Approved by Government of Nepal, Ministry of Education, Curriculum Development
Center (CDC).
Blooming
SCIENCE
&
ENVIRONMENT
Book
9
Authors
Raj Kumar Dhakal
Purushottam Devkota
Shubharambha Publication Pvt. Ltd.
Kathmandu, Nepal
Published by:
Shubharambha Publication Pvt. Ltd.
Kathmandu, Nepal
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Blooming Science Book-9
Authors : Raj Kumar Dhakal
Purushottam Devkota
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Edition : 2077
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Preface
The series Blooming Science has been brought out as an indispensable resource
for school level students and has intended to provide concise and comprehensible
explanation of key concepts, facts and principles across science disciplines.
Organized around the National Science curriculum prescribed by Curriculum
Development Centre, Sanothimi, Bhaktapur, the series presents solid overviews of
the most commonly encountered school science topics with sound academic and fun
activities.
The clear and accessible definitions, concise language, helpful diagrams and
illustrations and other science activities offered in this series will nonetheless help
teachers understand science concepts to the degree to which they can develop
rich and exciting inquiry approaches to exploring these concepts with students in
the classroom. As the series has been brought out considering the age and other
psychological factors of children, the learning materials in this series appeal to the
sense of the children and they are related to the world of young learners. Activities
with varieties of questions in this series are meant to assess and evaluate the level of
students’ inquisitiveness.
As each unit begins with its objectives and estimated teaching periods which help
teachers to complete the course in time. Moreover, each lesson in the series ends
with Let's Learn, Points to Remember and Boost Up Exercises; these two sections
are meant to provide good review to students and enhance their ability to solve the
exercise questions. Each lesson has Multiple Choices Questions, Project Work that are
meant to arouse more creativity and interest in the students for better understanding
and adjustment with their scientific world.
We are grateful to students, parents and principals who shared their valuable
suggestions in materializing this series. Any constructive suggestions and
recommendations for the betterment of this series will be highly acknowledged.
AUTHORS
Contents
PHYSICS
1. Measurement............................................................................................................ 7
2. Force and Motion................................................................................................... 15
3. Machines................................................................................................................. 38
4. Work, Energy and Power....................................................................................... 58
5. Light......................................................................................................................... 75
6. Sound...................................................................................................................... 88
7. Electricity and Magnetism................................................................................... 105
CHEMISTRY
8. Classification of Elements................................................................................... 123
9. Chemical Reactions............................................................................................. 143
10. Solubility............................................................................................................... 152
11. Some Gases.......................................................................................................... 168
12. Metals.................................................................................................................... 188
13. Carbon and Its Compounds................................................................................ 197
14. Water...................................................................................................................... 208
15. Materials used in Daily Life................................................................................. 216
BIOLOGY
16. A. Classification of Living Things....................................................................... 221
B. Life Cycle of Mosquito.................................................................................... 241
17. A. Adaptation of Organisms................................................................................ 248
B. Micro Organisms............................................................................................. 257
18. Body Systems....................................................................................................... 266
19. Sense Organs....................................................................................................... 290
20. Evolution............................................................................................................... 300
21. Nature and Environment...................................................................................... 310
ASTRONOMY & GEOLOGY
22. Natural Disasters.................................................................................................. 322
23. Green House......................................................................................................... 330
24. The Universe......................................................................................................... 336
Practical Work sheet............................................................................................351
Specification Grid................................................................................................. 353
Model Questions..................................................................................................354
List of Video Experiments...................................................................................357
Chapter MEASUREMENT
1
Learning Outcomes Estimated Periods: 3+1
On the completion of this unit, the students will be able to:
• define measurement and its importance.
• show the inter relation of fundamental and derived units.
• define fundamental units and derived units.
• define SI system of measurement with its types.
Measurement is a common term used in our daily life without which our daily life is incomplete.
We measure the length of clothes, mass of sugar, volume of kerosene, edible oil, temperature of
our body, etc. All these activities are related to the measurement.
When you go to a shop to buy potatoes and you will ask some quantities of potatoes such as 1
kilogram or 2 kilogram of potatoes to a shop-keeper, the shop-keeper uses a physical balance to
measure the quantity of potatoes and he/she keeps standard quantity (dhak) in one pan and the
potatoes in the another pan until the pans are balanced. If a teacher asks to you in a class room to
measure the length and breadth of science book, what will you do? Certainly you will use a ruler
to measure the length and the breadth of the book.
You will put your ruler/ scale side by side with the book edge and see the graduated values on the
scale. Here, what you have done is just the comparison. The scale has “Known fixed values” of
length and book length is unknown. This comparison is known as measurement
The comparison of an unknown quantity with known standard quantity is called the measurement.
The known quantity which is used as standard of measurement and in terms of which other
physical quantities of same kind can be expressed is called the unit.
In other words measurement is the process of determining the ratio of a physical quantity, such
as length, mass, time, temperature etc., to a unit of measurement, such as the meter, kilogram,
second or degree Celsius. For example, your height is 5 feet means your height is five times
greater than 1 foot, your weight is 55 kg means, your mass is 55 times greater than 1kg etc.
The science of measurement is called metrology.
1. Importance of Measurement
The measurement has a great importance in our daily life and some of the importance of
measurement are given below:
1. It is essential for selling and buying goods.
2. It is a must to perform scientific experiments.
3. It is a must to use medicine for proper treatment of diseases.
Blooming Science Book 9 7
2. Physical Quantity
While learning about objects and events we come across quantities like mass, length, time,
temperature, velocity, volume, momentum etc. These quantities are the physical quantities.
Those quantities which can be measured directly or indirectly are called the physical quantities.
The physical quantities may be fundamental and derived. Mass, length and time are the
fundamental quantities, whereas area, volume, speed, force, work etc. are derived quantities.
Actually fundamental quantities can be measured directly and derived quantities cannot be
measured directly.
Those quantities which do not depend on other physical quantities are called the fundamental
quantities and those quantities which are derived from fundamental quantities or which depend
on fundamental quantities are called the derived quantities.
So, there are two types of physical quantities. They are
i) Fundamental physical quantity ii) Derived physical quantity
3. Unit
A unit is a standard reference quantity used to find out an unknown quantity of same kind. Measurement
is not possible without unit. For example meter per second (m/s) is the unit of velocity, Joule (J) is the
unit of work, etc.
Need for the Introduction of Standard Unit
It is difficult to make correct judgment about an object without making actual measurement. From
the years back, men have been facing the need of measuring and estimating various quantities.
The units used traditionally to measure different quantities are listed below:
Units of mass = mana, pathi, muri, paau, chhatak , tola etc.
Units of length = hand span, arm length, foot step etc.
For measuring time men were used to watch the position of sun in day time and moon or stars
at night time. Astrologers used Ghadi, Pala, for the unit of time. Such use of units caused non-
uniformity in buying and selling.
So, modern scientific standard units are needed to make measurement simple, reliable and uniform
and to get the correct measurement. A standard unit must have the following characteristics:
1) It should be easily accessible.
2) It should be widely acceptable.
3) It should not alter with place, time and other physical conditions.
4) It must not be too small or too large in size.
5) It must be easy to define without any ambiguity.
6) It must be easy to re-make.
8 Blooming Science Book 9
Depending on the type of physical quantities, units are also of two types. They are:
1. Fundamental unit 2. Derived unit
Fundamental unit : It is a unit which is independent on the other units. Metre (m), kilogram
(kg), second (s) and ampere (A) are some examples of basic units.
The unit which is independent of other units, can neither be derived from others nor be further
resolve into simpler form is called fundamental or basic unit.
Fundamental quantities and their units
S.N. Physical Quantity Unit Symbol of Unit
1. Length metre m
2. Mass kilogram kg.
3. Time second s
4. Temperature kelvin K
5. Current ampere A
6. Amount of Substance mole mol
7. Intensity of Light candela cd
8. Electric Charge coulomb C
Derived unit : It is a unit which depends on other units. It is formed by the combination or
deformation of basic units. There are lots of derived units. Joule (J), meter per second (m/s),
Newton (N), Hertz (Hz) and Pascal (Pa) are some examples.
The unit which depends on fundamental units is called derived unit.
Way of writing Derived Units
First of all write the relation of a derived quantity with other basic quantities. Then write the unit
of each basic quantity, and get the unit of the derived quantity.
1. Force = mass × acceleration
F=m×a
The SI unit of mass (m) = kg
acceleration (a) = ms–1 ?Do
Force (F) =N You
1kg standard mass is the mass of Know
= kgms–1 platinum-iridium cyclinder whose
height is equal to its diameter,
2. We know, preserved at International Bureau
of Weight and Measurements in
Frequency (f) = 1 France
T
Blooming Science Book 9 9
= 1 = sec-1 or Hertz
second
Derived Units of some Important Physical Quantities
1. Area = length × breadth Scan for practical experiment
= m × m = m2 visit: csp.codes/c09e01
2. Volume = length × breadth × height v
= m × m × m = m3
3. Density = mass = kg = Kgm-3
volume m3
distance
4. Velocity = time = m/s = ms-1
5. Acceleration = Velocity = m/s = ms-2
time
s
6. Force = mass × acceleration = kg × m/s2
= kgms-2 or Newton
Force
7. Pressure = area
Newton = Nm-2 or Pascal
8. Work m2
= force × displacement
= Newton × meter
= Nm
= Joule
9. Power
= work
time
= Joule/second
=Js-1
= Watt
10. Resistance = Pd
I
= kgm2/S3A2
= ohm
10 Blooming Science Book 9
5. Rules for writing Units
1) Some units are named after famous scientists in honour. Such units when written in short
form are taken capital letters and if written in full length it is written with small first letter.
