a) A car of mass 800 kg is moving at a uniform velocity of 72 km/hr. Find its
momentum. [Ans: 16000 kgm/s]
b) A body of mass 5 kg has momentum of 125 kg m/s. Find the velocity of the body
in motion. [Ans: 25 m/s]
c) A bus is moving with a velocity of 72 km/hr. On seeing the red signal of traffic
at 27 m ahead on the road, the driver applied brakes and the bus stopped at a
distance of 25 m. Calculate the time taken by the car to come at rest. [Ans: 2.5 s]
d) A bus is running with a velocity of 60 km/hr. On seeing a child at 11m ahead on
the road, the driver applied brakes and the bus stops at a distance of 10 meter.
Calculate its retardation. [Ans: -13.89 m/s2]
e) A vehicle starts to move from the rest gets an acceleration of 5 m/s2 within 2
seconds. Calculate the velocity and distance covered by the vehicle within the
given time. [Ans: 10 m/s, 10 m]
f) The mass of a car along with its rider is 1000 kg. It is moving with a velocity of
72 km/h and takes 5 seconds to stop after the brakes are applied. Calculate the
retardation and retarding force exerted by the brakes on the car. [Ans: -4 m/s2, 4000 N]
g) Find the force required to produce an acceleration of 2 m/s2 on a body of mass 10
kg. What would be its acceleration if the force is doubled? [Ans: 20 N, 4 m/s2]
h) A stone dropped from the top of a building reaches the ground with a velocity of
49 ms-1. If the acceleration due to gravity is 9.8 m s-2, calculate the time for which
the stone is falling freely. [Ans: 5 seconds]
i) A ball is thrown vertically upward with the velocity 20 m/s. Calculate
i) how high it goes
ii) the time taken to reach the maximum height (taking acceleration due to
gravity g = 9.8 m/s2) [Ans: a. 20.4 m, b. 2.1 s]
8. Draw the diagrams
a) to show the uniform motion of a body moving in a straight line.
b) to show the velocity-time graph for a body moving with
i) uniform velocity
ii) uniform acceleration
STEP 4
9. Derive the following equations of motion
a) v = u + at b) s = ut + 12at2 c) v2 = u2 + 2as
10. State Newton's second law of motion and prove F = ma.
Modern Concept Science - 9 43
UNIT Estimated teaching periods Theory Practical
5 2
3
Simple Machine
Syllabus issued by CDC Archimedes
Introduction to simple machine
Mechanical Advantage(MA)
Velocity Ratio (VR)
Efficiency (η)
Lever, Pulley, Inclined plane and wheel and axle
Moment and law of moment
LEARNING OBJECTIVES
At the end of this unit, students will be able to:
describe different types of simple machines (lever, pulley, inclined plane and wheel and axle).
define MA, VR and efficiency related to different simple machines.
solve the numerical problems related to simple machines.
explain the moment and law of moment in lever.
Key terms and terminologies of the unit
1. Simple machine : The device that makes our work easy, fast and convenient is called a simple machine.
2. Complex machine : A machine made from two or more simple machines working together in a complex
structure is called a compound or complex machine.
3. Load : Load is the resistance to be overcome or weight being lifted by a simple machine.
4. Load distance: The distance moved by load in a simple machine is called the load distance.
5. Effort : Effort is the force applied directly to a simple machine to move the load or to do work.
6. Effort distance: The distance moved by effort applied in a simple machine is called the effort distance.
7. Mechanical advantage : The ratio of the load lifted to the effort applied in a simple machine is called the
mechanical advantage.
8. Velocity ratio : The ratio of the distance travelled by effort to the distance travelled by load in a simple
machine is called the velocity ratio.
9. Input work : The work done on a simple machine by a given effort is called an input work.
10. Output work : Work done by a simple machine on the load is called output work.
11. Efficiency : The percentage ratio of output work to input work in a simple machine is called
efficiency.
12. Practical machine : The machine which we use in our daily life is called a real or practical machine.
13. Perfect machine : A hypothetical frictionless machine, in which the total input work is converted into output
work, without any wastage of energy is called an ideal or a perfect simple machine.
14. Lever : A lever is a rigid bar, which is capable of rotating about a fixed point called fulcrum.
44 Simple Machine
15. Principle of lever : The principle of lever states, "When a lever is in an equilibrium condition, the product
of effort and effort arm is equal to the product of load and load arm."
16. First class lever : A lever with load and effort on either side of its fulcrum is called a first class lever.
17. Second class lever : A lever with its fulcrum and effort on either side of the load is called a second class
lever.
18. Third class lever : A lever with load and its fulcrum on either side of effort is called a third class lever.
19. Pulley : A metallic or wooden circular disc, having a groove along its rim, which is capable of
rotating about an axis passing through its center is called a pulley.
20. Fixed pulley : A pulley that does not move up and down with load is called a single fixed pulley.
21. Movable pulley : The pulley which moves up and down with load is called single movable pulley.
22. Block and tackle : The arrangement of pairs of blocks, consisting of one or more pulleys, is called a block
and tackle system.
23. Wheel and axle : A system of two co-axial cylinders of different diameters which rotate together is called
a wheel and axle.
24. Inclined plane : A flat supporting surface, with one end higher than the other in the form of a slope,
which is used for raising or lowering a load is called an inclined plane.
25. Moment : The turning effect of the force acting on a body about an axis is called the moment of
the force.
26. Moment arm: The perpendicular distance of the line of action of a force from the axis of rotation or
fulcrum is called the moment arm.
27. Principle of moments : The principle of moments states: "In an equilibrium condition, the sum of the clockwise
moments about a turning point is equal to the sum of the anticlockwise moments."
Introduction
We use a variety of tools to do our everyday work. For example, we use sharp objects for
cutting, we use pulleys to lift loads, the wheel and axle helps us multiply our effort or to speed
our work, and a slanted surface helps us to move loads. Such devices give us an advantage
by changing the amount, speed, or direction of forces. Thus, the device that makes our work
easy, fast and convenient is called a simple machine. For example, scissor, knife, nut cracker,
bottle opener, spoon, pulley, screw, etc. These machines use muscular energy to work.
Most of the machines we use nowadays are compound in structure. They are made by
combining many simple machines. Thus, a machine made from two or more simple machines
working together in a complex structure is called a compound or complex machine. For
example, clock, bicycle, motor bike, sewing machine, etc. Compound machines use different
types of energy to work such as electrical energy, chemical energy, etc.
Scissors Beam balance Wheelbarrow Pulley Screw Axe
Some simple machines
Modern Concept Science - 9 45
FACT WITH REASON
Why do we use simple machines?
We use simple machines to make our work easier, faster and more convenient.
Advantages of Using Simple Machines
i) Simple machines increase the magnitude of effort applied.
ii) They change the direction of effort applied.
iii) They increase the speed of work.
iv) They transform a force from one place to another.
Terms Related to Simple Machines
Load and Load Distance
Load is the resistance to be overcome or weight being lifted by a simple machine. The SI Unit of
load is newton (N). Load is represented by 'L'. The distance moved by load in a simple machine
is called the load distance or load arm. Its SI Unit is meter (m). It is represented by 'Ld'.
Effort and Effort Distance
Effort is the force applied directly to a simple machine to move the load or to do work. The
SI Unit of effort is newton (N). It is represented by 'E'. The distance moved by effort applied
in a simple machine is called the effort distance or effort arm. Its SI Unit is meter (m). It is
represented by 'Ed'.
Mechanical Advantage
The mechanical advantage is a measure of the force amplification achieved by using a simple
machine. The ratio of the load lifted to the effort applied in a simple machine is called the
mechanical advantage.
MA = Load (L)
Effort (E)
Crowbar
In the figure alongside, the load lifted by the crowbar is 3 times 300 N Fulcrum 100 N
greater than the effort applied. So, when we say the mechanical
advantage of a simple machine is 3, we mean the simple
machine multiplies the effort applied by 3 times.
FACT WITH REASON
MA does not have unit. Why?
MA doesn't have units as it is a simple ratio of two forces.
MA of a simple machine is 2. What does it mean?
MA of a simple machine is 2. It means that the ratio of the load lifted to the effort applied in a simple machine
is 2.
46 Simple Machine
Magnitude of mechanical advantage Memory Tips
The mechanical advantage of different types of simple Force multipliers have a mechanical
machines can be greater than one (MA > 1), equal to one advantage greater than 1 (MA > 1).
(MA = 1) and less than one (MA < 1).
i) If load lifted by a simple machine is greater than the effort applied, then MA of the
simple machine becomes greater than one (i. e. MA >1)
ii) If load lifted by a simple machine is equal to the effort applied, then MA of the simple
machine becomes equal to one (i. e. MA =1)
iii) If load lifted by a simple machine is less than the effort applied, then MA of the simple
machine becomes less than one (i. e. MA <1).
Factors that Affect Mechanical Advantage
Weight and friction of a simple machine are the two factors that affect the mechanical advantage
of a simple machine. In a simple machine, friction causes wastage of energy and reduces its
MA. Friction should be reduced to increase the mechanical advantage of a machine.
FACT WITH REASON
In a simple machine MA is less than VR. Why?
Weight and friction are the two factors that affect the mechanical advantage of the simple machine. We
cannot make these two factors zero in a simple machine. So, the machine has MA less than VR.
Velocity Ratio
The velocity ratio is the ratio of the velocity at which an effort is applied on a machine to the
velocity at which the load moves. Simply, the ratio of the distance travelled by effort to the
distance travelled by load in a simple machine is called the velocity ratio.
VR = Distance travelled by effort (Ed) = Effort distance (Ed)
Distance travelled by load (Ld) Load distance (Ld)
VR does not have unit because it is a simple ratio of two distances.
FACT WITH REASON
VR does not have unit. Why?
VR does not have units as it is a simple ratio of two distances.
VR of a simple machine is 4. What does it mean?
VR of a simple machine is 4. It means that the ratio of the effort distance (Ed) to the load distance (Ld) in a
simple machine is 4.
i) Velocity ratio of a simple machine is independent of friction
Velocity ratio is the ratio between effort distance and load distance, which are constant for a
simple machine. Friction doesn't affect these distances. So the velocity ratio is independent of
friction.
Modern Concept Science - 9 47
ii) Velocity ratio of a simple machine is always greater than its mechanical advantage
The mechanical advantage of a simple machine decreases due to friction and weight of the
moving parts in a simple machine but its velocity ratio remains constant. So the velocity ratio
of a simple machine is always greater than its mechanical advantage.
Input Work
The work done on a simple machine by a given effort is called an input work. It is calculated
by using the formula,
Input work = Effort (E) × Effort distance (Ed)
SI Unit of input work is joule (J).
Output Work
Work done by a simple machine on the load is called output work. It is calculated by using
formula,
Output work = Load (L) × Load distance (Ld)
SI Unit of output work is joule (J).
Efficiency
The percentage ratio of output work to input work in a simple machine is called efficiency.
Efficiency (η) = Output work × 100%
Input work
Efficiency doesn't have a unit except for its percentage sign. It is a simple ratio of two works.
