Class-IX

Physics

Chapter-11

Work and Energy

Work Done: Work is defined as the product of the force applied on an object and

displacement caused due to the applied force in the direction of the force. Work is a

scalar quantity. It has no direction of its own but a magnitude.

Work done = Force x Displacement

When you play a certain force ‘F Newton’ on an object and the object moves a distance

of ‘s meters’ in the direction where you applied the force then, the amount of work done

can be calculated as:

W = F x S

SI unit of Work: N-m or J (Joule)

1 Joule Work

When 1 Newton force is applied on an object that can move the object by a distance of 1m in the direction of the applied force, then 1 joule of work is said to be done. The bigger units of work are gigajoule (GJ), megajoule (MJ), etc. Let us see the relation between joule, megajoule and kilojoule 1 GJ = 109 J 1MJ = 106 J 1 KJ = 103 J Conditions of work done

So, we can conclude that work is done if and only if:

A force is applied to an object.

If the object is displaced from one point to another point.

Work-done is a scalar quantity.

Work done against gravity

If we pick or drop anything, it falls to the ground. Like a child drops the ball on the ground

or a person lifts the bucket from well. So, in this case, work is done in response to gravity.

So, in this case, the amount of work done is equal to the product of weight of the object

and the vertical distance through which the object is lifted.

As we know

Work done = force x displacement …… (i)

Force = mass x acceleration……...(ii)

F = m x g [acceleration due to gravity]

Hence Work done = mass x acceleration x displacement

Or W = m x g x h

W = mgh

where m=mass, g=acceleration due to gravity and h=height to which the body is raised or

dropped).

Work done when the force makes an angle with the direction of

displacement

Suppose the child is playing with a toy where he is pulling it with the help of a string.

Now, in this case, the force is applied on a string and displacement is caused in it due to

force applied.

In this case, we have to consider an angle also which force makes with the ground or with

the direction of displacement, which is usually taken in terms of theta.

So, expression for work becomes:

W= Fcosθ x s

Where �= Angle between the direction of force and direction of motion.

Fcosθ = Horizontal component of force F

S = displacement

Now, the value of work depends upon the magnitude of angle. Accordingly, it can be

maximum or minimum.

Types of work

Positive work

Negative work

Zero work.

Positive work(maximum work):When force applied causes displacement of body in its

own direction means angle between the direction of force and direction of motion is 00

if angle �= 0⁰ then:

W=FScos0⁰

Therefore, W=FS (because cos 0⁰ = 1)

Example: Like pushing of door, kicking football if we kick a ball, it goes in the direction in which it is being kicked.

etc.

work done is maximum, when θ = 0⁰

Negative work:When applied force causes displacement of body in its opposite

direction. Example: In case of friction.

W= Fcosθ x s

W = F cos 1800 x s

W = F (-1) x s [ cos 1800 = -1]

W = - F x S (negative work is done).

Similarly, if you notice, while walking on the floor, one foot pushes the ground backward

and the other moves forward. This is how we move. But you are familiar that for walking,

running, etc we need to apply force. The reason is that the ground doesn’t allow us to

move because of the frictional force (opposing force that comes into play when two

bodies are rubbed with each other).

Zero work (minimum work done): It is done when force acts at a right angle to the

direction of displacement.

We know:

W = F. S cos θ

W= F.S cos 90o

W=F.S.0

W = 0

Example: work done is zero when a person carrying suitcase vertically in handwalks in a

horizontal direction. This is because the angle between the direction of force and the

direction of displacement is 90o.

Similarly, for a body moving in a circular path, the work done is zero due to similar

reasons.

Energy

Energy is defined as ‘Energy is the ability to do work.

Or

‘Energy possessed by an object is the amount of work it can do.’

If an object can do more work, it has more energy and vice versa.

For example; a raised hammer can do work so it has energy and similarly a bomb can do work so it has also energy, a running bike can do work so it has energy, etc.