For example: Unit of force is named after famous scientists Sir Isaac Netwon so,
10 newton is written but not 10 Newton.
or 10N is written
5 joules is written but not 5 Joules.
or 5 J is written.
2) The symbol for a unit which is not named in the honour of scientists is written in small
letter. eg. The symbol for meter is ‘m’ and second is ‘s’
3) A compound unit obtained by multiplying two or more units is written after putting a dot
(.) dash (-) between the individual units for example; The unit of moment is written as N.m
or N-m
4) A unit in short form is never written as plural for example,
10 kilograms is written as 10kg but not 10 kgs
50 kilometers is written 50 km but not 50 kms.
System of Units
The units of the fundamental quantities taken together forms the system of units; i.e. system of
unit means units of length, mass and time taken together. Different countries use different system
of units. The commonly adopted systems of unit are as follows:
a. CGS system (french system) b. MKS system (Metric system)
c. FPS system (British system) d. SI system.
1. CGS System: It is the system of units in which the unit of length is centimetre (cm), the
unit of mass is gram (g) and the unit of time is second (s). Therefore, CGS stands for
centimeter, gram and second respectively.
2. MKS System: It is the system of units in which the length is measured in metre (m), the
mass is measured in kilogram (kg) and time is measured in second (s). Therefore, MKS
?Do
stands for meter, kilogram and second respectively.
It is also known as metric system. You
3. FPS System: It is the system of units in which the Weight of wrestlerJohn Know
length is measured in foot (ft), the mass is measured Cena is 396 lbs. Can you
in pound (lb) and time is measured in second (s). tell his weight in kg?
FPS stands for foot, pound and second respectively.
It is also known as British system.
Blooming Science Book 9 11
4. SI System: It is the system of units given by 11th convention of International Bureau of
Weights and Measures (IBWM) in 1960 AD, in France. The French name for this system
is “system international de’ units.” It is a well accepted system of units all over the world.
It is developed and extended form of MKS system.
Advantages of SI system
1) It is a rational system of unit as it brings uniformity in the system of measurement all over
the world.
2) It has more number of fundamental quantities which allows us to get all the derived
quantities.
3) It is a metric system i.e. multiples and sub-multiples can be expressed as power of 10.
Differences between Fundamental and Derived Unit
Fundamental Unit Derived Unit
1. It is a unit which is independent on 1. It is a unit which depends on two or
other units. more basic units.
2. It can not be resolved into simpler 2. It can be expressed in terms of power of
units. fundamental units.
3. Metre, second, kg, kelvin etc are basic 3. Units of area (m2), vol (m3), velocity (m/s),
units. acceleration (m/s2) etc are derived units.
Let’s Learn
1. Atomic clock is called more accurate clock because it measures time with the help of
electromagnetic radiation released by caesium - 133 atoms.
2. The unit of work Joule is called derived unit because it is combination of more than two
fundamental units i.e. kgm2s-2.
3. Metre is called basic unit. It is because it is the unit of length which measures physical
quantity independently.
4. It is convenient to express distance of stars in terms of light year rather than in kilometre.
This is because the stars are at very large distance from the earth. As an example, the
nearest star is four light years away. In terms of kilometre, it is 4 × 9.5 × 1012 km. Clearly,
it is inconvenient to express the distance in kilometre or metre.
5. We use SI units for scientific purposes all over the world. This is because the results of
experiments conducted in different countries are comparable.
6. Sometimes a special name is given to derived units. This is done to honour a noteworthy
physicist. For example, the derived SI unit of force (kg ms-2) is called Newton in honour
of Isaac Newton.
12 Blooming Science Book 9
7. The unit of pressure is derived unit. It can be proved by the following calculations:
Force
Pressure = Area
Mass× Accleration
= length ×breadth
= Kg m
m×m × s2
Kg
= ms2
= Pascal (Pa)
Main Points to Remember
1. Measurement is the comparison of unknown quantity with a standard known quantity.
2. The standard quantity used to measure unknown quantity is called a unit. It is of two
types: basic unit and derived unit.
3. A basic unit is a unit which does not depend on other units. For example: metre, second,
kilogram, etc. A derived unit is a unit which depends on other units. For example: Joule,
Newton, Watt, Square metre, Pascal, etc.
4. SI system is internationally accepted system of units and it was given by 11th convention
of IBWM in 1960 AD in France.
5. MKS system is the system of units in which the length is measured in metre (m), the mass
is measured in kilogram (kg), and time is measured in seconds (s).
6. The quantities which can be measured are called physical quantities. Length, mass, time
etc are physical quantities.
7. Mass is the quantity of matter contained in it. It is measured with a physical balance.
PRO J ECTWORK
Take a wooden stick of certain length. Ask few of your friends to measure its length by local
units like ‘Hat’, Bitta etc and note down the lengths measured by all. Now find the measurement
by using a metre scale or measuring tape. Discuss why the measurements done in local units
are not accurate and what are the advantages of standard units?
Blooming Science Book 9 13
Exercise
A. Choose the correct answer from the given alternative.
1. The reference standard with which we carry out the measurement of physical quantity
of same kind is .............................
a. unit b. measurement c. derived unit d. fundamental unit
2. The SI unit of amount of substance is :
a. candela b. kilogram c. ampere d. mole
3. CGS system is also known as
a. Bristish system b. Metric system c. French system d. none of above
4. Pressure is .................... quantity
a. Physical b. Derived c. Fundamental d. Both a and b
5. Derived Unit of resistance is
a. (kg×m×m) / (s×s×s) b. (kg×m×m)/ (s×s×s×A×A) c. (kg×m×m)/(s×s×s×A)
d. kg/(m×s×s)
B. Answer the following questions.
1. What is measurement? Write its importance.
2. What is a unit? Write down any two differences between basic unit and derived unit.
3. What are the systems of units? Explain each of them.
4. The unit of pressure is called derived unit, why?
5. What do you mean by the term “Physical quantity”?
6. Give reason:
i) SI system is accepted by all nations in the world.
ii) Unit of force is derived unit
7. Prove the following units as derived units.
a) Joule b) Watt c) Pascal d) Hertz
d) mole
8. Classify the given units as fundamental and derived units.
a) kg b) m3 c) kelvin
f) Newton g) Hertz
14 Blooming Science Book 9
Chapter FORCE AND MOTION
2
Learning Outcomes Estimated Periods: 5+1
On the completion of this unit, the students will be able to:
• define and demonstrate inertia of rest and inertia of motion.
• explain Newton’s laws of motion and their examples.
• differentiate balanced force and unbalanced forece.
• derive the equations of motion and solve simple numerical problems.
The use of word “force” is very common in our daily life. We use force to move, to lift objects etc.
Generally, force is required to do works. Forces are of two kinds they are, contact force and force at a
distance. In general, a contact force can be described as a force to push, pull, stretch or squeeze an object.
The force of push or pull generally causes displacement. The work is done when sufficient push
or pull force is applied and the displacement takes place. If the force is not enough to cause the
displacement, the work is not done. The applied force is always wasted and converted into heat.
The force of stretch or squeeze changes the shape or size of the object. Force is not only the push,
pull, stretch or squeeze. It also includes gravitational force, electrostatic force and magnetic
force, which could cause any sort of motion on the object. Such a force, which exists due to the
presence of an object in the surroundings is known as the force at a distance.
The gravitational force is the most common of the three kinds of forces at a distance. The
gravitational force of the earth pulls all the objects on the surface of the earth.
Force can be defined as a cause that changes or tends to change the dimensions or the state of rest
or the state of uniform motion in a straight line or the direction of the motion of a body.
In other words, the force is defined as the push or pull on a body in contact or near by it, which
changes or tends to change the state of rest or uniform motion of a body in a straight line. Force
is a vector quantity as it has both magnitude and direction. The SI unit of force is newton (N)
which is measured by spring balance.
The force can cause the following effects on a body on which it acts:
1. Changes the shape and size of the body.
2. Can start or stop motion in the body.
3. Changes the speed of a body with which it is moving.
4. Changes the direction of motion.
Blooming Science Book 9 15
Balanced and unbalanced forces Force due to push of table
Balanced force
To understand balanced force let us take an example of a book placed
on the table as shown in the fig.
There are two forces acting on the book, one due to gravity of the earth Weight of the book
(weight of the book) acting vertically downwards and other push of the table (normal reaction)
acting vertically upward. These two forces have equal magnitude and in opposite direction so
they balance each other. This means when balanced force acts on the object it will remain at
equilibrium i.e. body does not change its state of rest or uniform motion and it will not be
accelerated. Other examples are forces in “Tug of War “ game, forces while pushing the concrete
wall, etc.
So, the number of forces acting on a body which maintain the equilibrium position and body will
not be accelerated are called balanced forces.
Unbalanced force
Now in the same example which is mentioned Force due to push of table
above let us consider a book sliding from right to
left as shown in the fig. Pulling force which Friction
produces left hand
In the fig book is sliding towards right and friction frictional force
acts to the left to slow the book down. Yet there
is no force to balance the friction. This means the Weight of the book
book is not at equilibrium and as a result it accelerates.
So, the number of forces acting on a body which are the causes of motion and acceleration of the
body are called unbalanced forces.