FACT WITH REASON
A simple machine has efficiency 75%. What does it mean?
When we say the efficiency of a simple machine is 75%, that means only 75% of the total energy is utilized
to do useful work and the remaining 25% energy is changed into other forms of energy while overcoming
the frictional force.
Effect of Friction in a Machine
The frictional force converts the applied energy in a simple machine into other forms of energy
such as heat. So the efficiency of a machine decreases as the frictional force increases. Friction
should be reduced to increase the efficiency of a machine.
Methods of Reducing Friction in a Machine
i) Use of Grease or Lubricants : Proper greasing or lubrication between sliding parts of
a simple machine reduces friction.
ii) Use of Ball Bearing : Sliding friction can be reduced by rolling friction with the help of
ball bearings.
iii) Designing Smooth Surfaces : Smooth surfaces cause less friction than rough surfaces do.
48 Simple Machine
Real or Practical Machine
The machine which we use in our daily life is called a real or practical machine. A real simple
machine is never 100 % efficient because of the following reasons:
i) Friction affects the efficiency of a simple machine. Not all input work in a real machine
changes into the output work. Some of the energy applied to do wok changes into other
forms of energy such as heat and sound while overcoming the frictional force.
ii) No any machine is weightless and the weight affects its efficiency.
So, in a real machine, the output work is less than the input work and its efficiency is always
less than 100 %.
Ideal or Perfect Simple Machine
A hypothetical frictionless machine, in which the total input work is converted into output
work, without any wastage of energy is called an ideal or a perfect simple machine.
Since,
Efficiency (η) = Output work × 100%
Input work
In the case of an ideal simple machine, Input work = Output work
Efficiency = 1 × 100% = 100%
So an ideal simple machine has 100 % efficiency.
FACT WITH REASON
An ideal simple machine is a hypothetical concept, why?
No any machine can be weightless and frictionless. It means, the total input work cannot be converted into
the output work without wastage of energy. So an ideal simple machine is a hypothetical concept.
Differences between Real Simple Machines and Ideal Simple Machines
Real Simple Machines Ideal Simple Machines
i. They do not have 100% efficiency. i. They have 100% efficiency.
ii. In real simple machines, output work is ii. In ideal simple machines,
less than input work. Output work = Input work.
Relationship between MA, VR and Efficiency
Efficiency of a simple machine is given by,
Efficiency (η) = Output work × 100%
Input work
or, Efficiency (η) = Load × Load distance × 100%
Effort × Effort distance
Modern Concept Science - 9 49
Load
or, Efficiency (η) = Effort × 100%
Effort distance
Load distance
or, Efficiency (η) = MA × 100%
VR
Types of Simple Machines
a) Lever b) Pulley c) Wheel and axle
d) Inclined Plane e) Wedge f) Screw
Lever
Effort
A lever is a rigid bar, which is capable of Load Effort arm
rotating about a fixed point called fulcrum.
Fulcrum
The weight to be lifted by using a lever is Typical lever
called the load (L) and the force applied on
the lever to lift the load is called the effort Load arm
(E). The effort distance (Ed) is the distance
of the effort from the fulcrum. The distance
of the load from the fulcrum is called the load distance (Ld).
Principle of Lever
The principle of lever states, "when a lever is in an equilibrium condition, the product of effort
and effort arm is equal to the product of load and load arm."
Effort (E) × effort arm (Ed) = Load (L) × load arm (Ld)
Types of Lever
Depending on the relative position of load, effort and fulcrum, levers are classified into three
groups.
First Class Lever
A lever with load and effort on either side of its fulcrum is called a first
class lever. For example, crowbar, seesaw, scissors, DHIKI, etc.
Crowbar See-saw Scissors Pliers Nail cutter
First class lever
The mechanical advantage of the first class lever depends on Crowbar
the position of the fulcrum, which determines the Ed and Ld.
i) When Ed > Ld, M.A. > 1 Load
ii) When Ed < Ld, M.A. < 1 Effort
iii) When Ed = Ld, M.A. = 1
Fulcrum
50 Simple Machine
Second Class Lever
A lever with its fulcrum and effort on either side of the load is called a second class lever. For
example, nutcracker, bottle opener, lemon squeezer, wheelbarrow, etc.
Wheelbarrow Nutcracker Bottle opener
Second class lever
In case of the second class lever, the effort distance (Ed) is always
greater than the load distance (Ld), i.e. Ed > Ld, so M.A. > 1.
Thus, by using a second class lever, a greater load can be lifted with
lesser effort, i.e. the second class levers are used as force multipliers.
FACT WITH REASON
MA of second class lever is always more than one, why?
In case of the second class lever, the effort distance (Ed) is always greater than the load distance (Ld), i.e.
Ed > Ld. So, MA of second class lever is always more than one.
Second class lever is called a force multiplier. Why?
In case of the second class lever, the effort distance (Ed) is always greater than the load distance (Ld), i.e.
Ed > Ld. Thus, by using a second class lever, a greater load can be lifted with lesser effort. So, a second class
lever is called a force multiplier.
Third Class Lever
A lever with load and its fulcrum on either side of effort is called a third class lever. For
example, fishing rod, broom, shovel, fire tongue, etc.
Shovel Fishing rod Fire tongs Broom
Third class lever
In case of a third class lever, the effort distance (Ed) is always less
than the load distance (Ld).
i.e. Ed < Ld. So, M.A. < 1
Thus, by using a third class lever, a greater load cannot be lifted
with lesser effort, i.e. the third class levers cannot be used as
force multipliers. Instead, the third class levers are used as speed
multipliers.
Modern Concept Science - 9 51
FACT WITH REASON
MA of a third class lever is always less than one, why?
In case of the third class lever, the effort distance (Ed) is always less than the load distance (Ld), i.e. Ed < Ld.
So, MA of third class lever is always less than one.
Third class lever is called a speed multiplier. Why?
By using a third class lever, a greater load cannot be lifted with lesser effort, i.e. the third class levers cannot
be used as force multipliers. Instead, the third class levers are used as speed multipliers.
Solved Numerical 3.1
The efficiency of a wheelbarrow shown in the given figure is 80%. Calculate the effort
required to carry 20 kg sand with the help of the wheelbarrow.
Solution: Given, Effort
Mass carried (m) = 20 kg Sand
Load (L) = mg = 20 kg ×10 m/s2 = 200 N
Load distance (Ld) = 50 cm = 0.5 m 50 cm 75 cm
Effort distance (Ed) = 50 + 75 = 125 cm = 1.25 m Pivot
Efficiency of the wheelbarrow (η) = 80%
According to the formula, Weight of sand 20 Kg
Efficiency (η) = Output work × 100%
or, Input work
or,
or, 80% = 200 × 0.5 × 100%
∴ E× 1.25
E = 80 100 × 100
× 1.25
E = 100 × 100
100
E = 100
The effort required to carry sand with the help of the wheelbarrow is 100 N.
Pulley
A pulley consists a grooved disc, with a rod passing through its center to facilitate its free
rotation. A thread or cable over the groove is used to rotate the disc. Thus, a metallic or wooden
circular disc, having a groove along its rim, which is capable of rotating about an axis passing
through its center is called a pulley. Pulleys are an age-old simple machines. They are widely
used in daily life even today. A common traditional use of pulley is to lift buckets of water from
a well. Nowadays several electrical devices, vehicles, cranes, etc. are handled with the pulleys.
52 Simple Machine
Types of Pulley
Effort
Force
Force
Single fixed pulley Single movable pulley Block and tackle system
Single Fixed Pulley
A single fixed pulley is attached to a rigid support. It has a load attached on one end of the
rope. Load moves up over the pulley while pulling the other segment of rope downward.
Thus, a pulley that does not move up and down with load is called a single fixed pulley.
FACT WITH REASON
The velocity ratio of a single fixed pulley is always one, why?
In case of a single fixed pulley, the distance moved downward by the effort is equal to the distance moved
upward by the load (i.e. Ed = Ld). So, the velocity ratio of a single fixed pulley is always one.
A single fixed pulley uses more effort than the load to be lifted. It doesn't multiply the effort
applied but it is widely used due to the following reasons:
i) A single fixed pulley changes the direction of effort applied to make our work easy.
ii) While working with a single fixed pulley, it is easier to apply force downward due to
our body weight.
Some common uses of single fixed pulley
i) A single fixed pulley on fishing rod helps us to catch fish.
ii) Hoisting a flag on a flagpole becomes easier with the help of a single fixed pulley.
iii) A single fixed pulley is used to drop a bucket into the well, collect water, and pull it up again.
FACT WITH REASON
A single fixed pulley works like a first class lever, why?
In a single fixed pulley, the fulcrum, i.e. the axis of the pulley, is in between the force and the load. So, a
single fixed pulley works like a first class lever.
Solved Numerical 3.2
How much is the distance moved by effort to lift 250 N load by 1 m in a pulley shown in the
given figure? Calculate the efficiency of the pulley if effort applied is 300 N.
Solution: Given,
Load (L) = 250 N
Effort (E) = 300 N Force
Modern Concept Science - 9 53
Load distance (Ld) = 1 m
In case of a single fixed pulley,
Distance moved by effort (Ed) = Distance moved by load (Ld)
∴ Distance moved by effort (Ed) = 1 m
According to the formula,
Efficiency (η) = Output work × 100%
Input work
or, Efficiency (η) = 250 × 1 × 100% = 25 × 100% = 83.33%
300 × 1 30
The efficiency of the pulley shown in the given figure is 83.33%.
Single Movable Pulley
A single movable pulley has a pulley suspended on a rope. One end of the rope is attached to
a fixed rigid support and effort is applied at another end. The load to be lifted is hanged on
pulley. Thus, the pulley which moves up and down with load is called single movable pulley.
FACT WITH REASON
The velocity ratio of a single movable pulley is always two, why?
In case of a single movable pulley, the distance moved by the effort is twice the distance moved by the load
(i.e. Ed = 2Ld). So, the velocity ratio of a single movable pulley is always two.
Mathematically, VR = Distance moved by effort (Ed) = 2 LD =2
Distance moved by load (Ld) LD
A single movable pulley is used to multiply force in Memory Tips
modern elevators, weight lifting machines, etc. However,
the disadvantage is that the weight of the pulley should be Velocity ratio of a single movable
pulled up. pulley = the number of rope segments
to support the load = two
FACT WITH REASON
A single movable pulley works like a second class lever, why?
In a single movable pulley, the load suspended from the pulley is in between effort and the fulcrum (i.e. the
end of supporting rope). So, a single movable pulley works like a second class lever.
Differences between a Single Fixed Pulley and a Single Movable Pulley
Single Fixed Pulley Single Movable Pulley
1. Single fixed pulley doesn't move up 1. Single movable pulley moves up and
and down with a load. down with a load.
2. It changes the direction of effort 2. It multiplies the effort applied.
applied.
