KE2 = 1 m(2v)2 = 1 ×4mv2 = 4× 1 mv2....................(ii)
2 22
Dividing equation (ii) by equation (i)

1
4× mv2
KE2 = 2
∴ KE2 = 4KE1
KE1
1
mv2
2

Thus, the kinetic energy increases by four times when
speed of a body is increases two times.

3. What conditions are necessary for work to be done?
The work is done if the following conditions are fulfilled:
a. Force must be applied to the body.

Times' Crucial Science Book - 9 80

b. The body must move through some distance in the direction of
force.

4. The power of an electric water pump of labeled as 5 HP.
What does it mean?

Horse Power (HP) is a unit of power and it is related to watt as follows:

1 HP = 746 Watt

∴ 5 HP = 5 x 746 = 3730 Watt

Hence, it means that the water pump can convert 3730 Joules of
electrical energy into kinetic and other forms of energy in one second.

5. An electric bulb is marked with 60W. What does it mean?

The mark 60W shows the power of the bulb. It means that the bulb
converts 100 joules of electrical energy in to heat and light energy in
one second.

Main points to remember

1. The product of force applied and displacement in the direction
of the force is called work.

2. When force is applied to a body and the body moves opposite to the
direction of friction, the work done is called work against friction.

3. When force is applied to a body against the gravity, the work
done is work against gravity.

4. Capacity of doing work is called energy.
5. The energy stored in a body which is released during chemical

change occurring in it is called chemical energy.
6. The energy possessed by a body due to its motion is called

kinetic energy.
7. The energy possessed by a body by virtue of its position or

configuration is called potential energy.
8. The process of conversion of energy from one form to another is

called transformation of energy.
9. The law of conservation of energy states that the energy can

neither be created not be destroyed but can only be changed
from one form to another.
10. The rate of doing work is called power.

Exercise
1. Choose the best alternative in each case.

a. In which case is work done?

81 Times' Crucial Science Book - 9

i. Sitting of a watchman at the gate to safeguard a building.

ii. Reading a book by sitting in a chair.

iii. Giving lecture to a class by standing in front of the class.

iv. None of the above.
b. One joule energy is equivalent to the work of

i. 1 Ns ii. 1 Nm iii. 1 N/m iv. 1 Nm2

c. A burning candle possesses

i. Chemical energy ii. Heat energy

iii. Light energy iv. All of these

d. A bread has

i. Kinetic energy ii. Chemical energy

iii. Heat energy iv. None

e. Which sentence is incorrect about power?

i. It is the rate of work done per unit time.

ii. Power is a vector quantity.

iii. Power is scalar quantity.

iv. An electric device labeled 2 HP has more power than the device
labeled 500W.

2. Answer these questions
a. What are various forms of energy? Explain any two of them.
b. Which form of energy is contained in following objects.
Kerosene, water stored in a reservoir, red hot iron, flowing
water, dry cell, stretched rubber, leg lifted to kick a ball,
magnet, glowing bulb.
c. Define nuclear fission and nuclear fusion with examples.
d. What will be the change in kinetic energy of a body when
its velocity is increased by three times?
e. What do you mean by the statement that the power of a
bulb is 60 watt?

3. Define:

a. Work b. Energy c. Power

d. Kinetic energy e. Potential energy

4. Write formula for: b. Kinetic energy
a. Work

Times' Crucial Science Book - 9 82

c. Potential energy d. Power

5. Derive: b. PE = mgh
1

a. KE = mv2
2

6. Distinguish between:

i. Potential energy and kinetic energy

ii. Work and energy

iii. Energy and power

7. Name the devices which convert energy in the following ways:

a. Chemical into electrical b.Electrical into mechanical

c. Electrical into heat d. Electrical into light

e. Chemical into mechanical f. Light into electrical

8. Give reasons:
i. A person feels hungry even though he does not do any work.
ii. A flying bird has both potential and kinetic energy.
iii. A person cannot do more work than the energy he has.
iv. Two persons who do the same work may have different
powers.