Motion: A body is said to be in motion if it changes its position with respect to the fixed point or
with time or a body is said to be in motion if it is changing its position relative to some together
objects. For example, a car moving on a road is said to be in motion with respect to the roadside
buildings.
Rest: A body is said to be at rest if it does not change its position with respect to the surrounding
objects. For example, a standing car or a bus is at rest with respect to its surrounding object.
Physical quantities associated with motion of a body
A. Distance Travelled and Displacement
D N R
AC WE 3m
BS
E P 4m Q
(a) (b)
In the figure (a), a body can move from the initial position A to the final position B through
several paths: ACB, ADB, AEB, etc. Among these paths, the straight path ACB is the shortest.In
the figure (b), a body moves 4m due east from P to Q and then 3m due north from Q to R. The
16 Blooming Science Book 9
actual distance travelled by the body is PQ + QR = 4m + 3m = 7m, but, the shortest distance
between its initial position P and final position R is the straight line PR joining P and R which is
5m.(PR = PR = PQ2+QR2 )
The length of the actual path travelled by a body is called the distance travelled by the body. It is
a scalar quantity. It is measured in metre (m) in SI system.
The shortest distance from the initial position to the final position of a body is called displacement
of the body. It is a vector quantity. It is measured in metre (m) in SI system.
In the figure (a), the straight path ACB represents displacement between the points A and B while
other paths AEB and ADE represent distance covered. In the figure (b), PR is the displacement
while the total length of PQ and QR, PQ + QR, is the actual distance covered. If we say, for
example, that the displacement of a body is 50m, the information is incomplete. This is because the
displacement is a vector, so it should have both magnitude and direction. However, the statement
that displacement of the body is 50m due east is correct and conveys meaningful information.
Differences between Distance Travelled and Displacement
Distance Travelled Displacement
1. It is the length of actual path covered 1. It is the shortest distance between the
between initial and final position. initial position and the final position.
2. It is a scalar quantity. 2. It is a vector quantity.
3. Net distance covered cannot be zero. 3. Net displacement may be zero.
B. Speed
The speed of a body is the distance travelled by it in unit time. It is measured by the distance cov-
ered by the body per unit time. Its unit is metre per second in MKS system. It is a scalar quantity.
Uniform and non-uniform speed
When a body travels equal distance in equal intervals of time, the body is said to be moving with the
uniform speed. In case it does not cover equal distance in equal intervals of time, then the speed is
non-uniform. Its average speed can be determined by the following expression;
Average speed = Total distance travelled
Total time taken
A car travelling at a constant speed of 20m/s cover 20 m distance in one second. If only two
speeds are involved, then average speed = D1 + D2 where D1 is the distance travelled in time t1
t1 + t2
with the first speed and D2 is the distance travelled in time t2 with the second speed.
C. Velocity:
The rate of change of displacement of a body in a particular direction is called its velocity. It is
a vector quantity as both magnitude and direction are required to express it.
Velocity = Displacement
Time
Velocity is just speed in specific direction. Its unit is also metre per second in the MKS system.
For example, a train is running at the rate of 60 km/hr. It is the speed of the train. But the train is
running towards north at the rate of 60 km/hr, then 60 km/hr towards north is its velocity.
Blooming Science Book 9 17
Average Velocity: The average or mean velocity of a body is the uniform velocity with which
if the body were to travel, it would cover the same distance in the same interval of time. It is
obtained by dividing the total distance covered by the total time taken. Thus, 300m
Total distance covered
Average Velocity = Total time taken X 200m Y
Suppose a car travels along the road from X to Y in 10 second.
Distance 300 ?Do
Then its speed = Time = 10 = 30m/s You
Know
But its velocity = Displacement Usain Bolt(fastest man) from
Time = 20m/s Jamaica can run 100m in
9.45sec. Can you calculate his
speed?
Differences between Speed and Velocity
Speed Velocity
1. Speed is a rate of change of position of 1. Velocity is the distance travelled by a
Distance
body in a specific direction in a unit
a body. Speed = Time Displacement
time. Velocity =
Time
2. Speed has magnitude only. So, it is a 2. Velocity has both magnitude and
scalar quantity. direction. So, it is a vector quantity.
Uniform Velocity and Non-uniform Velocity
1s 1s 1s 1s
2m/s 2m/s 2m/s 2m/s
ABCDE
Suppose a boy travels 2m in each second in a straight line as shown in the figure. The velocity
of the boy is then 2m/s throughout the motion. Such velocity is called uniform velocity. A body
is said to move with uniform velocity if covers equal distances in equal intervals of time in a
straight line. The velocity is same throughout the motion.
Suppose, a boy travels 2m in 1s, rests for 1s and again travels a further distance 4m in 1 s in
the straight line. The velocity throughout the motion is different. Such velocity is called non-
uniform or variable velocity. A body is said to move with non-uniform velocity if it covers
unequal distances in equal intervals of time in a straight line.
For a body moving with non-uniform velocity, we calculate average velocity. Average velocity is
defined as the ratio of total displacement to the total time taken.
18 Blooming Science Book 9
Mathematically,
Average velocity = Total displacement
Total time taken
D. Acceleration: The velocity of a body changes either by increase or decrease of speed
or by a change of direction or by change direction and speed both. So, rarely a body moves with
uniform velocity. Whenever the velocity of an object increases, it is said to have acceleration.
The acceleration of a body is defined as the rate of increase of the velocity.
Suppose a body moving with an initial velocity u, is acted upon by a force F which increases its
velocity to v in t seconds. Then the change in velocity in t second is (v - u). Then the increase in
v - u
velocity in 1 second is .
t
Mathematically,
Change in velocity
Acceleration = Time taken
= Final velocity - Initial velocity
Time taken
i.e., a = v-u ?Do
Where, t Penguine falcon, a bird has You
highest speed of 349km/hr Know
a = acceleration faster than fastest mammal
v= final velocity cheetah(112km/hr)
u= initial velocity
t = time taken
If the motion of the body is in a straight line, the acceleration occurs in the direction of the
velocity. Therefore, the acceleration is a vector quantity.
In SI system change in velocity is measured in m/s and time in second. So, acceleration is
measured in m/s2.
Activity
0m/s 2m/s 4m/s 6m/s
1s 1s 1s
AB C D
Suppose a boy starts to move in a straight line from the point A. His initial velocity at A is zero.
After one second his velocity at B is 2m/s, after two seconds his velocity at C is 4m/s, after
three seconds his velocity is 6m/s at D as shown in the figure. Here, the velocity of the boy is
increasing by 2m/s in every second. This increase in the velocity of the body per second is called
acceleration. The acceleration is defined as change in velocity per unit time.
For a body moving with uniform velocity the acceleration of a body is zero.
Blooming Science Book 9 19
E. Retardation: If the brakes of a moving bicycle are pressed, the velocity of the bicycle
decreases. The bicycle is then said to have retardation. Retardation is defined as the decrease in
velocity per unit time.
Thus, the negative acceleration is called retardation or deceleration. For example, if acceleration
(a) = -5m/s2, it means the retardation is 5m/s2. It shows that the body is decreasing its velocity by
5m/s in each second.
Equations of Motion
Equations involving displacement, initial velocity, final velocity, acceleration and time of motion
of a moving body are equations of motion. These equations are derived from the definitions of
average velocity and acceleration.
Consider a body moving in a straight line with uniform acceleration as shown in the figure.
Let, Displacement = s
Initial velocity = u u v
Final velocity = v Time = t
Acceleration = a s
Time taken = t
Relation between u, v, a and t
By the definition of acceleration, we have
Change in velocity
Acceleration = Time taken
= Final velocity - Initial velocity
a
a t Time taken
v-u
=
t
=v-u
∴ v = u + at …………… (i)
This is the first equation of motion
Relation between s, u, v and t
For uniform acceleration, we have
Average velocity = Final velocity + Initial velocity = v+u
2 2
Then, the distance travelled (s) by the body in time (t) is given by,
20 Blooming Science Book 9
Distance travelled = Average velocity × time
u+v
∴ s = 2 × t ………. (ii)
Relation between s, u, a and t
We already have,
v = u + at
Putting the value of v from the equation (i) in the equation (ii), we have
s = u + (u + at) × t
2
(2u + at)t
or, s = 2
∴ s = ut + 1 at2 ………… (iii)
2
This is the second equation of motion
From equation (ii), we have
u+v v-u v-u
s = 2 × a [where, t = a (from i) ]
or, s = v2 - u2 ⇒ v2 - u2 = 2as
2a
∴ v2 = u2 + 2as …………. (iv)
This is the third equation of motion
Case 1: For a body moving with uniform velocity, initial velocity (u) = final velocity (v). Hence,
a = 0. Therefore, from the equation (iii) we have s = ut …………. (v)
Case 2: For a freely falling body under gravity, equations (i), (ii), (iii) and (iv) are respectively
written as,
v = u + at ⇒ v = u + gt
u+v u+v
s = 2 × t ⇒ h = 2 × t
⇒ h = ut + 21gt2
s = ut + 1 at2
⇒ v2 = u2 + 2gh
2
v2 = u2 + 2as
Notice that a is replaced by g (acceleration due to gravity) and s by h (height) in equations (i),
(ii), (iii) and (iv).
Blooming Science Book 9 21
Case 3: For a body thrown vertically upwards, equations (i), (ii), (iii) and (iv) are respectively
written as
v = u + at ⇒ v = u - gt
u+v u+v
s = 2 × t ⇒ h = 2 × t
h = ut + 12at2 ⇒ h = ut - 21gt2
v2 = u2 + 2as ⇒ v2 = u2 - 2gh
Notice that a is replaced by -g and s by h in equation (i) to (iv). Here, negative sign is assigned
for g. This acceleration due to gravity (g) is oppositely directed i.e., motion is directed vertically
upwards but g is directed vertically downwards.