3. Its velocity ratio (VR) is one. 3. Its velocity ratio (VR) is two.
4. It works like a first class lever. 4. It works like a second class lever.
54 Simple Machine
Solved Numerical 3.3
How much is the distance moved by effort to lift a 300 N load by 2 m in the pulley shown in
the given figure? Calculate the efficiency of the pulley. If effort applied is 200 N.
Solution: Given,
Load (L) = 300N Force
Effort (E) = 200N
Load distance (Ld) = 2m
In case of a single movable pulley,
Distance moved by effort (Ed) = 2 × Ld
∴ Distance moved by effort (Ed) = 2 × 2 = 4 m
According to the formula,
Efficiency (η) = Output work × 100%
Input work
or, Efficiency (η) = 300 × 2 × 100% = 6 × 100% = 75%
200 × 4 8
The efficiency of the pulley shown in the given figure is 75 %.
Block and Tackle System fixed pulley block
A combination of pulleys is called a block. The arrangement fixed end of rope T spring balance
of pairs of blocks, consisting of two or more pulleys, is T T reading the effort force
called a block and tackle system. The upper set of pulleys
attached to a rigid support is called block and the lower set T E
of pulleys which carries the load is called tackle. It is also
called a compound pulley due to the presence of both fixed moving pulley block
block and movable block in a block and tackle.
slotted masses load
FACT WITH REASON A block and tackle with VR = 4
Block and Tackle
A block and tackle system is usually used to lift or pull heavy loads easily, why?
The block and tackle changes the direction and multiplies the force at the same time. The fixed block
changes the direction and movable block magnifies the force. So, a block and tackle system is usually used
to lift or pull heavy loads easily.
In a crane, the block and tackle system helps to lift heavy loads and machines. However, the
disadvantage is that the effort applied travels long distances in a block and tackle. Velocity
ratio of a block and tackle system is equal to the number of rope segments to support the load.
It is also equal to the number of pulleys used. For example, in a block and tackle system with
two pulleys in the block and one pulley in the tackle, the velocity ratio is equal to three.
Solved Numerical 3.4
How much is the distance moved by effort to lift a load by 2m in the block and tackle
system having five pulleys? If the efficiency of the pulley system is 75%, then calculate the
effort applied to lift the 3000N load.
Modern Concept Science - 9 55
Solution: Given,
Load (L) = 3000N
Load distance (Ld) = 2m
In case of a block and tackle system with 5 pulleys,
velocity ratio = number of pulleys = 5
or, 5 = Distance moved by effort (Ed)
Distance moved by load (Ld)
or, 5 = Ed
2
or, Ed = 5 × 2 = 10 m
Efficiency of the block and tackle system (η) = 75%
Now, efficiency (η) = MA × 100%
L VR
or, 75% = E × 100%
5
or, 75 = 3000 × 100
E×5
or, E = 3000 × 100 = 800 N
75 × 5
The effort required to lift the load by the given block and tackle system is 800 N.
ACTIVITY 1
Measure the weight of a 1kg mass (i.e. Load) by a spring balance. Use spring balance at one end of the
rope to lift the load with the help of a single fixed pulley, single movable pulley and block and tackle
system. Fill the data in the given table after your measurements. Also, calculate the corresponding
efficiencies of the different types of pulleys. Analyze the data and write the conclusion that you draw
from your results in different cases.
S.N. Type of Pulley VR Load (L) Effort (E) MA Efficiency(η)
1. Single Fixed Pulley
2. Single Movable Pulley
3. Block and Tackle System
Wheel and Axle Wheel
A system of two co-axial cylinders of different diameters which Axle
rotate together is called a wheel and axle. The cylinder with the
larger diameter is called the wheel and the one with the smaller Effort Load
diameter is called the axle. We make a frequent use of wheel and
axle in our daily life. For example, door knob, knob of the tap, Wheel and axle
screw driver, etc. Wheel and axle cannot increase both the force
and the speed at the same time. It can work either like a force or a
speed multiplier.
56 Simple Machine
Wheel and Axle as a Force Multiplier
Effort distance longer than the load distance is the condition to multiply effort applied in
a simple machine. When effort is applied from wheel and load is attached to the axle of a
wheel and axle, effort distance becomes longer than the load distance. This is the condition to
multiply effort in a wheel and axle. For example, steering wheel, screw-drivers, doorknob etc.
Force multiplication can be adjusted by changing diameter of the wheel.
FACT WITH REASON
The truck steering wheel is larger than a car steering wheel, why?
A larger diameter steering wheel in trucks multiplies more force than that of a smaller diameter steering
wheel in cars. This makes drivers easy to control on movement of the front wheels of a heavily loaded truck
through the steering linkage. So, the truck steering wheel is larger than a car steering wheel.
Wheel and Axle as a Speed Multiplier
Load distance longer than effort distance is the condition for speed multiplication in a simple
machine. When load is attached to the wheel and effort is applied from axle of a wheel and
axle, load distance becomes longer than the effort distance. This is the condition for speed
multiplication in a wheel and axle. For example, LATTAI, wheels on vehicles, fan etc. Vehicles
can move forward quickly due to the great amount of turning force applied by engine to the
axle attached with the wheel.
FACT WITH REASON
Wheel and axle can't increase both the force and the speed at the same time, why?
A wheel and axle multiplies force when the force applied is on its wheel. On the other hand, if the force
applied is on the axle of the wheel and axle, it increases the speed of work. So wheel and axle can't increase
both the force and the speed at the same time.
Wheel and Axle as a Continuous Lever C
The wheel and axle is a continuous first class lever. This is because the Y
common axis of wheel and axle acts as a fulcrum and lies in between load X
and effort. In wheel and axle, effort can be applied in a continuous manner
until the load reaches the required height. In the given figure, C is fulcrum,
X is effort and Y is load.
MA, VR and Efficiency (η) of Wheel and Axle
Simple Machine MA VR Efficiency (η)
Wheel and Axle VR = Effort distance η = MA × 100%
Load distance VR
Wheel
When effort is applied from wheel, L
Axle
MA = L VR = Circumference of wheel (2πR) η = E × 100%
E Circumference of axle (2πr) R
Radius of wheel (R) r
Radius axle (r)
Effort Load VR = L × r
E × R
η = × 100%
Modern Concept Science - 9 57
Solved Numerical 3.5
In a wheel and axle, the radius of the wheel is 30 cm and that of the axle is 10 cm. If a load
of 600 N is lifted by applying an effort of 250 N then calculate its MA, VR and efficiency.
Solution: Given,
Load (L) = 600 N
Effort (E) = 250 N
Radius of wheel (R) = 30 cm
Radius of axle (r) = 10 cm
Now, MA = L = 600 = 2.4
E 250
In case of a wheel and axle,
VR = R = 30 = 3
r 10
According to the formula,
Efficiency (η) = MA × 100% = 2.4 × 100% = 80%
VR 3
The efficiency of the wheel and axle is 80 %.
Solved Numerical 3.6
In a wheel and axle, the radius of the wheel is 0.5 m and that of the axle is 25 cm. How much
should be the distance moved by effort to lift a load of 450 N by 2 m? If the effort applied
is 300 N then calculate:
i. MA ii. VR iii. Input work
iv. Output work v. Efficiency
Solution: Given,
Load (L) = 450 N
Effort (E) = 300 N
Radius of wheel (R) = 0.5 m = 50 cm
Radius of axle (r) = 25 cm
Distance moved by load (Ld) = 2 m
Now, MA = L = 450 = 1.5
E 300
In case of a wheel and axle,
VR = R = 50 = 2
r 25
Also, VR = Effort distance = 2
Load distance
or, Effort distance (Ed) = 2 × Load distance (Ld)
58 Simple Machine
or, Effort distance (Ed) = 2 × 2 = 4 m
Again, Input work = Effort × Effort distance = 300 × 4 = 1200 J
Output work = Load × Load distance = 450 × 2= 900 J
According to the formula,
Efficiency (η) = Output work × 100% = 900 × 100% = 75%
Input work 1200
The efficiency of wheel and axle is 75 %.
Differences between Wheel and Axle and Pulley
Wheel and Axle Pulley
1. Wheel and axle consists of two cylinders of 1. Pulley consists of a grooved disc
different diameters. with axis through its center.
2. In a wheel and axle, both the cylinders 2. In a pulley, the disc rotates about
rotate together. the fixed axis.
3. Its velocity ratio is given by 3. Its velocity ratio is given by VR =
VR = Radius of wheel (R) number of rope segments to support
Radius axle (r ) the load.
Inclined Plane h l
An inclined plane is a simple machine with a slanted Inclined Plane
surface. Thus, a flat supporting surface, with one end
higher than the other in the form of a slope, used for
raising or lowering a load is called an inclined plane. It
is also known as a ramp. For example, staircase, a ramp
used to load goods into trucks, a road winding uphill.
Inclined Plane as a Force Multiplier
In an inclined plane, the length (slope-l) acts as the effort distance and the height acts as the
load distance. The length (slope -l) of an inclined plane is always greater than its height. This
is the condition to multiply the effort in an inclined plane.
MA, VR and Efficiency (η) of Inclined Plane
Simple Machine MA VR Efficiency (η)
VR = Effort distance η = MA × 100%
Load distance VR
Inclined Plane
VR = Length of incline plane (l) L
l Height of incline plane (h)
h MA = L η = E × 100%
E l
l
VR = h h
η = L × h × 100%
E × l
Modern Concept Science - 9 59
Solved Numerical 3.7
Study the given figure and calculate:
i. MA ii. VR iii. Input work
iv. Output work v. Efficiency
Solution: Given,
1m 200 N 500 N
Load (L) = 500N 4m
Effort (E) = 200N
Load distance (Ld) = 1m Inclined Plane
Effort distance (Ed) = 4m
Now, input work = E × Ed = 200 × 4 = 800 J
Again, output work = L × Ld = 500 × 1 = 500 J
Now, MA = L = 500 = 2.5
E 200
VR = Effort distance = 4 = 4
Load distance 1
According to the formula,
Efficiency (η) = Output work × 100% = 500 × 100% = 62.5%
Input work 800
Alternatively,
Efficiency (η) = MA × 100% = 2.5 × 100% = 62.5%
VR 4
The efficiency of inclined plane is 62.5 %.
Moment of a Force Nut Spanner Effort
In our daily life, we turn the valve knob or tap lever to
turn the water supply on and off, we push the door to
open and close it, we turn the screw with the help of a
screw driver, we turn a spanner to tighten and loosen its
nuts and bolts. These activities are possible due to the
turning effect of a force. Spanner
A force acting on a body can cause either a displacement
or a rotation about an axis. Thus, the turning effect of the force acting on a body about an axis is
called the moment of the force. This turning effect of force may be clockwise or anticlockwise.
We apply a force on the handle of a door to close and open it. Have you ever experienced the
difference in the force applied to open a door, while applying forces at different positions from
the hinge of the door? We find that the force needed to open the door is less when the force is
applied at the handle of the door. So the moment of force depends on the perpendicular distance
of the line of action of a force from the axis of rotation or the fulcrum (i.e. the moment arm).
60 Simple Machine
When the force applied is perpendicular to the lever then the moment of the force is equal to
the product of the force applied and the moment arm.