9. Numerical problems
a. Calculate the work done when you lift a load of 50 kg
through a height of 6m.
b. How much work is done when a body of mass 80 kg is pushed
to distance of 2m?
c. A bullet of mass 50 g is moving with a velocity of 40 m/s.
Calculate its kinetic energy.
d. Calculate the energy stored in a body of mass 40 kg when it
is at a height of 30m.
e. How much energy is stored in 4m3 water collected in a reservoir
at a height of 50m. (Given, 1m3 water = 1000 kg)
f. Calculate the power of a crane if it can lift a load of 2400 N
to a height of 10 m in 15 seconds.
g. An engine supplies 40,000 J of heat energy per minute.
Find the power of the engine in horse power.
h. A stone is thrown upward with a kinetic energy of 10 J. If it
goes up to a maximum height of 5 m, find the initial velocity
and mass of the stone.

i. If power of an engine is 600 W, how much time will
it take to lift a box of 20 kg by a distance of 10 m?

83 Times' Crucial Science Book - 9

Answers 9. a. 3000 Joule b. 1600 Joule c. 40 Joule
f. 1600 Watt g. 0.8936 HP
d.1176 Joule e. 1960000 Joule

h. 10m/s, 0.2 kg i. 3.33 s

Project Work

1. Measure your weight.
2. Count the number of steps and measure height of each step of

staircase of your house.
3. Measure the time you take to run over all the steps of the staircase.

Calculate work done and your power by using the results of above
activity.

Glossary
Overcome: defeat,overpower, lift a load
Gravity: the force with which the earth pulls every other object

toward its centre
Compresed: pressed tightly together
Configuration : form, shape
Posess: have, have ownership
Reservoir: a large collection or storage of water
Upright: erect, vertical, straight up

Times' Crucial Science Book - 9 84

Chapter

5 Light
Willebord Snell
He is known for the Snell's Law.
Estimated Periods : 9

ObjAetctthiveeesnd of the lesson, students will be able to:

• explain the laws of refraction with examples;

• explain the causes of total internal reflection and their effects;

• define dispersion of light with diagrams;

• explain the structure of spectrum;

• explain the uses of light waves of different frequencies.

Mind Openers

• How is it possible to see things?

• Why does refraction of light occur?

• What are various types of light waves? Discuss.

Introduction
Light is invisible itself but makes the other things visible on which it
falls. It is defined as the form of energy which produces the sensation
of vision. In physics, there is a separate branch to study light and
related phenomena. The branch of physics which deals with the
study of light and its phenomena is called optics.
Refraction of light
Light travels with different velocities in different media. It travels
with maximum velocity in vacuum or air. But, it has less velocity
in water as compared to air. Again it has less velocity in glass as
compared to water. The velocity of light in air, water and glass is
3×108m/s, 2.2×108m/s and 2×108m/s respectively.
Light travels in a straight line as long as it is travelling in the same
medium. But, when light passes from one medium to another, it
bends at the junction of two media. This bending of light is due
to the change in its velocity. The process of bending of light while
passing from one optical medium to the another is called refraction
of light.

85 Times' Crucial Science Book - 9

In the figure, A M Air Q
AO = Incident i Glass
Refracted ray ray, OB =
MN = Normal P o B1 R
interface r C
at air-glass

M’N’ = Normal at gas-air N M1
interface

∠AOM = i = Angle of incidence S Air B
∠BON = r = Angle of refraction e

BC =Emergent ray Refraction of Light

∠CBN’ = e = Angle of emergence

PQRS = Glass slab N1

OB’ = Original path of the

incident ray.

The medium through which light travels is called optical medium.
The optical media can be classified into two types: rarer medium
and denser medium. The medium in which the velocity of light is
more is called rarer medium. On the other hand, the medium in
which the velocity of light is less is called denser medium. The terms
rarer and denser are the relative terms and the same substance
may act as a rarer as well as a denser medium. For example, in
the pair of air and water, air is rarer and water is denser medium.
It is because the velocity of light in air is more than that in water.
But, for the pair of water and glass, water is a rarer and glass is a
denser medium.

Cause of refraction

As stated earlier, light travels with different velocities in different
media. Its velocity is more in optically rarer medium and less in
denser medium. When light passes from optically rarer to denser
medium, it travels with slower velocity as compared to that in
rarer medium. The light bends due to the change in velocity while
entering from one optical medium to the another. Hence, the change
in velocity of light while passing from one optical medium to the
next is the cause of refraction of light.

Laws of refraction

The refraction of light obeys the following laws:
1. The incident ray, refracted ray and normal all lie at the same
plane.

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2. The ratio of sine of angle of incidence to the sine of angle of
refraction for a given pair of media is constant, i.e,

Sin i = µ (a constant, and is read as myu)

Sin r

The constant (µ) is known as refractive index of the medium. This
law is popularly known as Snell’s law.