Case 5: For a body just released from rest, u = 0, and a = g and s = h, then the equations of motion
becomes,
v = u + at ⇒ v = gt
s = ut + 1 at2 ⇒ h = 12gt2
2 ⇒ v2 = 2gh
v2 = u2 + 2as
Case 6: When a body is thrown vertically upwards, final velocity (v) = 0.
Case 7: When a body is allowed to fall vertically downwards, initial velocity u = 0.
Solved Numerical Problems
1. A bus is moving with a velocity of 15 m/s. The driver brings the bus to rest in 2
seconds. Calculate its retardation.
Given,
Initial velocity (u) = 15m/s
Final velocity (v) = 0 m/s
Time taken (t) = 2 seconds
Retardation (-a) = ?
According to the formula
a = v-u
t
= 0 - 15
2
a = -7.5m/s2
-a = 7.5 m/s2
Thus, the acceleration of the bus is -7.5m/s2. It is negative in sign, the negative acceleration is
known as retardation. So the car has a retardation of 7.5m/s2.
22 Blooming Science Book 9
2. If a car is travelling at a velocity of 4m/s along a straight line speeds up uniformly to
velocity of 10m/s in 2s. Find the acceleration.
Solution:
Here,
Initial velocity (u) = 4m/s
Final velocity (v) = 10m/s
Time taken (t) = 2s
Acceleration (a) = ?
We know that,
a= v-u
t
10 - 4
=2
6
=
2
= 3m/s2
3. A bus starts from rest. If the acceleration of the bus is 0.5 m/s2, what will be its
velocity at the end of 2 minutes and what distance will it cover during that time?
Solution:
Here,
Initial velocity (u) = 0
Acceleration (a) = 0.5 m/s2
Time taken (t) = 2 minutes = 120s [ 1 min = 60 sec.]
Final velocity (v) = ?
Distance covered (s) = ?
We have,
v = u + at
or, v = 0 + 0.5 × 120
∴ v = 60m/s
Again,
u+v
s= 2 ×t
0 + 60
= × 120 = 3600m
2
Therefore, the final velocity of the bus is 60m/s and it will cover 3600m in 2
minutes.
Blooming Science Book 9 23
4. A ball is thrown vertically upwards with a velocity of 40m/s. Calculate (i) the
maximum height travelled by it and (ii) the time taken for it to return the initial
position. (neglect air resistance)
Solution:
Here, Initial velocity (u) = 40m/s
Acceleration (a) = -g = -10m/s2
The velocity of the ball goes on decreasing as the ball attains height. At the highest
point, final velocity (v) = 0
We have,
v = u + at
or, 0 = 40 + (-10)t
∴ t = 4s
Again, we have
s = ut + 1 at2
or, s = 40 ×
2 + 1 (-10) (4)2
4 2
or, s = 160 - 80 = 80m
Since 4s is the time taken by the ball to reach at maximum height, so time taken to
return the initial position is 2t = 2 × 4s = 8s.
Therefore, the maximum height attained is 80m and the time taken for it to return
the initial position is 8s.
5. A car is travelling at a speed of 90 km/hr. On seeing a baby 20m ahead on the road,
the driver of the car applies brakes and the car stops at a distance of 15m. What is its
retardation and how long time does it take to come to rest?
Solution:
Although the drives sees a baby 20m ahead on the road, he stops the car at a distance
of 15m, hence,
Distance covered (s) = 15m
Initial velocity (u) = 90 km/hr = 90 × 1000m = 25m/s
Final velocity (v) = 0 60 × 60s
Retardation =?
Time taken (t) =?
We know,
v2 = u2 + 2as
or, (0)2 = (25)2 + 2a × 15
or, - 625 = 30a
∴ a = -20.83 m/s2
24 Blooming Science Book 9
Again, we have
v = u + at
or, 0 = 25 + (-20.83) t
or, -25 = 20.83 t
∴ t = 1.2 s
Therefore, the acceleration of the car is -20.83 m/s2 i.e., its retardation is 20.83 m/
s2 and it takes 1.2s to come to rest.
Mass and Inertia
If a body is at rest, it begins to move only when an external force is applied. Similarly, if an object
is moving, it goes faster, slower or in different directions only when external force is applied.
The resistance to change in velocity of an object is called inertia.
Inertia is the property or tendency of object to resist any change in its state of rest or uniform
motion in a straight line. Scan for practical experiment
There are three types of inertia. They are
a. Inertia of rest.
b. Inertia of motion.
c. Inertia of direction.
Inertia of Rest visit: csp.codes/c09e02
If an external force is not applied to a body then the body at rest will
continue to remain at rest. This is the inertia of rest.
Some illustrations of inertia of rest are given below: Coin
Cardboard
1. When a postcard with a coin is placed over the mouth of a
glass and given a flick on the post card, the postcard flies off, Glass
but the coin falls into the glass. When flick is given to the
postcard, the postcard is knocked off or comes into motion,
but the inertia of heavy coin prevents it from moving easily.
The coin stays in place and falls into the glass.
2. A carpet is usually hung out on a line and beaten with a stick to clean it. The carpet on
beating moves forward suddenly. The dust particles at rest get separated from the carpet
and falls to the ground.
3. In a train or bus at rest, the body of the passenger is also at rest. When the bus or train starts
to move, the lower portion of the body, which is in direct contact with the bus or train, comes
into motion whereas the upper portion of his body is still at rest. Due to the inertia, he takes
longer time to acquire the motion of the train or bus. So he seems to be jerked backward.
4. Fruits fall from the trees when its branch is shaken or jerked. On shaking the branch, it
moves and attain motion but the fruits, which are at rest (inertia of rest), cannot attain the
motion. Thus the fruits separated from the tree and fall down to the gravity of the earth.
Inertia of Direction: It is the property of a body by virtue of which it maintains or tends to
maintain its direction of motion unless unbalanced forces act on it. For examples,
Blooming Science Book 9 25
1. When a running bus suddenly takes a turn, the passengers experience a jerk in the outward
direction. This is because the passengers tend to maintain their original direction of motion
due to inertia of direction.
2. When the wheel rotates at a high speed, the mud sticking to the wheel flies off tangentially.
This is due to inertia of direction.
Differences between Inertia of Rest and Inertia of Motion
Inertia of Rest Inertia of Motion
1. The inertia of rest is the property of a 1. The inertia of motion is the property of a
substance by virtue of which it is unable substance by virtue of which it is unable to
to change its own state by itself to motion change its own state by itself to rest state
without the help of an external force. without the help of an external force.
2. Bus passengers sitting in a bus are jerked 2. Bus passengers standing in a moving bus
backward when the bus moves suddenly. are jerked forward when the bus stops
suddenly.
Activity
To illustrate the effect of mass on inertia
Empty can Can filled with mud
B
A
Method : 1. Hang two empty cans A and B of same size.
2. Fill B with wet mud.
3. Pull them 15 cm and leave so that they oscillate.
4. Record how many times each can oscillate before coming to rest.
Observation : Can B filled with wet mud oscillates less. Can A is empty and it oscillates
more.
Reason : Can B filled with wet mud has more mass and has more inertia. It is
difficult to put it in motion. So it oscillates slowly but for longer time.
Can A is empty. It has less mass and has less inertia. It is easy to put it in
motion. So it oscillates more but for less time. It is also easy to stop by
using little force. It shows that mass is directly proportional to the inertia
ie,more the mass more is the inertia and vice-versa.
26 Blooming Science Book 9
Activity
To illustrate the concept of inertia of rest:
The property that tries to maintain rest position.
Method : 1. Place a coin on a postcard or cardboard which is placed on a glass.
2. Flick the postcard quickly with a finger.
Observation : The postcard flies off and the coin drops into the glass.
Reason : The inertia of a coin keeps it in position even though the postcard is
flicked away. This activity illustrates the inertia of rest of the coin.
Coin
Force Cardboard Force
Beaker Beaker
Coin inside the beaker
The above activity shows that the object with more mass has more inertia. Mass is
therefore, a measure of the inertia of an object.
Object of more mass has more inertia, object of less mass has less inertia. So inertia is directly
proportional to mass.
Newton’s Laws of Motion
After Galileo, Sir Isaac Newton (1642-1727 A.D.) of England made a detailed and systematic
study of the motion of bodies and formulated the three laws of motion. These laws are known
after his name as Newton’s laws of motion.
Newton’s First Law of Motion
Newton’s first law of motion states that “Every object in the universe continues in its
state of rest or of uniform motion along a straight line unless an external force acts on it.”
If an external force is not applied to a massive body, then the body in motion will continue to
move in the same straight line, the body in rest will remain at rest.
Newton’s first law of motion implies that all matter possess inertia. The inertia is the property
of a body due to which it resists the change in its state of rest or state of uniform motion. The
greater the inertia of a body, the large force is required to bring about a change in its state of rest
or uniform motion. Thus Newton’s first law of motion is also known as law of inertia.
Inertia of Motion
A body in a state of motion possesses inertia of motion and it continues to be in a state of motion
with the same speed in the same direction in a straight line unless an external force is applied to
change its state.
Blooming Science Book 9 27
Some illustrations of inertia of motion are given below.