Mathematically,
Moment = F × s
Where, F = force applied at right angle to the moment arm, s = moment arm
The SI Unit of moment of a force is newton meter (Nm). 50 N 0.15 m Effort
Solved Numerical 3.8
Calculate the moment of the force applied on the spanner
in the given figure.
Solution: Given,
Force applied at right angle to the moment arm (F) = 50N
Moment arm (s) = 0.15 m
Now, moment of a force is given by Moment = F × s = 50 × 0.15 = 7.5 Nm
Factors Affecting the Moment of a Force
When a force applied is perpendicular to the lever,
Moment = F × s
The moment of a force depends on:
i) length of the moment arm
ii) magnitude of the force acting at a right angle to the moment arm
Some Examples of Turning effect of Force
i) It is easier to loosen a tight nut using a long spanner.
ii) During the storm, a tall tree has a greater probability of breaking than a short tree.
iii) Probability of breaking of a branch increases when a person moves towards the end of
the branch of a tree.
iv) The handle of a door is fixed at a greater distance from the hinge.
v) The handle of a screwdriver is made wider.
vi) The steering wheel of a truck is made larger than the average for vehicles.
FACT WITH REASON
It is easier to loosen a tight nut using a long spanner. Why?
A long spanner has a longer moment arm. The moment of a force depends on the moment arm. The longer
the moment arm, the greater the turning effect of a force applied on it. So it is easy to loosen a tight nut using
a long spanner.
During the storm,a tall tree has a greater probability of breaking than a short tree. Why?
A tall tree has a longer moment arm than that of a short tree. Due to this, there is a greater turning effect of
force on the taller tree during the storm and its probability of breaking is higher than in the case of a short tree.
Modern Concept Science - 9 61
Probability of breaking of a branch increases when a person moves towards the end of the branch of a tree. Why?
When a person moves towards the end of the branch of a tree, the length of moment arm increases, producing
a greater turning effect on the branch. Therefore, the probability of breaking the branch increases.
The handle of a door is fixed at a greater distance from the hinge. Why?
A handle of a door fixed at a greater distance from the hinge has a longer moment arm. This causes the force
applied to produce more turning effect on the door. Hence, less force is required to open and close the door.
The handle of a screw-driver is made wider. Why?
A wide handle of a screw-driver produces more tuning effect of a force. As a result it becomes easy for us
to loosen a tightly stuck screw.
The steering wheel of a truck is made larger than the average for vehicles. Why?
Larger steering wheel has a longer distance from its axis. So, it has a longer moment arm and more turning
effect of force. As a result, it makes easy for the truck driver to control the movement of the front wheels
through the steering linkage.
Principle of Moment
The clockwise turning effect of a force is called the clockwise moment and the anticlockwise
turning effect of a force is called the anticlockwise moment.
The principle of moments states "In an equilibrium condition, the sum of the clockwise
moments about a turning point is equal to the sum of the anticlockwise moments."
i.e. in equilibrium condition,
The sum of clockwise moments = The sum of anticlockwise moments
Solved Numerical 3.12 400N 1m
Study the given figure and calculate: 200 N 300 N
i) clockwise moment. 2m
ii) distance of the second boy from the fulcrum shown
in the given figure by using principle of moment.
Solution: Given,
Weight of the first boy (W1) = 300N
Moment arm for the first boy (d1) = 2m
Weight of the girl (W2) = 200N
Moment arm for the girl (d2) = 1m
Weight of the second boy (W3) = 400N
62 Simple Machine
Moment arm for the second boy (d3) = x
Now, sum of the clockwise moments = W1d1 + W2d2 = 300 × 2 + 200 × 1 = 800 Nm
According to the principle of moment,
Sum of the anticlockwise moments = sum of clockwise moments
400 × d3 = 800
or, d3 = 800 = 2 m
400
The distance of the second boy from the fulcrum should be 2m.
ANSWER WRITING SKILL
1. Which pulley can multiply force as well as change the direction of force?
Ans: Block and tackle system is the pulley that can multiply force as well as change direction of force.
2. Write any two application of a simple machine.
Ans: Simple machines have many uses to us. Among them, any two applications are:
i) Simple machine helps to multiply force, increase the speed of work and also helps to work safely
and conveniently.
ii) Simple machine transfers force from one point to another and also changes direction of the force.
3. Single fixed pulley cannot multiply force but it is widely used by people in well and many other places,
why?
Ans: Single fixed pulley cannot multiply force but it is widely used because it changes the direction of force.
As a result the work becomes easier.
4. Door handles are kept near the edges of the door planks. Why?
Ans: Door handles are kept near the edges of the door planks because it helps to increase the length of
moment arm. As a result, it helps to increase the moment of force. Thus, it will be easier to open the door.
5. Differentiate between output work and input work.
Ans: Differences between output work and input work are:
Output work Input work
1. Work done by the machine is called output work. 1. Work done in the machine is called input work.
2. Output work = Load x load distance 2. Input work = Effort x effort distance
3. Output work in a practical machine is always 3. Input work in a practical machine is always
less than input work. more than output work.
6. List the types of lever and define them with examples.
Ans: There are three types of lever. They are:
i) First class lever: It is a lever in which fulcrum lies between load and effort. Examples: see-saw,
nail cutter, etc.
ii) Second class lever: It is a lever in which load lies between fulcrum and effort. Examples: lemon
squeezer, nutcracker, etc.
iii) Third class lever: It is a lever in which effort is applied between fulcrum and load. Examples:
spoon, shovel, etc.
Modern Concept Science - 9 63
7. Calculate MA, VR and η of the inclined plane to lift 300N load by applying 200N effort. If the length and
height of the inclined plane are 7.5 m and 4 m respectively.
Solution:
Length of inclined plane (l) = effort distance =7.5 m
Height of inclined plane (h) = load distance = 4 m
Load (L) = 300 N
Effort (E) = 200 N
Mechanical advantage (MA) = ?
Velocity ratio (VR) = ?
Efficiency (η) = ?
Using formula, MA = L = 300 = 1.5
E 200
Again, VR = l = 7.5 = 1.875
Now, h 4
Efficiency = MA × 100% = 1.5 × 100% = 80%
VR 1.875
Therefore, MA is 1.5, VR is 1.875 and the efficiency is 80%. 50 cm
8. Study the given diagram and answer the following questions. 20 cm
i) Name the device shown in the diagram.
Ans: I t is a diagram of wheel and axle.
ii) Give one example of such machine.
Ans: Steering of a truck is an example of wheel and axle. 1000 N 2000 N
iii) Write one use of this machine.
Ans: This device can be used to multiply force. Examples: sewing machine, bicycle, etc.
iv) Calculate the efficiency of the given machine.
Ans: Solution:
Radius of wheel (R) = 50 cm = 0.5 m
Radius of axle (r) = 20 cm = 0.2 m
Load (L) = 2000 N
Effort (E) = 1000 N
Efficiency (η) =?
Using formula, MA = L = 2000 =2
E 1000
Again, VR = R = 0.5 = 2.5
Now, r 0.2
Efficiency = MA × 100% = 2 × 100% = 80%
VR 2.5
Therefore, efficiency of the given machine is 80%.
9. What is a pulley? Make a list of different types of pulleys and distinguish them.
Ans: Pulley is a simple machine which has a cylindrical disc with a groove on its circumference from where
rope can pass.
64 Simple Machine
There are three types of pulleys. They are:
i) Single fixed pulley
ii) Single movable pulley
iii) Block and tackle system
Distinguishing between these pulley
SN Single fixed pulley Single movable pulley Block and tackle system
1 It is a pulley in which disc is fixed It is a pulley in which disc is It is a compound pulley made
in a rigid surface. allowed to move up and down by combining fixed pulleys and
freely in a rope. movable pulleys.
2 Velocity ratio is always 1. Velocity ratio is always 2. Velocity ratio is equal to the
number of pulleys used.
3 It can change direction of force It can multiply the force but cannot It can change the direction of
but cannot multiply the force. change the direction of force. force and also multiply force.
10. A load of 500N is lifted by applying an effort of 200N with the help of a lever. The effort distance and load
distance are 60cm and 20cm respectively, calculate MA, VR, and efficiency of the simple machine used.
Solution:
Load (L) = 500N
Effort (E) = 200N
Effort distance (Ed) = 60cm
Load distance (Ld) = 20cm
Now, mechanical advantage is given by
MA = L = 500 = 2.5
E 200
Ed 60
Velocity ratio is given by VR = Ld = 20 =3
Efficiency = MA × 100% = 2.5 × 100% = 83.33%
VR 3
Therefore, the efficiency of the simple machine is 83.33%.
11. The efficiency of a lever is 60% and its mechanical advantage is 4.
(i) Find the effort to be applied to lift a load of 1000N.
(ii) What is the velocity ratio of the lever used?
(iii) Find the output work when the load is moved by a distance of 20m.
Solution: Efficiency of the lever = 60%
(i)
Mechanical advantage (MA) = 4
Load lifted (L) = 1000N
or, Now, MA = L
E
or, 1000
4= E
E= 1000 = 250N
4
Modern Concept Science - 9 65
(ii) Efficiency of a simple machine is given by
Efficiency = MA × 100%
VR
4
or, 60% = VR × 100%
or, VR = 4 × 100
60
or, VR = 6.667
(iii) When the load distance (Ld) = 20m
Output work = Load × load distance = 1000×20 = 20000 J
Therefore, effort = 250N, VR = 6.667, output work = 20000 J
12. A load is lifted with the help of a pulley as shown in the given figure. Calculate
i) MA of the pulley
ii) Efficiency
iii) How much percentage of energy is wasted while lifting the load?
Solution: Load (L) = 80N 80N 100N
Effort (E) = 100N
Mechanical advantage(MA) = L = 80 = 0.8
E 100
In case of a single fixed pulley, VR = 1
Now, efficiency is given by
Efficiency = MA × 100% = 0.8 × 100% = 80%
VR 1
Energy wasted = 100 – 80 = 20 %
13. In a wheel and axle, the radius of wheel (R) is 9cm and the radius of the axle (r) is 3cm. Find the effort
distance and load distance after one complete rotation of this wheel and axle. If the effort applied is
400N to lift a load of 500N with the help of this wheel and axle, calculate its efficiency.
Solution:
Radius of wheel (R) = 9cm
Radius of axle (r) = 3cm
Effort applied (E) = 400N
Load Lifted (L) = 500N
After one complete rotation,
Effort distance = circumference of wheel = 2πR = 2 × 22 × 9= 56.57 cm
7
Load distance = circumference of axle = = 2πr = 2 × 22 × 3 = 18.85 cm
Now, efficiency of wheel and axle 7
Efficiency = L×r × 100% = 500 × 3 × 100% = 41.667%
E×R 400 × 9
Therefore, efficiency of the wheel and axle is 41.667%
66 Simple Machine
14. A load of 100N is lifted up to 2m by using an inclined plane as shown in the given figure.
(i) Calculate MA, VR and efficiency.