The Snell’s law can also be stated in the following ways:
a. When a ray of light travels from rarer to denser medium, it
bends towards the normal.
b. When a ray of light travels from denser to rarer medium, it
bends away from the normal.
c. The ray of light does not bend if it passes through the
normal. It means that if a ray of light incidents on a surface
perpendicularl, it does not bend.

A M B

i Air Air o r
o
i Glass
Glass

rA

NB (b) (c)
(a)

Refractive index

The ratio of the velocity of light in vacuum or air to the velocity of
light in the given medium is called refractive index of the given
medium. Its value is constant for a given pair of media and is
denoted by µ.

Veloccity of light in vacuum or air
µ = Velocity of light in given medium

∴ µ = C
V

The refractive indices of some of the common optical media are
given in the table below:

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SN Optical Medium Refractive Index SN Optical Medium Refractive Index

1. Air 1.00 6. Alcohol 1.36

2. Water 1.33 7. Kerosene 1.39

3. Glass 1.5 8. Paraffin 1.44

4. Diamond 2.24 9. Glycerine 1.47

5. Ice 1.31 10. Ruby(Precious stone) 1.76

These values of refractive indices are calculated with respect to air.
Solved Numerical Problem 5.1

Calculate the velocity of light in alcohol if the refractive index of alcohol is
1.36 (Given, velocity of light in air (c) = 3×108m/s).

Solution

Given, Refractive index (w) = 1.36

Velocity of light in air (C) = 3×108m/s

Velocity of light in alcohol (V) = ?

We know that,

µ=C C 3×108 = 2.2×108m/s
or, V = µ =
V
1.36

Real and apparent depth Real depth

If you don’t have proper swimming skills, Apparent depth
it is unwise to jump into the swimming
pool seeing its apparent depth only. It is
because, we cannot see the actual depth
of a swimming pool while observing from
outside.

When the rays of light coming from an object at the bottom of the
pool travel from water (denser medium) to air (rarer medium),
the rays of light bend away from normal. If the refracted rays are
produced backwards, they meet the normal ray above the actual
position of the object. Thus, the bottom or any other object appears
above its actual depth. Such depth is called apparent depth.

The actual depth of an object from the surface of water is called
real depth, while, the virtual depth at which an object appears due
to the refraction of light is called apparent depth. The ratio of real

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depth to the apparent depth for a given pair of media is constant
and is the measure of refractive index (µ).

Thus, the refractive index may also be defined as the ratio of real
depth to the apparent depth.

Solved Numerical Problem 5.2

Calculate the apparent depth of a fish at the bottom of a pond if the real
depth of pond is 20m and refractive index of water is 1.33.

Solution:

Given,

Real depth (d) = 20m

Refractive index (w) = 1.33

Apparent depth (d’) = ?

According to formula,

Real depth 20
µ= or, 1.33 = Apparent depth

Apparent depth

20
or, Apparent depth = = 15m

1.33

Hence, the fish appears at the depth of 15m from the water surface.

Examples of refraction of light

We experience several events in our daily life due to the refraction
of light. Some of the examples are given below:

1. A straight stick appears bent if it is partially immersed
in water.

When a stick is partly
immersed in water, it appears
bent due to refraction of light.
The rays of light coming from
the immersed portion of the
stick pass from the water to
the air by bending away from
normal. Thus, the immersed
portion of the stick seems
to be raised up (as in the figure). But the light rays from the

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portion of stick outside the water come to the observer’s eyes
without bending. Hence, the stick appears bent at the air water
interface.

2. Stars twinkle at night

If you look at the clear sky at night,
you will observe the twinkling
of stars. The reason behind this
observation is the refraction of
light coming from the stars. As
you have studied in your previous
grades that the temperatures of
different layers of atmosphere are
different. The temperature changes continuously. This changes
the density of the layers continuously. The light coming from
the stars passes through the layers of varying density and
changes its direction of path due to refraction. Since the density
of layers changes continuously, the uneven refraction of light,
in turn, occurs continuously. These processes make the stars
twinkle at night.

Critical angle

When light passes from a denser medium to a rarer medium, it
bends away from the normal. In such case, the angle of incidence is
less than the angle of refraction. The angle formed by incident ray
with normal is called angle of incidence whereas the angle formed
by refracted ray with the normal is known as angle of refraction.
If the angle of incidence is increased, the corresponding angle of
refraction also increases. At a particular value of angle of incidence
in the denser medium, the corresponding angle of refraction in the
rarer medium is 90°. This value of angle of incidence is known as
critical angle.