1. A ball thrown vertically upwards in a moving bus comes back to the thrower. Due to
inertia of motion the ball continues to move with the velocity of the bus. So it comes back
to the thrower.
2. When a running bus or truck stops suddenly, the passenger jerks forward. This is because
in a running bus, the whole body of the passenger is in the state of motion. As the bus stops
suddenly, the lower portion of his body being to contact with the bus comes to rest but
his upper part remains in the state of motion. Due to the inertia of motion, the passenger
continues his forward movement for a few moments before he comes to rest. Hence, he
seems to be jerked forward.
3. A person riding a bicycle along a level road does not come to rest immediately after he
stops paddling. The bicycle continues to move forward due to inertia of motion. But the
bicycle does not go on moving forever, it comes to rest after sometime due to air resistance
and retarding action of friction. If there were no air resistance and no friction to oppose
the motion of bicycle, according to the first law of motion, a moving bicycle would go on
moving forever. It would not stop by itself.
4. An athlete often runs for some distance before taking a long jump. The reason is that by
running for some distance the athlete brings himself in the state of motion and then it
becomes easier for him to take a long jump.
5. When the electric current is switched off, the main part of the fan stops rotating, but the
blades attached to it continue to be in the state of rotation. Due to the inertia of motion in
the blades of the fan, the blades keep on moving for sometime.
Newton’s Second Law of Motion
It states that “acceleration produced in a body is directly proportional to the force applied to it
and inversely proportional to its mass”.
Let us consider a force ‘F’ produces an acceleration ‘a’ in a body of mass ‘m’ then Newton’s
second law of motion tells that,
a ∝ F .................... (i) (When mass is constant)
a ∝ 1 .................... (ii) (When force is constant)
m we have, a ∝
F
Combining these two equations, m .
or F ∝ ma .................... (iii)
It is a rule that whenever a sign ‘∝’ is replaced by a sign of equality, the right hand side of the
equation is always multiplied by a constant of proportionality.
Therefore equation (iii) becomes
F = kma .................... (iv)
Where k is the proportionality constant. The value of k depends on the system of unit chosen.
Let’s suppose
mass = 1 unit
acceleration = 1 unit
and force = 1 unit
28 Blooming Science Book 9
Then, on substituting these values in the eq. (iv) we get.
1 = k×1×1
or k = 1
Thus, equation (iv) now becomes
F=m×a
This is the mathematical interpretation of Newton’s second law.
Unit of force
If m = 1kg
a = 1m/s2 then, from (iv) we have,
F = (1kg) × (1m/s2 )
\ F = 1kg.m.s–2 = 1N
The SI unit of force is Newton and 1N force can be defined as the force acting on a body of mass
1 kg produces an acceleration of 1m/s2.
The force acting on a body is directly proportional to the product of the mass of the body and the
acceleration produced in it by the action of the force, and it acts in the direction of the force.
When a bus starts to move from the state of rest, a force due to the engine acts on it. Similarly a force,
due to the brakes, when acts on it, it slows down or comes to rest. In other words, to accelerate or
to retard a body a force must act on it. A constant force on a body produces a constant acceleration.
Newton’s second law of motion gives the magnitude of force which produces acceleration on a body.
Some illustrations of Newton’s 2nd law of motion
a) It is difficult to catch a cricket ball than the tennis ball of same size. The mass of cricket ball
is more as compared to tennis ball. As f∝m, the cricket ball gives more force of impact than the
tennis ball so, it easy to catch tennis.
b) A probilility of getting hurt increase when we jump from greater height, when we jump from
great height, the velocity of falling bady increases. As, F ∝ v [∵ f = ma= mv/t]
the force of collision on body increase due to increase in velocity so, a person get more hurt while
jumping from great height.
Solved Numerical Problem
A bus of mass 4000 kg is moving with a velocity of 72 km/hr. The brakes are suddenly applied
and it is brought to rest in 8 seconds. Calculate-
a) The retardation.
b) The force applied by the brake to stop the bus.
c) The distance travelled in 4 seconds.
Solution:
Mass (m) = 4000 kg
Blooming Science Book 9 29
Initial velocity (u) = 72 km/hr = 72 × 1000 m/s = 20m/s
60 × 60
Final velocity (v) = 0m/s
Time (t) =8s
a) Retardation (-a) = ?
b) Force (F) = ?
c) Distance (S) = ?
v-u
a) We have, a = t
0 - 20
=8
= - 20
8
= - 2.5 m/s2
∴ -a = 2.5 ms/2
b) To calculate the force, we have, F = m × a
F = 4000 × 2.5
F =10,000N
Thus, the retarding force (-F) required is 10,000N.
c) To calculate the distance, we have,
S = ut + 1 at2 = 20 × 4 + 1 (-2.5) × 4 × 4 Scan for practical experiment
2 2
= 80 - 20
= 60m
Thus, the distance travelled is 60m.
Newton’s Third Law of Motion visit: csp.codes/c09e03
Newton’s third law of motion states that “to every action, there is an equal Book
and opposite reaction.”
Here the action means the external force applied on a body and reaction
means the opposite force exerted by the body. For example: When a Table
man jumps from a boat on the side of the pond, he applies force on
the boat in forward direction which is action and the boat moves backward due to the force of
reaction.
30 Blooming Science Book 9
Experiments to demonstrate that forces exist in pairs.
A book lying on a table exerts a force equal to its weight on the table in the downward direction.
The table exerts an equal force on the book in upward direction. The first is called action and the
second is called reaction.
If a body exerts a force on another body, the second body exerts an equal force on the first body
but in the opposite direction. These forces are called action and reaction.
12 6 0
0 6 12
Action Reaction
The force exerted by first object on the second object is called action and the force exerted by
second object on the first in return is called reaction. Action and reaction act on different bodies
but simultaneously.
Some illustrations of Third Law of Motion
1. When a balloon filled with air is hold with its mouth in a upside down position, is released,
the air inside rushes out downward (action) and the balloon goes upward (reaction).
2. For a ship floating on water, its weight acts downward is the action and the up thrust of
water is the reaction.
3. When a person jumps out of the boat to the bank of river, the boat is pushed back because
of action force. The force by which the person jumps out of the boat is the action force and
the boat is pushed backward by the reaction force.
4. When a bullet is fired from gun, the gun recoils. It is because the bullet comes out with
some force(action)which gives the reaction force to the gun to recoil back in opposite
direction.
5. Birds flap the wings while flying. It is because the wings push the air down (action) and
gets the up thrust of air (the reaction in opposite direction) in order to fly.
6. The rocket launches in space on the principle of newton’s third law of motion.
Momentum
The linear motion contained in a body is called momentum.
It is given by momentum (p) = mass (m) × velocity (v)
Its SI unit is Kg m/sec
Relationship between force and momentum
Since,
F = ma
Blooming Science Book 9 31
F = m v–u [a = v–u ]
t t
mv–mu
F = t
Here, mv is final momentum and mu is initial momentum. So, (mv–mu) gives change in mo-
mentum.
So, F = Change in momentum = Rate of change of momentum
time
Hence, Newton’s II law of motion can be stated as, force applied to a body is directly proportional
to the rate of change of momentum in the body.
Let’s Learn
1. A person gets more hurt while falling down on the cemented floor than on the sandy floor.
As we know the relation.
F = mv–mu ,
t
(mv–mu) is constant while a person falling down either on the cemented floor or on the
sandy floor (because a person fall under the action of gravity only). So, from above relation
we get,. F∝1/t . As we know, that the cemented floor is harder than that of sandy floor so
time of impact is less in cemented floor which provides more force to the body of person.
Hence, person gets more hurt while falling on the cemented floor than on the sandy floor.
2. Net displacement can be zero but not the net distance. Suppose a body moves from A to
B in a straight line and then returns again at point A. Since the displacement is a vector,
hence if the displacement AB is taken as positive, then we should take the displacement
BA as negative. So, net displacement is AB+ (- BA) = 0 but net distance covered is twice
the distance of AB. Thus the total displacement of a body is zero but total distance covered
by the body is twice the distance of AB (2AB).
3. An object can be accelerated without change in its speed. If an object is moving in a
circular path with a constant speed, the direction of the motion of the object is continuously
changing and hence its velocity. Due to the change in direction of the velocity, it possesses
acceleration. Thus, a body moving with constant speed can have acceleration. This
example also explains that a body can have constant speed but varying velocity.
4. When the switch is off, the blades of fan continue their state of motion for a while due to
inertia of motion.
5. A cricketer moves his hand backwards while catching a cricket ball:
By moving hands backward the player increases the time of catching the ball. As a result
the rate of change of momentum decreases and by Newton’s second law, the force exerted
hands is less so he is less likely to hurt.
6. Chinaware’s or glass vessel’s or instruments are wrapped in straw paper before packing:
The straw paper between the china wares increases the time of experiencing jerks during
transportation. Hence they strike with each other with less force and are less likely to be
damaged.
32 Blooming Science Book 9
7. Vehicles are fitted with springs and shock absorbers to reduce jerks while moving on
uneven or way roads.
8. A horse cannot pull a cart or run in empty space:
While trying to pull a cart, a horse pushes the ground backwards with a certain force at
an angle. The ground offers an equal reaction in the opposite direction, on the feet of the
horse. The forward component of this reaction is responsible for motion of the cart. In
empty space, there is no reaction and hence a horse cannot pull the cart or run.
Main Points to Remember
1. Force is an external agent that changes or tends to change a stationary body or stop a
moving body.