(ii) What should be the length of the plane to pull the same load with effort of 25N remaining the
efficiency constant.
Solution: Load (L) = 100 N E = 50 N
Effort (E) = 50 N 5m
Length of the inclined plane (l) = 5 m 100 N
Height of the inclined plane (h) = 2 m
(i) Now, mechanical advantage is given by
MA = L = 100 =2
E 50
l 5
Velocity ratio is given by VR = h = 2 = 2.5
Efficiency is given by
Efficiency = MA × 100% = 2 × 100% = 80%
VR 2.5
(ii) To lift the load with 25N
Efficiency = MA × 100%
VR
or, 80% = MA × 100%
VR
L
or, 80% = E × 100%
l
h
or, l = L × 100 = 100 × 100 =5
h E 80 25 80
or, l = 5 × h = 5 × 2 = 10m
Therefore, the length of plane should be made 10m.
STEPS EXERCISE b) Complex machine
d) Effort
STEP 1 f) Velocity ratio
h) Output work
1. Define j) Practical machine
a) Simple machine
c) Load
e) Mechanical advantage
g) Input work
i) Efficiency
Modern Concept Science - 9 67
k) Perfect machine l) Lever
m) Principle of lever n) First class lever
o) Second class lever p) Third class lever
q) Pulley r) Fixed pulley
s) Movable pulley t) Block and tackle
u) Wheel and axle v) Inclined plane
w) Moment x) Principle of moments
2. Very Short Answer Questions
a) 'Mechanical advantage of a simple machine is 3.' What does that mean?
b) Write an expression to show the relationship between mechanical advantage,
velocity ratio and efficiency for a simple machine.
c) Write the condition for the following to happen:
i) to multiply effort with the help of a simple machine
ii) to complete our work faster with the help of a simple machine
iii) to multiply effort with the help of a wheel and axle
iv) to speed up work with the help of a wheel and axle
v) to make work easier by using an inclined plane
d) Write the formula to calculate velocity ratio of following
i) pulley ii) wheel and axle iii) inclined plane
e) Write the SI Unit and CGS unit of moment of force.
STEP 2
3. Short Answer Questions
a) Write the purpose of using simple machines.
b) What is the relationship between mechanical advantage and velocity ratio for
i) an ideal simple machine ii) a practical machine
c) Explain the basis on which levers are classified.
d) How does a single fixed pulley help us to draw water from a well?
e) Explain any two applications of the moment of force.
f) Explain the factors affecting the moment of force.
g) 'The wheel and axle is called a continuous lever.' Explain
4. Differentiate Between:
a) simple machine and complex machine
b) single fixed pulley and single movable pulley
c) pulley and wheel and axle
68 Simple Machine
5. Give Reason.
a) The efficiency of a practical simple machine can never be 100 %.
b) A single fixed pulley does not multiply effort though it is widely used.
c) The velocity ratio of a single fixed pulley is one.
d) The velocity ratio of a single movable pulley is two.
e) Use of lubricants increases efficiency of a machine.
f) A long spanner is used to unscrew a rusted or tight nut.
g) The handle of a door is fixed at an end opposite of the hinge.
h) In a storm, the probability of breaking tall tree is more than that of the dwarf tree.
STEP 3
6. Numerical Problems
a) A wheel barrow is used to carry a load of 200N by applying an effort of 100N.
The effort distance is 125cm and the load distance is 50cm. Find its MA, VR, and
efficiency. [Ans: MA=2, VR=2.5, η = 80%]
b) A load of 200N is moved 2m by an effort of 100N moving through 8m. What is the
efficiency of the machine? [Ans: MA=2, VR= 4, η = 50%]
c) The efficiency of a lever is 60% and its mechanical advantage is 4.
i) Find the effort to be applied to lift a load of 1000N.
ii) What is the velocity ratio of the lever used?
iii) Find the output work when the load is moved by a distance of 20m.
[Ans: effort = 250N, VR = 6.667, output work = 20000J]
d) The mechanical advantage of a machine is 5 and its efficiency is 80 %. It is used to
lift a load of 500N to a height of 20m. Calculate:
i) the effort required ii) the effort distance
iii) the work done on the machine iv) the output work
[Ans: a. 100N b. 125m c. 12500J d. 10000J]
e) A load is lifted with the help of a pulley as shown in the given figure.
Calculate
i) MA of the pulley
ii) Efficiency 80N 100N
iii) How much percentage of energy is wasted while lifting the
load? [Ans: MA = 0.8, η = 80% , 20%]
f) A block and tackle system has five pulleys. If an effort of 1000N is required to lift
a load of 4500N, find
i) MA ii) VR iii) Efficiency [Ans: i. 4.5 ii. 5 iii. 90%]
Modern Concept Science - 9 69
g) A worker uses a pulley system to raise a 250N carton by 16.5m. A force of 150N is
exerted and the rope is pulled 33m. Find:
i) mechanical advantage (MA)
ii) velocity ratio
iii) efficiency of the pulley system [Ans: i. 1.667, ii. 2 iii. 83.35% ]
h) In a wheel and axle, the radius of wheel (R) is 9cm and the radius of the axle (r)
is 3cm. Find the effort distance and load distance after one complete rotation
of this wheel and axle. If the effort applied is 400N to lift a load of 500N with
the help of this wheel and axle, calculate its efficiency. [Ans: 41.667%]
i) Find MA, VR and efficiency of the wheel and axle shown in the given figure.
[Ans: MA= 2.5, VR= 5, η = 50%]
20 cm
4 cm
20 N 50 N
j) A force of 50N is applied to a body at a distance of 20cm from the point at which
it is pivoted. Calculate the moment of force about the pivot. [Ans: 10Nm]
k) When a force of 100N is applied about the axis of rotation of a body, it produces
a moment of 50Nm. Find the distance of the point of application of the force from
the axis of rotation. [Ans: 0.5m]
7. Draw the Diagram
a) to show a single fixed pulley and a single movable pulley.
b) to show a block and tackle system of pulleys having a velocity ratio of 5. Also
indicate the position of load and effort.
c) to show a wheel and axle.
STEP 4
8. Derive a formula to show the relationship between mechanical advantage, velocity
ratio, and efficiency.
9. Explain different types of levers with a suitable diagram.
10. Describe the types of pulley with the help of their diagram.
11. Explain the structure and working of a wheel and axle.
70 Simple Machine
UNIT Estimated teaching periods Theory Practical
8 2
4
Work, Energy and Power
Syllabus issued by CDC Albert Einstein
Work (work against friction and work against gravity).
Energy (potential energy, kinetic energy, electrical energy, heat energy, light energy, sound energy,
magnetic energy, nuclear energy and chemical energy)
Power
Numericals related to work, energy and power
LEARNING OBJECTIVES
At the end of this unit, students will be able to:
differentiate and relate work, energy and power.
describe the types of energy.
solve the problems related to work, energy and power.
Key terms and terminologies of the unit
1. Work : Work is said to be done when a body moves in the direction of the force
applied.
2. One joule of work : One joule of work is done when a force of 1N displaces an object through a
distance of one meter in the direction of the force.
3. Work done against friction : The work done in pushing or pulling a load by applying a force against friction
is called the work done against friction.
4. Work done against gravity : The work done in lifting weights by applying a force against gravity is called the
work done against gravity.
5. Energy : The capacity of a body to do work is called energy.
6. Mechanical energy : The energy possessed by a body due to its motion or position is called its
mechanical energy.
7. Kinetic energy : The energy possessed by a body in motion is called the kinetic energy.
8. Potential energy : The energy possessed by a body due to its position or deformation is called
the potential energy.
9. Gravitational potential energy : The energy possessed by a body by virtue of its vertical position above the
ground is called the gravitational potential energy.
10. Elastic potential energy : The energy possessed by a body due to its deformed shape or configuration
is called the elastic potential energy.
11. Heat : Heat is a form of energy that produces a sensation of warmth in us.
Modern Concept Science - 9 71
12. Light : Light is a form of energy that produces a sensation of vision in us.
13. Sound : Sound is a form of energy produced by vibrating bodies.
14. Electrical energy : The transfer of electrons from an insulator and the flow of electrons through a
conductor result into the electrical energy.
15. Magnetic energy : Energy possessed by a magnet is called the magnetic energy.
16. Chemical energy : Chemical energy is the energy caused by a chemical reaction.
17. Nuclear energy : The nuclear energy liberated during nuclear reactions (nuclear fusion and
nuclear fission) is called the nuclear energy.
18. Energy transformation : Energy transformation is the change of energy from one form to another.
19. Law of conservation of energy : The law of conservation of energy states that energy can neither be created
nor destroyed, it can be changed from one form to another.
20. Power : The rate of doing work is called power.
21. One watt power : Power is said to be one watt when one joule of work is done in one second.
Introduction
In general conversations, the word 'work' means the different activities (physical and mental)
that people do each day. In physics, however, work has a specific meaning. It is related to
the displacement of a body in a particular direction by the application of a force. Naturally,
the water in a river flows down a slope, meteors hit the earth’s surface and animals perform
several basic life processes. Such activities are some types of work. Behind all these activities,
there is the need of energy, too.
In the case of machines, they need different sources of energy, such as electricity, petrol, diesel,
etc. to do the work. Different machines have different capacities to do work. The rate of a body
to do work is known as power. In this unit we will learn about, work, energy and power. We
will also learn the principle of conservation of energy with the help of some examples.
FACT WITH REASON
How are work and energy interrelated?
Generally, we say we have no energy to do any more work. The capacity of doing work is called energy
and work is done when energy gets transformed from one form to another. Both energy and work are also
measured in joule (J). So, work and energy are interrelated.
Work Memory Tips
Work is a very common term. It is used everywhere in our In physics, you must displace a body
daily life. Reading, writing, playing, ploughing, meditation, in the direction of the force applied
etc. are the examples of work. But in physics, the word to do work.
'work' is used only in cases where there is a force acting on
a body and the body moves by a certain distance. Thus, work is said to be done when a body
moves in the direction of the force applied. The work done by a constant force is a product of
the displacement of a body and the force applied on it in the direction of displacement.
72 Work, Energy and Power
W=F×s
Where, F = Force applied in the direction of the displacement
s = Displacement in the direction of the force
The meaning of work in our daily life is quite different from that Pushing a wall
in physics. For example, a watchman standing in front of a gate, a
person standing with some load on his head or a dog tied to a gate
do no work in the language of physics.
FACT WITH REASON
Work is a scalar quantity, why?
Although, work is measured as the product of two vector quantities (force and displacement), it has only
magnitude but no matter of its direction. So, work is a scalar quantity.
Factors Affecting Work
Magnitude of the applied force
Work done is directly proportional to the force applied. In case of a particular work to be
done, the more the value of the force applied,the greater is the amount of resulting work done.
Magnitude of displacement
Work done is directly proportional to the displacement. The greater the displacement, the
greater is the work done.
Units of Work Memory Tips
SI Unit of work is joule (J).
CGS unit of work is erg. The word erg is derived from the
Greek word for work, that is, ergon.