`We need to do a lot of work and for doing work we need strength and that strength

comes from the food we eat. For example, if you need to ride a bicycle, you need to

paddle it and for paddling you need to do work and for it you need strength which comes

from food.

It is a scalar quantity

SI Unit of Energy:

Its unit is the same as that of work. SI unit of energy or work = Joule (Nm) or Kgm2s−2. Which is denoted by ‘J’.

Larger unit of energy is kilo joule and is denoted by kJ.

1kJ = 1000J

1Joule of energy ‘Energy required to do 1J of work is 1J of energy.’

Different forms of Energy:

Things have different forms of energy due to different reasons.

Mechanical Energy

Chemical Energy

Sound Energy

Light Energy

Heat Energy

Electrical Energy

Mechanical energy is the sum of:

(i) Kinetic energy (K.E)

(ii) Potential energy (P.E)

Kinetic Energy

Objects in motion possess energy and can-do work. This energy is called Kinetic Energy.So,Kinetic energy is the energy possessed by a body by virtue of its motion. For example, a fast-moving pebble can injure a person or break glass pane of window, energy of moving vehicle, a fast-moving wind can damage many houses, or wind can move blades of wind mill, etc.

Kinetic energy (K.E.) = 1/2mv2

Here,

m = Mass of object;

v = Speed of object;

When two identical bodies are in motion, the body with a higher velocity has more K.E.

Factors affecting kinetic energy

(i) Mass

(ii) Velocity

(iii) Momentum.

Derive expression for kinetic energy

Kinetic energy is the energy possessed by a body by virtue of its motion.

Suppose, the mass of a moving object = m

The initial velocity of a moving object = u

The acceleration of the object = a

The final velocity of the object = v

Displacement of object to achieve the final velocity = s.

We know from the equation of motion that,

v2=u2+2as

⇒2as=v2−u2

⇒s=�����

�� -----(i)

Now, we know that, Work done, W=F×s…………(ii)

Thus, by substituting the value of ‘s’ from equation (i) in the equation (ii)

we get

W=F�����

��

Now, according to Newton’s Second Law of motion,

Force = mass x acceleration

Or, F = m x a

Therefore, by substituting the value of F in equation (ii) we get,

W=m×a×�����

��

⇒W=1/2m(v2−u2) ---(iii)

If the object starts moving from the state of rest, therefore, initial velocity (u) will be

equal to zero.

Therefore, equation (iii) can be written as

⇒W=1/2m(v2−02)

⇒W=1/2mv2 ------(iv)

Equation (iv) shows that work done is equal to the change in kinetic energy of an object.

Therefore, if an object of mass ‘m’ is moving with a constant velocity,

Thus, the Kinetic Energy (Ek)=1/2mv2 ----(v)

From the above equation it is clear that kinetic energy of a moving object increases with

increase of mass and velocity of the object.

Work-energy theorem

The work-energy theorem states that the net work done by a moving body can be

calculated by finding the change in KE.

⇒ W net = KE final − KE initial

⇒ Wnet= 1/2 m[v2−u2]

Potential Energy

Energy possessed by an object because of its position or change in shapeis called

potential energy.

There are two types of potential energy:

(i) Gravitational potential energy:The energy of a body due to its position above

the ground. For example; when a stone is kept at a height, it possesses some

energy because of its height. Because of this potential energy, object kept at a

height falls over the ground.

(ii) Elastic potential energy: The energy of a body due to change in its shape and

size. For example; a stretched rubber band possesses some energy because of

its change in shape or configuration. Because of that energy, when the

stretched rubber band is released it acquires its original position by movement.

A stretched bow possesses energy because of its change in shape or

configuration.

Potential energy (Ep) = mgh

Here,

m = Mass of object;

g =acceleration due to gravity.

h =displacement of the object

Expression for Potential Energy:

Potential energy possessed by an object due to its height

Let the object of mass ‘m’ is placed over a height, ‘h’ against gravity.