2. Force is a pull or push of one body over another body that causes the change in the state
of the body i.e., rest into motion and motion into rest.
3. The tendency of a body to remain in the state of rest or of uniform motion in a straight line
unless external force acts on it is called inertia.
4. Inertia of a body depends upon its mass.
5. It is the inertia of a body that makes it difficult to start or to stop, to change its direction of
motion or to accelerate or decelerate.
6. A vector quantity has both magnitude and direction. Velocity is a vector quantity.
7. A scalar quantity has only magnitude but no direction. Speed is a scalar quantity.
8. Displacement is the distance covered in the fixed direction. It is the shortest distance
travelled by a body between any two points.
9. Acceleration is the change in velocity of a moving body per unit time. Its unit is ms-2.
10. The equations of motion for a body moving with uniform acceleration are:
v = u + at………………….. (i)
s = ut + 1 at2 ………………..(ii)
2
v2 - u2 = 2as ……………... (iii)
u+v
s = 2 × t …………….. (iv)
11. Newton’s first law of motion states that everybody continues to be in its state of rest or of
uniform motion in a straight line unless an external unbalanced force acts on it.
12. Newton’s second law of motion states that acceleration produced on a body is directly
proportional to the force applied and inversely proportional to the mass contained in it.
13. Newton’s third law of motion states that to every action, there is an equal and opposite
reaction.
Blooming Science Book 9 33
PRO J ECTWORK
To demonstrate Newton’s Third Law of Motion
1. Take a long nylon rope and stretch it across the class room.
2. Tie its two ends on opposite walls making slight slope at one end. This is done to
compensate the friction produced when something slides on it.
3. Take a piece of paper and roll it to make a spool and insert the nylon rope into it.
4. Place the spool at the higher level of the rope.
5. Take a balloon and inflate it and tie its mouth with a thread.
6. Fix the inflated balloon in the spool with the help of tape pointing the mouth of the
balloon towards the higher level of the rope.
7. Open the mouth of the balloon.
Observation: Balloon moves forward. The air inside the balloon when comes out (action)
and the motion of the balloon moves in opposite direction (reaction). The force with which air
rushes out from the balloon equals to the force which pushes the balloon forward. “In every
action there is equal and opposite reaction.”
Exercise
A. Choose the correct answer from the given alternatives.
1. Rest and motion are...................................
a. Relative terms b. unlike term
c. different terms d. similar terms
2. Property of a body due to which it remains or tends to remain in the original state of rest or
uniform motion is called....................
a. momentum b. inertia of rest
c. inertia of motion d. inertia
3. Formula to calculate momentum is .............................
a. P = m×u b. P= F
A
c. F = m×a d. P = w
t
34 Blooming Science Book 9
4. ........................... is that which produces 1m/s2 acceleration on a body of 1 kg mass.
a. 1 J work b. 1N force c. force d. speed
5. “To every action there is an equal and opposite reaction” is
a. 1st law of motion b. Principle of lever
c. 3rd law of motion d. All of above
B. Answer the following questions.
1. Distinguish between speed and velocity.
2. What do you mean by inertia? On what factor does the inertia of a body depend?
3. Which has more inertia, a cricket ball or a rubber ball of the same size? Why?
4. Define inertia of rest. What inertia is present in a stretched rubber?
5. What is the relation between mass and inertia of an object?
6. Define inertia of motion. Why an athlete runs some distance before taking up a long jump?
7. State Newton’s first law of motion. Newton’s first law is also called law of inertia. Explain.
8. State Newton’s second law of motion and prove F = ma. (Deduce the mathematical equation
of Newton’s second law of motion.)
9. State Newton’s third law of motion. How does this explain the action of a rocket?
10. Define balanced and unbalanced forces with examples.
11. What is meant by one Newton force?
12. Define Velocity? Is velocity a vector or a scalar quantity? Give reasons for your answer.
13. What do you mean by a variable velocity and uniform velocity?
14. Two objects of mass 20 kg and 2 kg are at rest. Which one needs more force to move.
Why?
15. Prove: (i) v2 = u2 + 2as (ii) s = ut + 1 at2
2
16. When the electric current is switched off, the blades of the fan keep on moving for some
time. Which of the Newton’s law of motion is explained by the above statement?
17. Study the given diagram and answer the following questions:
Blooming Science Book 9 35
Coin
Cardboard
Beaker
a) What will happen if the cardboard is suddenly pulled away? Give reason.
b) What will happen if the cardboard is slowly pulled away? Why?
c) Which Newton’s law of motion is explained by the given experiment? State it.
18. Why is it dangerous to jump off a running vehicle?
19. The graph shows the time and velocity of a certain vehicle. Study
the graph and answer the following questions:
a) Between which two points did the vehicle retain uniform Velocity KL
velocity? M
b) At which point did the vehicle start moving and at which O Time N
point did it stop?
c) At which point did the retardation of vehicle start?
d) Where did the vehicle have maximum acceleration and deceleration?
e) Where did the acceleration of the vehicle remains zero?
20. What will happen to the passengers standing on a stationary bus when the bus suddenly
moves forward? Why?
21. Give reasons:
a) If you shake the branches of a tree, the fruits fall.
b) A swimmer pushes water backwards.
c) A cricketer moves his hands backwards when holding a catch.
d) A person has to run in the direction of bus over some distance after getting down
from a moving bus.
e) Passengers of a bus jerk forward when it stops suddenly.
f) The gun recoils when a bullet is fired.
g) A moving truck takes a much longer time to stop than that taken by a car when
brakes are applied to both.
36 Blooming Science Book 9
h) When you jump on a concrete surface, the feet are more seriously hurt than that
when you jump on sand.
i) An athlete runs some distance before taking a long jump.
j) We beat a blanket with a stick to remove dust particles.
Numerical Problems
22. Solve the following mathematical problems:
a) A truck of mass 5000 kg is moving with the speed of 72 km per hour. If the driver
applies the brakes and brings the truck to rest in 2 seconds:
(i) What is the retardation of the truck?
(ii) What distance does the truck cover in that time?
(iii) How much force is applied by the brakes to stop the truck?
[Answers : (i) 10 m/s2 (ii) 20 m (iii) 5 × 104N]
b) A car is running at the speed of 45 km per hour. If the car stopped in 3 seconds
after the driver jammed on the brakes what must be the retardation of the car? What
distance did it cover before stopping? [Answer: 4.16 m/s2, 18.75 m]
c) When a stone is dropped into a well, sound of the splash was heard only 3 seconds
later. How deep is the well? Ignore the speed of sound. [Answer: 44.1 metre]
d) A driver of a vehicle running at the speed of 45km per hour sees a child 25 meters
ahead and suddenly applies the brakes. If the retardation of the vehicle is 2m/s2, is
the child spared? [Yes, s = 39.06m]
e) When brakes were applied to a car travelling with uniform velocity, it experiences
a retardation of 1 m/s2 and comes to halt in 5 seconds, what is its initial speed?
[Answer: 5m/s]
f) If a vehicle starting from rest has an acceleration of 0.5 m/s2, what will be its speed
40 seconds later? What distance will the vehicle cover? [Answer: 20m/s; 400m]
g) What acceleration will be produced on a body of mass 10 kg when a force of 500 N is
applied on it? If the object starts from rest, how far will it reach in 5 seconds? Assume
friction to the negligible [Answers: 50 m/s2, 625 m]
h) A body of mass 4 kg is kept at rest. A constant force of 8 kg F starts acting on it.
Find the time taken by the body to move through a distance of 20 m.
(1Kg = 9.8 N) [Answer: 1.4 sec]
Blooming Science Book 9 37
Chapter MACHINES
3
Learning Outcomes Estimated Periods: 5+2
On the completion of this unit, the students will be able to:
• explain M.A, VR and efficiency in simple machines (lever, pulley, wheel and axle and
inclined plane)
• define principle of lever and types of lever
• explain moment and law of moment in lever.
• solve numerical problems related to MA, VR and efficiency of simple machines (lever,
inclined plane, wheel and axle, pulley).
Introduction
In our everyday life we have to perform various types of work. We perform some of these works
by hand and some of these by using simple devices. For example, to pull water from well, a
pulley is used. If the tyre of a car is to be replaced, the screw jack is used to lift the car. Loading
of truck is done with the help of an inclined plane. Similarly, in our daily life we usually use
scissors, forceps, knives, punching machines, bicycles, fire tongs, etc. All these devices are
simple machines.
A machine is a device, which when a force is applied on it, makes work easier, changes the
direction of force and enhances the speed of work.
We do different types of works in our daily life. In some cases we do not use any tool to perform
our work but in some cases we use various types of tools. The tools or simple devices are used
for making our work easier, faster and more convenient, are called simple machines. Such simple
machines do not do our work themselves but we have to apply force to do work with them.
Simple machines are those tools or devices which make our work easier, faster and convenient.
Purposes of using simple machine ?Archimeds’ once Do
said,“Give You
1. It multiplies force.
2. It changes the direction of force. me a lever I would lift the earth Know
3. It transfers force from one point to other.
4. It increases the rate of doing work. taking moon as fulcrum. ’’ This
also explains the importance of
simpl machine
1. Mechanical Advantage:
The ratio of load lifted to the effort applied is called the mechanical advantage.
Load (L)
i.e. Mechanical Advantage (MA) = Effort (E)
L
or M. A. = E
38 Blooming Science Book 9
Load and Effort both have same unit so MA has no unit. It is expressed in number only. The
mechanical advantage of a machine actually measures by how many times the effort is multiplied
by the simple machine for example, if for a simple machine MA = 2,it can lift a load with half
effort i.e. 500N load can be lifted with 250N effort.