FACT WITH REASON
Moment is not measured in joules and work should not be measured in newton meter, why?
The unit joule is equivalent to a newton meter, but work is not measured in newton meter because that unit
is reserved for moment. So moment is not measured in joules and work should not be measured in newton
meter.
Relationship between joule and erg
Since, W = F × s
1 J = 1 N × 1m
1 J = 105 dyne × 100cm
1 J = 107 erg
Other units of work
i) 1 kilo joule (KJ) = 103 joule (J)
ii) 1 mega joule (MJ) = 106 joule (J)
iii) 1 giga joule (GJ) = 109 joule (J)
Modern Concept Science - 9 73
Measurement of Work done by a Constant Force W = Fdcos θ
a) Measurement of the work done when the displacement Fdcos θ s
and the force applied are inclined at an angle to each Fθ
other
If 'θ' is the angle between the displacement(s) and the
force applied (F) then the work done is given by,
W = F s cos θ
Solved Numerical 4.1
Calculate the work done from the given figure.
Solution: Given, F = 50N
30°
Force applied (F) = 50N s = 30 m
Displacement (s) = 50m
The angle between the displacement(s) and the force applied (F) = 30°
Now,
W = F s cos θ = 50 × 50 × cos30° = 216.5 J
b) Measurement of the work done when the displacement is along the direction of the
force applied
If the angle between the force (F) and displacement (s), θ = 0° s F
W = F s cos 0° θ = 0°
W=F×s
Solved Numerical 4.2
The mass of a car along with the driver is 1000kg and it accelerates with 6m/s2within the
distance of 500m. Calculate the work done by the engine of the car.
Solution: Given,
Displacement of car (s) = 500m
Mass of the car (m) = 1000kg
Acceleration (a) = 6m/s2
Now,
Work done (W) = Force × displacement = ma × s =1000×6×500 J= 3000000 J = 3000kJ
FACT WITH REASON
Even with no work done, we get tired, why?
If we push against a wall for a long time, we will expend calories and get tired. This is because our muscles
need to continuously produce and consume ATP to maintain a force, even when there is no net displacement.
The energy produced is dissipated as heat. So, even with no work done, we get tired for having spent the
energy.
74 Work, Energy and Power
1 joule work 1 J of work
One joule of work is done when a force of 1N displaces an object 1N
through a distance of one meter in the direction of the force.
Mathematically,
W=F×s 1m
1 J = 1 N × 1m
1 J work
Types of Work
Work done against friction Applied force Friction force
The resistive force between two surfaces in a relative motion Work against friction
is called the frictional force. The work done in pushing or
pulling a load by applying a force against friction is called the
work done against friction. For example, pushing a book on a
table, pulling a box on the ground, etc.
If 'F' is the force of friction and 's' is the displacement of a body, then the work done against
friction is given by
W=F×s
Solved Numerical 4.2
A box is pushed on the ground for a horizontal distance of 3m and the frictional force
experienced by the box is 100N. Calculate the work done to overcome friction.
Solution: Given,
Frictional force (Ff) = 100N
Displacement (s) = 3m
Now, Work done to overcome friction (Wf) = Ff × s = 100 × 3 = 300J
Work done against gravity
Objects are pulled towards the center of the earth by gravity. In Work against gravity
order to lift an object, an upward force equal to the weight must
to be applied on the object. Thus, the work done in lifting weights
by applying a force against gravity is called the work done against
gravity. For example, throwing a ball up, lifting a load, climbing
stairs, etc.
i) The work done against gravity is equal to the product of the weight of a body and the
vertical distance through which the body is raised.
ii) If a mass 'm' is lifted to a height 'h' then the work done against gravity is given by
Work done against gravity (W) = Force of gravity × displacement
W = weight × height
W = mgh
Modern Concept Science - 9 75
FACT WITH REASON
We get more tired while climbing up a staircase than when walking along a horizontal surface, why?
When we climb up a staircase, we have to work against the force of gravity. For this, we need to use more of
our muscular power. But there is less use of muscular power while walking along a horizontal direction. So,
we get more tired while climbing up a staircase than in walking along a horizontal surface.
Solved Numerical 4.4
Calculate the work done by a cat of 5 kg when it jumps to a height of 4m.
Solution: Given, Memory Tips
Mass of the cat (m) = 5kg
Displacement (s) = 4m When an object is raised by pushing
it up an inclined plane, work is done
Now, the work done against gravity against friction and gravity. Total
work = Work done against friction +
W = mgh = 5× 9.8× 4= 196 J Work done against gravity.
The work done by the cat is 196J.
Energy
Survival of living beings is impossible without energy. We have the capacity to walk or to do
work due to the energy in our body. This energy comes from the food we eat. In machines,
there is some fuel, which supplies the energy for them to do work. No work can be done
without energy. Thus, the capacity of a body to do work is called energy.
Units of Energy
SI Unit of energy is joule (J) and its cgs unit is erg.
Unit Symbol Equivalence in joule
erg erg 1 erg = 10-7 J
calorie Cal 1 Cal = 4.2 J
kilowatt hour kWh 1 kWh = 3.6× 106 J
electron volt eV 1 eV= 1.6×10-19 J
FACT WITH REASON
The unit of energy is the same as that of work, i.e. joule (J), why?
Energy is the stored capacity to do work. It is equal to the amount of work the body can perform. For example,
1J energy is the capacity to do 1J of work. So the unit of energy is the same as that of work, i.e. joule (J).
Forms of Energy
Mechanical Energy
The energy possessed by a body due to its motion or position is called its mechanical energy.
A bird flying at a certain height has a mechanical energy. Kinetic energy and potential energy
are the two types of mechanical energy.
76 Work, Energy and Power
Kinetic Energy
Moving objects can do work. For example, blowing air can rotate
blades of a windmill, flowing water can rotate the turbines, etc. Thus,
the energy possessed by a body in motion is called kinetic energy. A
rolling football, a falling apple, a running athlete, a moving vehicle,
etc. possess the kinetic energy.
a) Expression for Kinetic Energy : Consider a body of mass 'm' Kinetic energy
initially at rest. The force 'F' on the body accelerates it with 'a'
and final velocity becomes 'v' after it travels the distance of 's'.
Now, from the equation of motion,
v2 = u2 + 2as
v2 – u2 = 2as
a = v2 – u2
2s
According to Newton's second law of motion, force on the body
F = ma
or, F = m × v2 – u2 = mv2
2s 2s
or, W = m2v2
[Since, W = F × s]
or, W = 12mv2
This work done is equal to the kinetic energy on the body.
So, the expression of kinetic energy is
KE = 21mv2
Solved Numerical 4.5
If a bullet having a mass of 150g is shot at a muzzle velocity of 960m/s, calculate the kinetic
energy of the bullet?
Solution: Given,
Mass of the bullet (m) = 150g = 150 = 0.15kg
1000
Muzzle velocity (v) = 960 m/s
Now, kinetic energy of the bullet is given by
KE = 12mv2 = 1 × 0.15 × (960)2 = 69,120 J
2
Therefore, the kinetic energy of the bullet is 69,120 J
Modern Concept Science - 9 77
Factors Affecting Kinetic Energy
a) Mass
The kinetic energy of a body is directly proportional to the mass of the body i.e.,
K.E. α m (when 'v' remains constant)
If mass of a body is doubled, its kinetic energy also gets doubled and if mass of the body
is halved, its kinetic energy also gets halved.
FACT WITH REASON
How does the kinetic energy of a body in motion change when the mass of the body is halved?
The kinetic energy of a body is directly proportional to the mass of the body, i.e., K.E. α m. The kinetic
energy of a body decreases by half when its mass is halved.
Solved Numerical 4.6
How does the kinetic energy of a body in motion change when the mass of the body is
doubled?
Solution: Given,
The kinetic energy of a body of mass 'm' moving with velocity of 'v' is given by
KE1 = 21mv2 ......(i)
When the mass of the body, 'm' changes to '2m', the new kinetic energy becomes,
KE2 = 12(2m)v2 = 2 × 12mv2
KE2 = 2 KE1
Thus, the kinetic energy of a body increases by two times when its mass is doubled.
b) Velocity
The kinetic energy of a body is directly proportional to the square of the velocity of the
body. i.e.
K.E. α v2
If the velocity of a body is doubled, its kinetic energy becomes four times and if the
velocity of a body is halved, then the kinetic energy gets reduced to one-fourth.
Solved Numerical 4.7
How does the kinetic energy of a body in motion change when velocity of the body is
doubled?
Solution: Given,
The kinetic energy of a body of mass 'm' moving with velocity of 'v' is given by
KE1 = 21mv2 ……….. (i)
When the velocity of the body, 'v' changes to '2v', the new kinetic energy becomes,
78 Work, Energy and Power
KE2 = 1 m (2v)2 = 4 × 21mv2
2
KE2 = 4 KE1
Thus, the kinetic energy of a body increases by four times when its velocity is doubled.
FACT WITH REASON
How does the kinetic energy of a body in motion change when velocity of the body is halved?
The kinetic energy of a body is directly proportional to the square of the velocity of the body, i.e. K.E. α v2.
The kinetic energy of a body decreases by one-four times when its velocity is halved.
Potential Energy
The potential energy is a stored energy. It is due its position or deformation. Thus, the energy
possessed by a body due to its position or deformation is called the potential energy. For
example, a compressed spring, stretched catapult, water in a dam, etc. possess the potential
energy. The potential energy is of two forms:
Gravitational Potential Energy
The energy possessed by a body by virtue of its vertical position above the h
ground is called the gravitational potential energy. For example, energy
possessed by the water collected in a dam, a stone on the roof of a building, Ground
etc.
Potential energy
Gravitational potential energy of an object at certain height
When a body is lifted vertically upward against the gravitational force, some work is done on
the body. The work done to raise the body against the pull of gravity is stored in the body in
the form of the gravitational potential energy.
Let a body of mass 'm' be placed at a height 'h' above the ground. Then, the potential energy
of the body = Work done against gravity
∴ Gravitational potential energy = weight × h = mgh
Potential energy = mgh
FACT WITH REASON
Potential energy, 'mgh', is called the gravitational potential energy, why?
The potential energy, 'mgh', arises due to the work done on the body against the pull of gravity. So, the
potential energy, 'mgh', is called the gravitational potential energy.
Solved Numerical 4.8
Calculate the potential energy of a stone of mass 10kg placed at a height of 4m above the
ground. (g = 9.8m/s2)
Solution: Given,
Mass of the stone (m) = 10kg
Height of the stone (h) = 4m
Modern Concept Science - 9 79
Acceleration due to gravity (g) = 9.8m/s2
According to the formula,
Potential energy = mgh = 10 × 9.8 × 4 = 392J
Therefore, the potential energy of the stone is 392J.
FACT WITH REASON
When a body is lifted higher, its potential energy keeps on increasing, why?
To lift of a body to a higher level, more work needs to be done. The greater the work done on the body to raise
it, the more the energy stored in it in the form of a gravitational potential energy. So when a body is lifted
higher, its potential energy keeps on increasing.