Therefore, the minimum force required to work done, F = mg

Where, ‘F’ is force, ‘m’ is mass and ‘g’ is the acceleration due to gravity.

We know that, work done = Force x displacement

Therefore, Work done, W = F x h

Where, ‘h’ is the displacement of the object. Since, the object is displaced at a height,

therefore, ‘h’ is taken at the place of ‘s’.

Or, W = mgh (since, F = mg)

The potential energy (Ep) is equal to the work done over the object

Therefore, Ep = mgh

Where, ‘h’ is height, ‘m’ is mass and ‘g’ is acceleration due to gravity.

The potential energy of an object depends upon the mass and height (position) of the

object and not upon the path.

Mechanical Energy:

It is defined as the sum of kinetic and potential energy. For example; bird flying in the air

has both kinetic and potential energy.

Mechanical Energy (M.E.) = K.E. + P.E.

= 1/2 mv2+ mgh

Transformation of Energy

Energy can transform from one form to another. For example; when a body falls from a

height to ground potential energy transforms to kinetic energy.

1.When we wind a watch, the mechanical energy of hands changes into potential energy

of the spring. When the spring unwinds, the potential energy changes into kinetic energy

and drives the hands of the clock.

2. When an arrow is stretched in a bow the mechanical energy changes into potential

energy. On releasing the string of the bow, the potential energy changes into kinetic

energy of the arrow.

3.Water stored in hydroelectric dams has potential energy. When this water is released,

the potential energy changes into kinetic energy of the flowing water. The kinetic energy

of the flowing water turns the blades of a turbine and drives the dynamo. The dynamo

then produces electrical energy.

4. When a torch is switched on, the chemical energy of the cell changes into electrical

energy, the electrical energy, on passing through the filament of a bulb, changes into

heat energy and light energy.

5. In an electromagnet, electrical energy changes into magnetic energy.

6. The electrical energy, on flowing through the coils of an electric motor or an electric

fan, changes into mechanical energy. It partly changes into heat energy and hence, heats

the coils.

7. In microphone, the sound energy changes into electrical energy.

8. Electrical energy, on flowing through the speaker of an audio system, changes into

sound energy.

9. In electric heaters, electric ovens and geysers, the electrical energy changes into heat

energy.

10. In a locomotive, the chemical energy of coal changes into heat energy. The heat

energy then changes into kinetic energy of steam which drives the locomotive.

11. In an electric generator, the mechanical energy changes into electrical energy.

12. In a photovoltaic cell, the light energy changes into electrical energy.

13. In television the electrical energy changes into light energy and sound energy.

14. On burning the fuels, their chemical energy changes into heat energy and light

energy.

15. When a match stick is rubbed against the side of a match box, the chemical energy

changes into heat energy and light energy.

16. When a cracker is exploded, the chemical energy (stored in the chemical used in the

cracker) changes into heat, light and sound energies.

17. During photosynthesis, light energy changes into chemical energy in the presence of

chlorophyll.

18. During respiration the chemical energy of food changes into heat energy. It is the

heat energy which keeps our bodies warm. It is also the heat energy which changes into

mechanical energy during locomotion.

Law of Conservation of Energy

Law of conservation of energy says that

“Energy can neither be created nor destroyed, but can be converted from one form into

another. When energy changes from one form to another, total amount of energy

remains constant or conserved”. It is valid in all situations and for all kinds of

transformations.

For example:

In an iron the electrical energy required to run it is 100J (say), then this energy is

converted into heat energy and the energy still remains 100J only its form gets converted

not its amount.

Proving:

Let a body of mass 'm' placed at a height 'h' above the ground, start falling down from

rest.

In this case we have to show that the total energy (potential energy + kinetic energy) of

the body at A, B and C remains constant i.e., potential energy is completely transformed

into kinetic energy.