Mechanical advantage of a simple machine can be less than 1, equal to 1 or more than 1.
L => L <
mIf aMch.iAne. s<is1,nio.et.toEex<er1t a large 1, input work is greater than output work. The purpose of such
force but to move a long distance. Such machines are distance
multipliers. A bicycle provides a good example of distance multiplier. In bicycle output distance
is more than input distance.
In most of the machine, the MA is more than 1, i.e. L>E i.e heavy load can be lifted with small
effort. Such machines are effort multipliers. No machines can ever be a force multiplier and a
distance multiplier.
Factors Affecting Mechanical Advantage of a Simple Machine
i. Friction:
Friction exists in simple machine. Due to friction certain amount of effort is wasted
and hence friction reduces MA.
ii. Weight of a simple machine:
The effort applied to a simple machine has to lift a part of simple machine itself in
addition to the load to be lifted. Thus more effort is required to raise small load and
mechanical advantage becomes less.
2. Velocity Ratio (VR) : Effort
The ratio of velocity with which effort (E)
is applied to the velocity with which load de
6cm
(L) is lifted is called the velocity ratio L
(V.R.). dl
i.e. V.R. = Velocity of effort (Ve) Fulcrum
Velocity of load (Vl)
Let an effort E be applied to a point in a lever and moves the point of application of the force
thorugh a distance ‘de’. As a result of this, let load (L) moves through a distance ‘dl’ in time ‘t’.
Here, load and effort will move for equal time (t) then,
Velocity of the effort (Ve) = de
t
Velocity of the load (Vl) = dl
t
Now, VR = Ve or VR = de
or Vl t
dl
t
VR = de × t
t dl
Blooming Science Book 9 39
or VR = de
dl
or VR = distance moved by effort (de)
distance moved by load (dl)
i.e. VR of a simple machine can be defined as the ratio of distance moved by effort to the distance
moved by load, in the same interval of time.
VR is unitless as it is the ratio of physical quantities with same unit. The VR of a machine
actually measures the extent to which speed of the work is increased by using the machine. For
example, if VR = 3, for a machine, it means the distance moved by effort is 3 times more than the
distance moved by load in the same time interval.
Velocity ratio is not affected by the friction. So VR is always greater than MA.
For every practical machine, MA<VR. because of the friction. Only ideal or perfect machine can
have MA = VR
3. Efficiency: Efficiency of a machine is defined as a ratio of work done by the machine to
the work done on the machine. Mathematically,
Work done by the machine
Efficiency (η) = Work done on the machine
In other words, it is the ratio of output work to the input work. Usually, efficiency is
expressed as a percentage.
So, output work
Efficiency (η) = input work × 100%
In a machine output work is always less than the input work because some work has to
been done in overcoming friction and to move parts of the machine itself. So in practice,
no machine is completely efficient.
4. Relationship between M.A, V.R and Efficiency: From the definition of efficiency
output work
Efficiency (η) = input work × 100%
= load × distance moved by load × 100%
effort × distance moved by effort
= LE ×× dl × 100%
de
= LE ×d1e × 100%
dl
= MA × V1R × 100%
Hence, Efficiency (η) = M. A. × 100%
V. R.
This equation gives the relationship between mechanical advantage (M.A.), velocity ratio
(V.R.) and Efficiency (η).
40 Blooming Science Book 9
5. Ideal Machine and Practical Machine: In a simple machine the output work should
be equal to the input work. Thus the efficiency of the machine should be equal to one or
100%. This type of machine which has the efficiency 100% and can convert the whole
input work into output work with no waste of energy is called an ideal machine (perfect
machine).
However in practice, no engine can convert a whole input work into an output work. Thus, in a
practical machine the output is always less than the input and efficiency is less than one or 100%.
When a person applies 1000 joules of work on a machine, he gets only 800 joules of work from
the machine. How can you account this loss of 200 joules of work? This 200 joules of work done
has been converted into heat in overcoming the friction.
There is always friction between the moving parts of a machine. This friction wastes the kinetic
energy of the machine in the form of heat energy. The output work is less than the input work in
a machine. Thus the efficiency of a simple machine is always less than 100%. If a machine has
an efficiency of 80%, this indicates that 80% of the input work is converted into useful work, and
the remaining 20% energy is converted into heat energy while overcoming the friction.
By applying lubricating oil or grease the friction in the moving parts of a simple machine can be
decreased. This increases the efficiency of a machine.
Solved Problems
A machine raises a load of 1200N through a distance of 10cm by an effort of 400 N which
moves through 1 m. Calculate (i) M.A. (ii) V.R and (iii) efficiency of the machine.
Solution: Here,
L = 1200 N
E = 400N
Distance moved by load = 10 cm
Distance moved by effort = 1m = 100 cm
Then, M.A = L = 1200 N = 3
E 400 N
Also, V.R. = distance moved by effort
distance moved by load
= 100 = 10
∴ Efficiency 10
= M.A. × 100 %
V.R.
= 3 × 100 % = 30%
10
Effect of Friction on MA, VR and η
The force that resists the motion of one surface relative to another with which it is in contact is
called frictional force or friction. The value of friction depends on the nature of surface (rough
or smooth), type of material, type of motion (rolling or sliding) etc. Friction wastes the kinetic
energy of a machine in the form of heat energy. Practically, machines can not be made frictionless.
Therefore, friction reduces MA and efficiency of the simple machines.
Blooming Science Book 9 41
VR of a machine is not affected by friction because it is the ratio of two distances. Due to this
reason, value of MA is always found less than that of VR.
To increase MA and η of simple machine, we have to reduce friction. We can reduce friction by
the following methods:
(i) by using lubricants like oil, grease etc.
(ii) by using ball-bearings, wheels and rollers.
(iii) by making the surface smooth.
(iv) by rolling instead of sliding.
Principle of Simple Machine
The principle of simple machine states that “if there is no friction in a simple machine, work
output and work input are found equal in that machine.”
Mathematically,
[Output work = Input work]
or, L × Ld = E × Ed (If there is no friction).
Types of Simple Machines
Simple machines are of following six types:
1. Lever 2. Pulley
2. Inclined plane 4. Wheel and axle
5. Screw 6. Wedge
Lever
A lever is a rigid, straight or bend bar which is capable of rotating about a fixed point called a
fulcrum. In a lever, effort distance and load distance are measured from fulcrum. The distance
between fulcrum and load is load distance and the distance between fulcrum and effort is effort
distance. In the below diagram, BF is effort distance and AF is load distance.
Principle of Lever: Consider a lever AB capable of rotating about a fulcrum F. Let L be a load
and E be an effort applied. If the lever is in the equilibrium, then according to the principle of
moments. (Simple machine)
Load x Load arm = Effort × Effort arm
or, L × AF = E × BF A Load arm F Effort arm B
or, L = BF L E
E AF
i.e. Load = Effort arm
Effort Load arm
This is the principle of Lever
42 Blooming Science Book 9
Types of Lever
On the basis of the relative position of the fulcrum, load and effort levers are categorized in three
groups or classes. They are:-
First Class lever
A lever in which load and effort are on either LA EA
side of the fulcrum is called the first class lever.
In a first class lever it can be either L F
EA>LA or EA = LA or EA <LA
E
According MA>1, or MA= 1 or MA< 1 Scan for practical experiment
However, in any of the cases the speed of doing work increases.
Examples of first class lever: See saw, crowbar, scissors, pliers,
claw hammer, handle of water, etc.
Second Class lever visit: csp.codes/c09e04
A second class lever is that in which the load acts at any E
point between the fulcrum and effort. It is neither use to L
EA
change the direction of the force nor to accelerate the LA
work, but is used to multiply the force. It is because the
effort arm is always greater than the load arm. So, the
mechanical advantage of second class lever is always Fulcrum
greater than 1. Therefore, in this type of lever a small effort can always overcome a larger load.
Examples of second class lever: bottle opener, wheel arrow, nutcracker, paper cutter, oar of a
rowboat, etc.
Third Class Lever
A lever in which effort acts at any point in between the Effort
fulcrum and the load is called the third class lever. In this
type of lever, the effort arm is always smaller than load arm. EA
So its MA is always less than 1. Therefore larger effort is
always needed to overcome a smaller load. It is neither used LA
to change the direction of the force nor to multiply the force Fulcrum
but it is used to accelerate the work. This type of lever is
often used to do delicate jobs such as using fire tonges to pick up the coal from the fire. Examples
of third class lever: Sugar tongs, shovel, forceps, hammer, broom, a knife, fishing road etc.
Blooming Science Book 9 43
Solved Problems:
1. A lever with a velocity ratio of 32 overcomes a load of 600N with a force of 25N.
Calculate (a) MA and (b) Efficiency.
Solution: Here, L = 600 N
E = 25 N
V.R. = 32
M.R. = ?
Efficiency (η) = ?