B N N

Air r Air Or B2 Air O r B3∟
O
i Glass C Glass
i Glass

A A2 A3

MM

(a) (b) (c)
90
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Thus, the value of angle of incidence in the denser medium for which
the corresponding value of angle of refraction in the rarer medium is
90° is called critical angle. The critical angle is formed in the denser
medium as an angle of incidence for which the angle of refraction is
90° in the rarer medium.

The critical angle is denoted by C. It can be calculated by using a

formula:

1 1
µ
( )SinC = Refractive index or, C= sin−1

The critical angle of a particular medium is constant. The critical
angles of some optical media are given below:

SN Optical Medium critical angle SN Optical Medium critical angle
6. Paraffin 44°
1. Water 49° 7. Turpentine 43°
8. Glycerine 43°
2. Glass 42° 9. Flint glass 38°
10. Quartr 35°
3. Diamond 24°

4. Ice 50°

5. Alcohol 48°

Solved Numerical Problem 5.3

Calculate the critical angle of diamond if its refractive index is 2.24.

Solution:

Given,

Refractive index (µ) = 2.24

Critical angle (C) = ?

We have,

( ) ( )C= sin−11 1
µ or, = sin−1 2.24 = 24°

∴ Critical angle of diamond is 24°.

Total internal reflection

When light passes from a denser to a rarer medium, it bends away
from the normal. In this situation, angle of refraction is more than
the angle of incidence. According to Snell’s law, when angle of
incidence is increased, angle of refraction also increases.

When the angle of incidence is made greater than the critical angle,

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the whole light is reflected back into the same medium without any
refraction, obeying the laws of reflection. This process is known as
total internal reflection.

N N

Air O r B1 Air O r B2

(a) i Glass (b) i Glass

A1 A2
M M

NN

(c) Air O r (d) Air O Glass

C Glass A4 B4
M
A3
M

Thus, the process of returning of light into the original denser
medium, when the light passes from a denser to rarer medium with
the angle of incidence greater than the critical angle is called total
internal reflection.

Conditions for total internal reflection
1. Ray of light must pass from optically denser to rarer medium.
2. The angle of incidence must be greater than the critical angle.

Examples of total internal reflection

1. Mirage

Mirage is an optical illusion in which a
pool of water is seen in hot desert which
is produced by the phenomenon of total
internal reflection.

Mirage can be observed in hot desert
region. In the desert, the sand is
heated faster and the layer of air
in contact with sand becomes hot. The hot air expands and its
density decreases. But the upper layers are comparatively cooler
and denser than those below them. Due to this, the ray of light

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coming from the object is refracted for many times. For instance,
a ray of light coming from the top of a plant passes from denser to
rarer layers and is refracted away from normal in every step. This
increases the angle of incidence at every refraction and ultimately a
stage is reached where the angle of incidence becomes greater than
the critical angle. This results in the total internal reflection of the
incident ray, which then reaches the observer’s eyes. Due to this,
the observer views the inverted image of the plant as if reflected
in pond or lake. But as the observer reaches nearby the plant, its
image disappears.
2. Optical fibre or light pipe
Light always travels in a straight line. But it can be made to travel
in a curved path using the phenomenon of total internal reflection.
A bent tube through which light travels in a curved path is called
light pipe. Optical fibre is also a form of light pipe. An optical fibre is
a very thin, flexible glass or quartz rod which can carry information
in the form of wave by the process of total internal reflection.

In an optical fibre, a glass of high refractive index is coated with thin
layer of glass of low refractive index. A ray of light entering from
one end of the optical fibre strikes the interface between two glass
surfaces at an angle greater than critical angle. Thus, the entering
ray of light suffers multiple total internal reflections and travels
along the fibre.
Light pipes are used by doctors in endoscopy. The endoscopy is the
practice of viewing internal parts of a patient such as stomach using
a light pipe.
The optical fibres are becoming more popular in modern days. The
uses of optical fibres can be summarized as:

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a. It is used in communication as high speed internet cable.
b. It is used to study about blood vessels, arteries and tissues.
c. It is used for sending video signals.

3. Sparkling of diamond

Since the refractive index of diamond is high, its critical angle is
small. The faces of diamond are cut in such a way that a ray of light
entering into the diamond always strikes it with an angle greater
than the critical angle. Thus, the ray of light suffers total internal
reflection at each face. The light rays come out from a few points as
bright emergent rays. These rays make diamond sparkle.