At A,

Potential energy = mgh

Kinetic energy = 0 [the velocity is zero as the object is initially at rest]

Total energy at A = Potential energy + Kinetic energy

Total energy at A = mgh … (1)

At B,

Potential energy = mg (h - x) [Height from the ground is (h - x)]

Potential energy = mgh - mgx

Kinetic energy,

the body covers the distance x with a velocity v.

using the third equation of motion to obtain velocity of the body.

v2- u2 = 2aS Here, u = 0, a = g and S = x

v2 = 2ax

Kinetic energy = ½ mv2

= ½ m(2ax)

= mgx

Total energy at B = Potential energy + Kinetic energy

Total energy at B = mgh – mgx + mgx

= mgh … (2)

At C,

Potential energy = m x g x 0 (h = 0)

Potential energy = 0

Kinetic energy = ½ mv2

From third equation of motion

v2 - u2 = 2aS

Here, u = 0, a = g and S = h

V2 = 2gh

Kinetic energy = ½ m (2gh)

Kinetic energy = mgh

Total energy at C = Potential energy + Kinetic energy = 0 + mgh

Total energy at C = mgh … (3)

It is clear from equations 1, 2 and 3 that the total energy of the body remains constant at

every point. Thus, we conclude that law of conservation of energy holds good in the case

of a freely falling body.

Power

Power is defined as the rate of doing work. It tells how fast or slow a work is done.

Or

the rate of transfer of energy is called power.

It is denoted by P.

For example; an aero-plane covers more distance in less time than a car consequently so

we say that aero-plane is more powerful than car.

Power = Work / Time

=> P = W / t

Note –

SI unit of Power is Joule per second or Js-1.

1 Watt is the power when 1J of work is done in 1s.

The bigger unit of power is Kilowatt and represented by kW.

1kW = 1000 W

1 GW= 109 watts

1 MW= 106 watts.

Older unit is 1 Horsepower =746 Watts

If power is more, work is done fast and vice versa.

Power is a scalar quantity.

Commercial Unit of Energy

Since Joule is very small thus, large quantity of energy is expressed in kilo watt hour and

is written as kWh. KWh is the commercial unit of energy.

Electric consumption in house is measured in kWh. Therefore, kWh is called commercial

unit of energy.

1 unit = 1 kwh

Relation between kwh and joule

1 kWh is the energy consumed by a device of power 1kW in 1 hour.

1 kWh = (1 kW) (1 hr)

= (1000 W) (60 x 60s)

= (1000 J/t) (60 x 60s) = 3600,000 J

1 kWh = 3.6 x 106 J

NCERT intext questions

Page No. 148

Solution 1.

When a force F acts on an object to move it in its direction through a distance S, the work

is done

The work on the body is done by force

Work done = Force × Displacement

W = F × S

Where,

F = 7 N and S = 8 m

So, work done,

W = 7 × 8

W = 56 Nm

W = 56 J

Page 149

Ans 1.

Work is said to be done when a force causes displacement of an object in the direction of

applied force.

Ans 2.

Work done = Force x Displacement

Ans 3.

When 1 Newton force is applied on an object that can move the object by a distance of

1m in the direction of the applied force, then 1 joule of work is said to be done.

Ans 4.

Given: Force = 140 N

Displacement = 15m

Work done = Force x Displacement

= 140 N x 15m = 2,100 J

Page No. 152

Ans 1.

Objects in motion possess energy and can-do work. This energy is called Kinetic Energy.

So, Kinetic energy is the energy possessed by a body by virtue of its motion.

For example, a fast-moving pebble can injure a person or break glass pane of window,

energy of moving vehicle, a fast-moving wind can damage many houses, or wind can

move blades of wind mill, etc.

Ans 2.

If a body of mass m is moving with a speed v,

then its K.E. (Ek) is given by the expression,

E k = 1/2mv2

Its SI unit is Joule (J).

Solution 3.

Page No. 156

Ans 1.

Power is that the rate of doing work or the speed of transfer of energy. If W is that the

quantity of work wiped out time t, then power is given by the expression,

P = W/T

It is expressed in watt (W).

Ans 2.

A body is claimed to possess power of one watt if it will work on the speed of

1 joule in 1 s.