We have, (a) M.A. = L = 600 = 24
E 25
(b) η = M.A. × 100%
V. R
= 3224 × 100% = 0.75 × 100% = 75%
2. A crow bar (a first class lever) is used to lift a load of 200N by applying an effort
of 80N. If the load is lifted upto 0.05m and the force covers the distance of 0.25m,
calculate MA, VR and η:
We have,
Load (L) = 200N
Effort (E) = 80N
Distance covered by load = 0.05m
Distance covered by effort = 0.25m
According to the formula,
MA = Load = 200N = 20 = 2.5
Effort 80N 8
Again,
VR = Distance travelled by effort = 0.25m = 5 80N
Distance travelled by load 0.05m
200N
Again, 0.05m 0.25m B
η= 2MV5.5RA××10100%0%= 50%
=
Output work = L ×Ld
= 200 × 0.05
= 10J
Input work = E × EA
= 80 × 0.25
= 20J
44 Blooming Science Book 9
The calculation shows that the value of MA is less than the value of VR. Similarly, the value
of work output or useful work is 10J while work input is 20J. i.e., value of output work is less
than value of input work. It is because of the wastage of work input due to friction. Input work =
output work + wastage work.
The pattern used for calculating MA, V.R. and η of a first class lever, is also applicable in second
and third class levers.
3. A crowbar of 180cm long is pivoted about a point 20cm from its tip, the force of 100N is
applied to its other end to displace a load of 600N. Calculate MA, VR and η of the crowbar.
Solution:
Here, 100N
Load (L) = 600N 600N B
0.20
Effort (E) = 100N 1.6m
Load distance (Ld) = 0.20m
Length of lever (l) = 180cm = 180
100
= 1.80m
Effort distance (Ed) = Length of lever - load distance
= (1.80 - 0.20) = 1.60m
Now, according to the formula,
MA = L = 600N = 6
E 100N
VR = Ed = 1.60m = 8 Scan for practical experiment
Ld 0.20m
η = MA × 100% = 6 × 100%
VR 8
= 3 × 100% = 75%
4
∴ MA of the crowbar is 6, VR is 8 and η is 75%.
Pulley visit: csp.codes/c09e05
A pulley is a metallic or wooden disc with a grooved rim. The rim rotates about a horizontal axis
passing through its centre.
A pulley can be used as single fixed pulley as shown in fig ‘a’ single movable pulley as shown
in fig ‘b’ or in combined form (block and tackle) as shown in fig ‘c’. A single fixed pulley makes
our work easier by changing direction only, mechanical advantage is not gained by using this
pulley because value of effort distance and load distance is equal in it. Therefore, value of effort
and load is also equal in it.
But when a single pulley is used as single movable pulley, mechanical advantage is gained.
In this condition direction of force is not changed but velocity ratio is doubled. When two or
more pulleys are used in the form of block and tackle, direction of force is changed, as well as
mechanical advantage is gained.
Blooming Science Book 9 45
In case of single movable pulley VR is 2. It is because Ld is always half than Ed so
as we know the relation.
VR = Ed = Ed =2 Ed =2
Ld Ed Ed
2
This means effort should cover double distance than load.
Effort Fixed
pulley
Effort Effort
Load Movable
pulley
(a) Single fixed
pulley Load
(b) Single movable Load
pulley
(c) Block and tackle
In a block and tackle, MA and VR are directly proportional with the number of pulleys used in
that block and tackle.
From the study of the given figures, we find that if number of pulley increases in a block and tackle,
the value of VR also increases. In the same way value of MA increases but not exactly as given by
the formula because some of the applied effort is wasted due to friction. In pulleys velocity ratio is
equal to the number of pulleys or number of rope segments that support the load.
VR in pulleys = No. of pulleys used (except in single movable pulley) or number of rope
segments that support the load.
Effort Effort Effort Effort Effort
Load Load
Load Load
Load
(i) Two pulley system (ii) Three pulley system (iii) Four pulley system (iv) Five pulley system (v) Six pulley system
[VR = 2] [VR = 4]
[VR = 3] [VR = 5] [VR = 6]
46 Blooming Science Book 9
Solved Problems
1. A load of 650N is lifted by a 5 pulley system upto 4 meters by applying an effort of
300N. Calculate:
a) MA b) VR c) output work
d) input work e) efficiency
Solution:
Here,
Load (L) = 650N
Load distance (Ld) = 4m
No. of pulleys = 5
Effort (E) = 300N
a) MA =?
b) VR =?
c) Output work = ?
d) Efficiency = ?
According to the formula,
L 650N
a) MA = E = 300N
= 65 = 13
30 6
b) VR = No. of pulleys used = 5
Ed
VR = Ld
Ed
Or, 5 = 4 = Ed = 20m
c) Output work = L × Ld
= 650N × 4m
= 2600J
d) Input work = E × Ed
= 300N × 20m
= 6000J
e) η= Output work × 100%
Input work
2600L
= 6000J × 100%
26
= 60 × 100% = 43.33%
Hence, MA is 163, VR is 5, work output is 2600J, work input is 6000J and η is 43.33%.
Blooming Science Book 9 47
Inclined Plane
A plane making an angle with a horizontal plane is called an Lorry
inclined plane. It is smooth, flat and rigid surface inclined to
the horizontal. Less obvious is that screws and wedges are Load
also inclined planes. A familiar example of the use of the
inclined plane is to push heavy barrel up a wooden plank
onto a lorry. It is easier to push a barrel up a plank onto a Wo o d e n
lorry than to lift it vertically up. plank
Consider an inclined plane shown schematically as in figure alongside, in which effort (E) is
applied along the inclined plane to raise a load (L) through a vertical height ‘h’ let the length of
the inclined plane be ‘l’. Then, distance moved by effort = length of inclined plane = l
distance moved by load = height of the inclined plane = h
Therefore, VR = distance moved by effort/distance moved by load
VR = l
h
From the figure, if q is the angle of inclination of the inclined plane then,
sin q = h Scan for practical experiment C
1 B
l l
or Sinq = h Load distance
(h)
Therefore, VR = l EffoErftfort di(slt)ance
Sinq
Load(L) l
MA = Effort(E) A Loqad Sinq
Efficiency = MA ×100% visit: csp.codes/c09e06 MA =
VR
frictionless then, MA =
If the inclined plane is considered VR or
But practically MA<VR because of the friction.
Solved Problem
By studying the diagram to calculate:
a) output work
b) input work 550N 8m 5m
750N
c) mechanical advantage (MA)
d) velocity ratio (VR)
e) efficiency (η)
Here,
Load (L) = 750N
Effort (E) = 550N
Length of slope (l) = 8m
Height of slope (h) = 5m
(a) Output work = ?
48 Blooming Science Book 9
(b) Input work = ?
(c) M.A. =?
(d) V.R. =?
(e) η =?
According to the formula,
a) Output work = L × Ld (h)
= 750N × 5m = 3750J
b) Input work = E × Ed (l)
= 550N × 8m = 4400J
c) MA = L
E
= 750N = 1.36
550N
d) VR = l
h
= 8m = 1.6
5m
e ) η = MVRA × 100% Output work
15 or, η = Input work × 100%
= 11 × 100% = 3750 × 100%
8 4400
5
= 15 × 5 × 100% = 375 × 100%
11 8 440
= 75 × 100% = 75 × 100%
88 88
= 85.22% = 85.22%
Hence, in this inclined plane, output work is 3750J, input work is 4400J, MA is 15/11, VR
is 8/5 and η is 85.22%
Wheel and Axle
A wheel and axle is a combination of two co-axial cylinders Axle Big cylinder
of different radii fitted one into the other, the larger one being Small cylinder
called a wheel and the smaller one, the axle.
Rr
The wheel and axle both rotate and without groove at the
circumference. Two pieces of strings are coiled or wound one
each round the wheel and axle in opposite direction , when
string on wheel is unwound, the string on axle is wound round
it so that direction of movement of load and effort is opposite.
The load to be lifted is hung on the string of axle and effort is
applied from the string of wheel. There may be another type of wheel and axle in which handle
is rotated and load attached to string is raised up as shown in fig.
Blooming Science Book 9 49
Let the radii of the wheel and axle be ‘R’ and ‘r’ respectively. Then if effort ‘E’ be applied
downward, so that the wheel makes one full rotation, the axle does so.
At that time effort moves the distance equal to the circumference of the wheel (2πR) and load
moves the distance equal to the circumference of the axle (2πr) upward.
i.e. de = 2pR
dl = 2pr
Therefore, VR = distance moved by effort(de)
distance moved by load (dl)
= 2pR
2pr
Radius of wheel (R)
VR = Radius of axle (r) R
r
Since the radius of the wheel is greater than that of axle > 1
i.e. VR>1
Mechanical advantage (MA) = load (L)
effort (E)
Efficiency (η) = MA × 100%
VR
Examples of wheel and axle: wind lass use for drawing water from the well, screw driver, door
knob, pedal of bicycle, the sewing machine, steering of vehicles, lattai, etc.
Wheel and axle is also called a continuous lever. In the given Big cylinder
(wheel)
diagram, a load is lifted by using a wheel and axle. The load
is suspended at point ‘L’ at the circumference of axle and the L E
Small cylinder
effort is applied at point ‘E’ at the circumference of wheel. F (Axle)
Wheel and axle both are pivoted at point ‘F’ i.e., axis. Because Spring balance
there is load, effort and fulcrum, it works as lever. When the
wheel and axle is in use, the points of load and effort can vary
continuously for 360o on the circumference of the wheel and Load
axle, hence, it is considered as a continuous lever.
Solved Problems
In a wheel and axle, radius of wheel is 24cm and that of axle is 5cm. If a load of 1200N is
overcome by using an effort of 300N on it, calculate MA, VR and η.
Solution:
Here,
Radius of wheel (R) = 24cm
Radius of axle (R) = 5cm
Load (L) = 1200N
Effort(E) = 300N
50 Blooming Science Book 9
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