Solved Numerical 4.9
A window-washer stands on a scaffolding 30 meters above the ground. If he did 23,520
joules of work to reach the scaffolding, what is his mass?
Solution: Given,
The height of the window-washer above the ground (h) = 30m
Work done to reach that height (W) = 23, 520J
According to the formula,
Potential energy = mgh
or, m × 9.8 × 30 = 23520
or, m = 23520 = 23520 = 80 kg
9.8 × 30 294
The mass of the window-washer is 80 kg.
Therefore, the mass of the window-washer is 80kg.
Elastic Potential Energy
The energy possessed by a body due to its deformed shape or
configuration is called the elastic potential energy. The work
required to deform a body from its normal position is stored in
the form of the elastic potential energy. For example, energy in a
stretched rubber or compressed spring, a bent bow, etc. possess the
elastic potential energy.
Differences between Kinetic Energy and Potential Energy
Kinetic Energy Potential Energy
1. It is the energy possessed by virtue of 1. It is the energy possessed by virtue of
the motion of a body. the position or configuration of a body.
2. The greater the velocity, the greater is 2. The greater the height, the greater is
the kinetic energy. the potential energy.
3. Kinetic energy is given by 3. Potential energy is given by
K.E. = 12mv2 P.E. = mgh
80 Work, Energy and Power
Other Forms of Energy
Heat Energy
Heat is a form of energy that produces a sensation of warmth in us. It is the sum of the
kinetic energy of all the particles in a substance. Heat always flows from a body at a higher
temperature to a body at a lower temperature. Heat energy can be converted into other forms
of energy. The heat produced by burning of petrol in an automobile engine provides the
energy to run the vehicle.
Light Energy
Light is a form of energy that produces a sensation of vision in us. It can easily be converted
into the electrical energy by the use of photoelectric cells. Green plants directly use the light
energy to prepare food during photosynthesis. The light energy causes a chemical change to
take place. When the light energy falls on a photographic film, the images are recorded on the
photographic film due to a chemical change.
Sound Energy
Sound is a form of energy produced by vibrating bodies. Our eardrum vibrates when the
sound produced by a vibrating body falls on it and we hear the sound. We can experience it
as a form of energy. When a stone hits the floor, a part of its mechanical energy gets converted
into sound energy and heat energy.
Electrical Energy
The transfer of electrons from an insulator and the flow of electrons through a conductor result
into the electrical energy. We obtain it from different sources like, dry cell, solar panels, etc.
Electrical energy can be used to run a number of electrical devices like fans, bulbs, washing
machines, etc. It is possible to convert the electrical energy into other forms of energy easily.
Magnetic Energy
A magnet attracts magnetic substances. Thus, energy possessed by a magnet is called the
magnetic energy. Magnetic energy is used to make an electromagnet, which is widely used in
electrical devices. It is also used to separate magnetic substances from a mixture.
Chemical Energy
Chemical energy is the energy caused by a chemical reaction. Petrol, coal, kerosene, etc. have
the energy stored in a chemical form. Green plants prepare food by photosynthesis. Energy
from the food gets released during respiration.
Nuclear Energy
The nucleus of an atom has the energy stored in it. This energy gets released during a nuclear
reaction. Thus, the nuclear energy liberated during nuclear reactions (nuclear fusion and
nuclear fission) is called the nuclear energy.
Energy Transformation
Energy transformation is the change of energy from one form to another. Under suitable
conditions, energy can be transformed from one form into another.
Modern Concept Science - 9 81
Examples of Energy Transformation
1. Battery or Cell : Chemical energy to electrical energy
2. Solar cell : Light energy to electrical energy
3. Heater : Electrical energy to heat energy
4. Electric bulb : Electrical energy to light energy and heat energy
5. Turbine : Mechanical energy to electrical energy
6. Dynamo/Generator : Mechanical energy to electrical energy
7. Electric motor : Electrical energy into mechanical energy
8. Loudspeaker : Electrical energy into sound energy
9. Microphone : Sound energy to electrical energy
10. Electromagnet : Electrical energy into magnetic energy
11. Television : Electrical energy into light and sound energy
12. Burning of fuels : Chemical energy into heat and light energy
13. Explosion of crackers/bombs : Chemical energy into heat, light and sound energy
Law of Conservation of Energy
Whenever energy from one form disappears, an equal amount of energy appears in another
form. Also, when any form of energy appears, an equal amount of energy in another form
seems to vanish. The energy, which disappears form one form, actually gets transferred to
other forms. Hence, the law of conservation of energy states that energy can neither be created
nor destroyed, it can be changed from one form to another. For example, in a torch light with
dry cells, the chemical energy stored in the dry cells gets transformed into electric energy in
the wire and heat energy and light energy in the bulb filament.
FACT WITH REASON
Energy can neither be created nor destroyed. What does it mean?
The mass and energy of the universe are constant quantities. They can be changed from one form to another
but cannot be created and destroyed.
Power Memory Tips
Time required to complete a work varies by workers and Horsepower was first used by
machines. To find who is a more efficient worker, we seek Scottish engineer James Watt in
to know the value of work done by each worker per unit late 18th century. He employed it to
time. If a machine completes a work faster than another compare the power of steam engines
machine, then it has more power. Thus, the rate of doing with that of horses.
work is called power. It is also defined as the rate at which
energy is transferred.
82 Work, Energy and Power
Mathematically,
Power (P) = Work done (W)
Time taken (t)
P = W
t
Units of Power
The SI Unit of power is watt (W).
Unit Symbol Equivalence in watt (W)
horsepower h.p. 1 h.p. = 746W
kilowatt kW 1kW = 1000W
megawatt MW 1MW = 106 W
1 Watt power
Power (P) = Work done (W)
Time taken (t)
1 W = 1 J
1 s
Power is said to be one watt when one joule of work is done in one second.
Meaning of Power of Electrical Appliances
60W bulb
It means, the bulb converts 60J of electrical energy into heat and light energy in one second.
150W fan
It means, the fan converts 150J of electrical energy into mechanical energy in one second.
Solved Numerical 4.10
An electric motor lifts an elevator that weighs 1.2 × 104 N to a distance of 9 m in 15 seconds.
Find the power of the motor (i) in kilowatt (kW) (ii) in horsepower (h.p.).
Solution: Given,
Force (F) = 1.2 × 104 N
Distance (d) = 9 m
Time taken (t) = 15 seconds
According the formula,
Power (P) = Work done (W) = F × d = 1.2 × 104 × 9 = 10.8 × 104 = 7.2 × 103 W
Time taken (t) t 15 15
In kilowatt, 1000 W = 1 kW
P = 7.2 × 103 = 7.2 kW
1000
Modern Concept Science - 9 83
In h.p., 746 W = 1 h.p.
P = 7.2 × 103 = 9.65 h.p.
746
Therefore, the power of the motor is 7.2 × 103 W or 7.2 kW or 9.65 h.p.
Solved Numerical 4.10
An electric pump fills water in a distribution tank at a height of 40 m. If the power of the
pump is 4.9 kW, find the mass of water raised in 2 minutes.
Solution: Given,
Height of the water tank (h) = 40 m
Power of the pump (P) = 4.9 kW = 4900 W
Time (t) = 2 minutes = 2× 60 = 120 seconds
Acceleration due to gravity (g) = 9.8 m/s2
According to the formula,
Power (P) = Work done (W) = mgh
Time taken (t) t
m = P×t = 4900 × 120 = 588000 = 1500 kg
g×h 9.8 × 40 392
The mass of water raised by the pump in 2 minutes is 1500 kg.
Factors Affecting Power
Power is affected by two factors. They are:
i) Work done (W) ii) Time taken(t)
If work down is more, then there will be more power. Similarly, if the time taken to complete
the work is less, then the power is more and vice versa.
Solved Numerical 4.10
An adult lifts a load in 2 seconds. A boy performs the same job in 4 seconds. Whose power
is greater?
Solution: Given,
Let the work done = W
The time taken by the adult = 2 seconds
Power of the adult = W
2
The time taken by the boy = 4 seconds
Power of the boy = W
4
Since, W > W
2 4
Therefore, power of the man is greater.
84 Work, Energy and Power
FACT WITH REASON
Two machines performing the same task can have different power, why?
The work done (W) by the two machines may have completed in different times.
If the first machine completes the work in time 't1', its power is P1 = Wt1 .
If the second machine completes the work in time 't2', its power is P2 = Wt2 .
If t1 > t2, then P1 < P2 and vice versa. So, two machines performing the same task can have different powers.
Relationship between Power and Velocity
If 'F' be the force applied and 's' be the displacement of a body in time 't' then the power used
is given by,
P = W = F × s = F × s
t t t
P=F×v
where, v is the displacement per unit time.
Solved Numerical 4.13
A 30 h.p. car is moving with a uniform velocity of 45 km/h. Calculate the force exerted by
its engine.
Solution: Given,
Power of the car (P) = 30 h.p. = 30 × 746 W = 22,300 W
Velocity of the car (v) = 45 km/h = 45 × 1000 = 12.5 m/s
60 × 60
According to the formula,
P=F×v
or, F = P = 22300 = 1784 N
v 12.5
Therefore, the force exerted by the engine of the car is 1784 N.
Differences between Work and Power
Work Power
1. Work is said to be done when the force 1. Power is the rate of doing work.
acting on a body causes displacement
in the direction of the force.
2. Work = Force × displacement 2. Power = Work done
3. The SI Unit of work is joule (J). Time taken
3. The SI Unit of power is watt (W).
4. It is not affected by the time taken. 4. It is affected by the time taken.
Modern Concept Science - 9 85
ANSWER WRITING SKILL
1. At which condition 1 joule work is done? Write down the relation of 1J work with erg.
Ans: One joule of work is done when a force of 1N displaces an object through a distance of one meter in the
direction of the force. 1 joule = 107 ergs.
2. What do you mean by mechanical energy? Write its types.
Ans: The energy contained in a body due to its state of motion or rest or due to its position or configuration
is called mechanical energy. There are two types of mechanical energy. They are kinetic energy and
potential energy.
3. Name the factors on which the work done depends. Name the factors that affect power.
Ans: Force and displacement are the factors on which work depends upon. Similarly, factors affecting power
are work and time.
4. Write any two conditions in which the work done is positive.
Ans: Conditions in which work done is positive are:
i) When an object is pulled or pushed by applying force at an acute angle.
ii) When an object falls freely under the action of gravity.
5. Write any two differences between work and energy.
Ans: The differences between work and energy are:
SN Work SN Energy
1. Work is said to be done when the force 1. The capacity of doing work is called energy.
acting on a body causes displacement in
the direction of the force.
2. Work is outcome of transformation of 2. Energy is must for doing work.
energy.
6. Potential energy of an object kept on the surface of the earth is zero, why?
Ans: Potential energy of an object lying on the surface of the earth is zero because the height of the object
from the surface of the earth is zero. According to relation PE = mgh, object must have certain height for
the potential energy.