4. Totally reflecting prism P

A prism is a wedge shaped block of glass 45° B
A 45°

having three rectangular faces and two

triangular faces. A totally reflecting

prism is an isosceles right-angled glass 90° Q

prism. In the figure, PQR is a totally 45°
reflecting prism in which ∠Q = 90°, D 45°
∠P = ∠R = 45° and PQ = QR. In such
prism, the rays of light from an object C
are incident normally on the face PR of 45°

R

the prism. These rays pass straight and incident on face PQ with

45° as the angle of incidence. This angle of incidence (i.e. 45°) is

greater than the critical angle (i.e. 42°) of glass. Hence, the light

rays suffer total internal reflection. The same process is repeated

on face QR and the rays emerge from the prism forming the image

of the object.

A totally reflecting prism deviates the light through 180° similar to

a plane mirror. These prisms are used instead of plane mirrors in

binoculars and telescopes. It is because a prism produces a single

image but a plane mirror produces multiple images.

Prism a
A prism consists of two refracting faces and a bc

base. The two faces of a prism through which hh

light passes are called refracting faces. The

angle between these two refracting faces a
is called angle of prism. The face of prism bc
opposite to the angle is its base. Some prisms

are shown below:

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Dispersion of light

In rainy days, sometimes, we see a
rainbow (consisting of a beautiful
pattern of seven colours) in the direction
opposite to the sun. The seven colours of
rainbow are due to splitting of white rays
of sun light by the tiny water droplets in
the atmosphere. The colour pattern of
rainbow can be obtained when a narrow
beam of sunlight is passed through a
prism. It is due to the splitting of light rays by a prism. This process
is called dispersion.

The process of splitting of a white ray of light into its constituent
seven colours is called dispersion of light. The band of seven colours
obtained from a white ray of light due to dispersion is called spectrum
of light. It contains violet, indigo, blue, green, yellow, orange and
red colour in the respective order.

Cause of dispersion of light

In vacuum or air, the rays of all colours of white light travel with
the same speed (i.e, with the speed of 3×108m/s). When the optical
medium changes, the speed of rays of different colours of light
changes. Thus, the different colours of light move with different
speeds through a denser medium.

Light travels in the form of wave. The speed of a light wave is the
product of its frequency and wavelength, i.e.

V= f × l

Where, V = Speed of light, f = frequency and l = wavelength

When light enters from one medium to another, its frequency is
unaffected but its wavelength changes. The different colours of light
have different wavelengths. For example, the red colour has the
longest wavelength (8×10-4mm) and viole colour has the shortest
wavelength (4×10-4mm). The wavelengths of indigo, blue, green,
yellow and orange increase in order from violet to red. Similarly, the
different colours of light have different frequencres. For example,
frequence of red light is 3.75 ×1014 Hz and that of violet light is 7.5
×1014 Hz.

The relation above shows that the speed of light increases if its

95 Times' Crucial Science Book - 9

wavelength increases. Thus, the red colour of light has maximum
speed (due to long wave length) and hence it slows down less and
bends the least while entering into a denser medium. Similarly,
the violet colour has the least speed (due to short wave length)
and hence slows down the most and bends the most. The rest of
the colours of light bend between the red and violet due to their
intermediate wavelengths.

Thus, we can conclude that the dispersion of light is due to the
variation in the wavelength or speed when it enters from one optical
medium to another.

Recombination of spectrum of light

We have studied that when light changes medium, its wavelength
changes and dispersion occurs. But when light passes from air to
glass slab, we observe only refraction but not dispersion of light.
Why is it so?

Before thinking answer to this question, let’s do an activity. Take
two prisms of same shape, size, refracting angles and made up of
same materials, i.e. pure glass or plastic. Arrange these prisms
as shown in the figure. Now, pass a white ray of light by making
an angle in the first prism. The prism causes the dispersion of
the light ray. As the dispersed rays pass through the next prism,
they combine to form the white ray again. Thus, a single white ray
emerges from the second prism.

This is the reason why a glass slab cannot split the ray of light
into its constituent colours. A glass slab is made by combining two
prisms. Similarly, we can make two prisms by cutting glass slab
along its diagonal.

Electromagnetic waves

The waves which do not require any material medium for their
propagation and can travel even through vacuum are called

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