7. Write a use of each form of energy listed below: Heat energy, magnetic energy, light energy and nuclear energy.
Ans: The uses are:
i) Heat energy : heat energy is used for cooking, boiling water, drying grains etc.
ii) Magnetic energy : magnetic energy is used inside generator, dynamo, electric bell and also in crane.
iii) Light energy : light energy is used by plants for photosynthesis, also helps in vision and produces
electricity.
iv) Nuclear energy : nuclear energy releases tremendous amount of heat that can be used to produce
electricity or to make nuclear weapons.
8. How much work is done by a force of 10N in moving an object through a distance of 4m in the direction
of the force?
Solution:
Force applied (F) = 10N
Displacement (s) = 4m
86 Work, Energy and Power
Now, Work done (W) = Force × displacement = 10 × 4 = 40J
Therefore, 40 J work is done in moving 4m distance.
9. A ball of 200g is thrown with a velocity of 10m/s. Calculate the kinetic energy of the ball.
Solution:
Mass of the ball (m) = 200 g = 200 = 0.2 kg
1000
Velocity of the ball (v) = 10m/s
Now, kinetic energy of the ball is given by
KE = 1 mv2 = 1 × 0.2 × 102 = 10 J
2 2
Therefore, 10 J work is done in throwing the ball.
10. Calculate energy needed to take a 20 kg mass to a height of 10 m, if g = 9.8 m/s2.
Solution:
Mass (m) = 20 kg
Height (h) = 10 m
Acceleration due to gravity (g) = 9.8 m/s2
Work against gravity (W) = mgh = 20 × 9.8 × 10 = 1960 joules
11. A ball of mass 500g slows down from a speed of 5m/s to that of 3m/s. Calculate the change in the kinetic
energy of the ball.
Solution:
Mass of the ball (m) = 500 g = 500 = 0.5 kg
1000
Initial velocity (v1) = 5m/s
Final velocity (v2) = 3m/s
Now, kinetic energy of the bullet is given by
Change in KE = 1 m(v12 – v22) = 1 × 0.5 (52 – 32) = 4 J
2 2
Therefore, the change in kinetic energy will be 4J.
12. A ball has a mass of 500g. To what height should it be thrown up so that its potential energy will be 49J?
(g = 9.8m/s2)
Solution:
Mass of the ball (m) = 500 g = 500 = 0.5 kg
Potential energy (P.E.) = 49J 1000
Height from the earth surface (h) = ?
Now, the potential energy is given by
P.E. = mgh
or, 49 = 0.5 × 9.8× h
or, h= 49 = 10 m
0.5 × 9.8
Therefore, the height should be 10m.
13. What happens to the kinetic energy if velocity is tripled keeping the mass constant?
Solution:
Modern Concept Science - 9 87
Case I
Let mass of an object be 'm'
Velocity be 'v'
Then, kinetic energy will be
Kinetic energy (KE) = 1 mv2 ...............(i)
2
Case II
Let mass be constant, m
Velocity is tripled so v’ = 3v
Then kinetic energy,
KE = 1 m(3v)2
2
= 1 m × 9 × v2
2
=9× 1 m v2
2
From equation (i), we have
The new (KE) = 9 KE
Thus, when velocity is tripled, kinetic energy will increase by 9 times.
14. A man of 50kg climbs a staircase of a height 10 m in 20 seconds. Find his power. If the value of g is 9.8m/s2.
Solution:
Mass of the man (m) = 50 kg
Height (h) = 10 m
Time taken (t) = 20 seconds
According the formula,
Power (P) = Work done (W) = mgh
Time taken (t) t
= 50 × 9.8 × 10 = 4900 = 245 W
20 20
Therefore, the power will be 245 W.
15. The power of an electric heater is 1 kW. Find the electrical energy consumed when it is used for 1 hour.
Solution:
Power of the electric heater (P) = 1 kW = 1000 W
Time (t) = 1hr = 60 ×60 = 360 seconds
Acceleration due to gravity (g) = 9.8 m/s2
According to the formula,
Power (P) = Work done (W)
Time taken (t)
W = P × t = 1000 × 360 = 360000
Therefore, the electric energy consumed is 360000 J.
88 Work, Energy and Power
16. Compare and contrast between work, energy and power.
Ans: Compare and contrast of work, energy and power are:
SN Energy Work Power
1 Energy is the capacity of Work is said to be done when the The rate of doing work is called
doing work. force acting on a body causes power.
displacement in the direction of
the force.
2 The SI unit of energy is joule. The SI unit of work is also joule. The SI unit of power is watt.
3 Energy is equal to work. Work is calculated by using Power is calculated by the relation
relation W = F × s or W = mgh P = W/t
4 Energy can change from one Work is independent of time. Power is function of time.
form to another.
STEPS EXERCISE
STEP 1
1. Define
a) Work b) One joule of work
c) Work done against friction d) Work done against gravity
e) Energy f) Mechanical energy
g) Kinetic energy h) Potential energy
i) Gravitational potential energy j) Elastic potential energy
k) Heat l) Light
m) Sound n) Electrical energy
o) Magnetic energy p) Chemical energy
q) Nuclear energy r) Energy transformation
s) Law of conservation of energy t) Power
u) One watt power
2. Very Short Answer Questions
a) When is work said to be done?
b) Can work done by a force be negative?
c) Write the relationship between joule and erg.
d) Is power a scalar or a vector quantity?
e) Write the SI Unit of the following:
i) Work ii) Energy iii) Power
f) Name the devices in which
i) heat energy changes into electrical energy
ii) nuclear energy changes into heat energy
Modern Concept Science - 9 89
iii) light energy changes into electrical energy
iv) chemical energy changes into electrical energy
g) 60 W is written on a bulb. What does it mean?
STEP 2
3. Short Answer Questions
a) Explain the two factors on which the work done by a force on a body depends.
b) How is the work related to the applied force?
c) What are the two conditions for a work to be done?
d) Is it possible that a force is acting on the body but still the work done is zero?
Explain with an example.
e) What is the potential energy of a body of mass ‘m’ at a height of ‘h’ above the
earth's surface?
f) Explain by an example that a body may possess a mechanical energy even when
it is not in motion.
g) Give two examples where a body possesses both kinetic and potential energy.
h) What happens to the kinetic energy of an object
i) if the mass is tripled?
ii) if the mass and its velocity both are doubled?
i) On what factors does the gravitational potential energy of a body depend?
j) When a cricket ball is thrown vertically upward, its velocity goes on decreasing.
What happens to the kinetic and potential energy of the ball when it is at its
maximum height?
k) What happens to the potential energy of an object when its mass and its height
both are doubled?
l) What is the relationship between work and power?
4. Differentiate Between
a) Kinetic energy and potential energy
b) Gravitational potential energy and elastic potential energy
c) Chemical energy and nuclear energy
d) Work and power
5. Give Reason
a) Work is a scalar quantity.
b) No work is done if you push against the wall of a building.
c) The unit of energy is the same as that of work, i.e. joule (J)
d) When a body is lifted higher, its potential energy keeps on increasing.
e) Two machines performing the same task can have different powers.
90 Work, Energy and Power
STEP 3
6. Numerical Problems
a) An object of mass 100kg is pushed up to a distance of 10m with an acceleration of
5m/s2. Find the amount of work done on that object. [Ans: 5000J]
b) An object of mass 10kg is moving with a uniform velocity of 5m/s. What is the
kinetic energy possessed by the body? [Ans: 125J]
c) A motor bike of 100kg is moving on a straight road with a velocity of 20m/s. Find
the kinetic energy of the bike. [Ans: 20,000J]
d) A ball of mass 500g slows down from a speed of 5m/s to that of 3m/s. Calculate
the change in the kinetic energy of the ball. [Ans: 4J]
e) The velocity of a 1000kg car changes from 5m/s to 20m/s. Calculate the change
in the kinetic energy of the car. [Ans: 187500J]
f) Calculate the potential energy of a stone of mass 5kg placed at a height of 4m
above the ground. If the value of g is 9.8m/s2. [Ans:196J]
g) Calculate the potential energy in 10000 liters of water stored in the dam at a height
of 200m from the earth’s surface. If 1 litre is 1 kg. [Ans: 19600kJ]
h) The body mass of Narayan is 70 kg. He climbs a ladder of a height of 3m in 20
seconds. Find his power. [Ans: 102.9W]
i) The mass of a brick is 5kg. A man carries 5 bricks on the roof of a building of a
height 10 m in 3 minutes. A boy carries 5 bricks on the same roof in 5 minutes.
Find out which of the two does more work and which of them has more power.
[Ans: 2450J, 13.61W; 8.17W]
j) A machine raises a load of 1000 N through a height of 15m in 10 seconds. Calculate
the power at which the machine works. [Ans: 1500W]
k) The power of a water heater is 1.5kW. Find the electrical energy consumed by the
heater in 15 minutes. [Ans: 1350kJ]
STEP 4
7. Derive 1
2
a) The expression of kinetic energy, i.e.,KE = mv2, where the terms used have their
usual meanings.
b) The expression of potential energy, i.e., P.E. = mgh, where the terms used have
their usual meanings.
c) Discuss the change in energy that occurs when the water collected in a dam is
allowed to fall over turbines while generating electricity in a hydropower station.
d) Explain the variation in the kinetic energy and potential energy of a ball when it is
thrown up in the sky to reach the maximum height and return to the earth.
Modern Concept Science - 9 91
UNIT Estimated teaching periods Theory Practical
3 1
5
Light
Syllabus issued by CDC Willebrord Snell
Introduction to light
Refraction of light
Laws of refraction of light
Total internal reflection of light
Dispersion of light
Electromagnetic waves (x-rays and UV-rays)
LEARNING OBJECTIVES
At the end of this unit, students will be able to:
define refraction of light and explain the laws of refraction.
describe dispersion of light and demonstrate the spectrum of light.
explain the electromagnetic wave with its nature.
describe the frequency and wavelength of electromagnetic waves (X – rays, UV – rays,).
Key terms and terminologies of the unit
1. Light : Light is a form of energy that produces the sensation of vision.
2. Optical medium : Optical medium is a material medium through which the electromagnetic waves
propagate.
3. Rarer medium : The medium in which light travels faster is called an optically rarer medium
4. Denser medium : The medium in which light travels relatively slower is called an optically denser
medium.
5. Refraction of light : The phenomenon of bending of light as it passes obliquely from one optical medium
to another is called the refraction of light.
6. Cause of refraction : The change in speed of the light wave upon crossing the boundary of two optical
media is the cause of refraction.
7. Refractive index : The refractive index of a material medium can be defined as the ratio of the speed of
light in vacuum (c) to the speed of light in the medium (v).
8. Absolute refractive index : The refractive index of a medium, with respect to a vacuum, is called the absolute
refractive index of the medium.
9. Real depth : The real position of the bottom or a point inside water is called a real depth.
10. Apparent depth : The position of the bottom or a point inside water which is observed from outside is
called an apparent depth.
11. Critical angle : The angle of incidence in a denser medium for which the corresponding angle of
refraction in the rarer medium is 900is called the critical angle.
92 Light
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Modern Concept Science and Technology 9
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