That is,

One W = 1 J/1 S

Solution 3.

Power = Work/Time

P = W/T

Time = 10 s

Work done = Energy consumed by the lamp = 1000 J

Power = 1000/10 = 100 Js-1 =100 W

Ans 4.

The average Power of an agent could also be outlined because the total work done by it

within the total time taken.

NCERT EXERCISES

Page No.158

Ans 1.

Work is done whenever the given conditions are satisfied:

(i) A force acts on a body.

(ii) There is a displacement of the body.

(a) While swimming, Suma applies a force to push the water backwards. Therefore, Suma

swims in the forward direction caused by the forward reaction of water. Here, the force

causes a displacement. Hence, work is done by Seema while swimming.

(b) While carrying a load, the donkey has to apply a force in the upward direction. But,

displacement of the load is in the forward direction. Since, displacement is perpendicular

to force, the work done is zero.

(c) A wind mill works against the gravitational force to lift water. Hence, work is done by

the wind mill in lifting water from the well.

(d) In this case, there is no displacement of the leaves of the plant. Therefore, the work

done is zero.

(e) An engine applies force to pull the train. This allows the train to move in the direction

of force. Therefore, there is a displacement in the train in the same direction. Hence,

work is done by the engine on the train.

(f) Food grains do not move in the presence of solar energy. Hence, the work done is zero

during the process of food grains getting dried in the Sun.

(g) Wind energy applies a force on the sailboat to push it in the forward direction.

Therefore, there is a displacement in the boat in the direction of force. Hence, work is

done by wind on the boat.

Ans 2.

Since the body returns to a point which is on the same horizontal line through the point

of projection, no displacement has taken place against the force of gravity, therefore, no

work is done by the force due to gravity.

Solution 3.

When a bulb is connected to a battery, then the energy of the battery is transferred into

voltage. Once the bulb receives this voltage, then it converts it into light-weight and

warmth energy. Hence, the transformation of energy within the given situation may be

shown as:

Chemical Energy → Electrical Energy → Light Energy + Heat Energy.

Solution 4.

Given:

Initial velocity u=5 m/s

Mass of the body = 20kg

Final velocity v = 2 m/s

The initial kinetic energy

Ei = (1/2) mu2 = (1/2) x 20 x (5 m/s)2 =250kgm/s2

= 250Nm = 250J

Final kinetic energy Ef = (1/2) mv2 = (1/2) x 20 x (2 m/s)2 =40kgm/s2 = 40 Nm =40J

Therefore,

Work done = Change in kinetic energy

Work done = Ef – Ei

Work done =40J – 250J

Work done = -210J

Where negative sign indicates that force acts contrary to motion direction.

Solution 5.

Work done by gravity depends solely on the vertical displacement of the body. It doesn’t

rely on the trail of the body. Therefore, work done by gravity is given by the expression,

W= m g h

Where,

Vertical displacement, h = 0

∴ W= mg × zero = 0

Therefore, the work done on the body by gravity is therefore zero.

Ans 6

No, the method doesn’t violate the law of conservation of energy. This is because once

the body falls from a height, then its mechanical energy changes into kinetic energy

increasingly. A decrease within the mechanical energy is capable a rise in the kinetic

energy of the body. Throughout the method, total energy of the body remains conserved.

Therefore, the law of conservation of energy isn’t desecrated.

Ans 7.

The chemical energy of the food changes into heat and then to muscular energy. On

paddling, the muscular energy changes into mechanical energy.

Ans 8.

When we push a large rock, there’s no transfer of muscular energy to the stationary rock.

Also, there’s no loss of energy as a result of muscular energy is transferred into energy,

which causes our body to become hot.

Solution 9

1 unit of energy is up to 1 kWh

1 unit = 1 kWh

1 kWh = 3.6 x 106 J

Therefore, 250 units of energy = 250 × 3.6 × 106 J

= 9 × 108 J.

Solution 10.

Gravitational mechanical energy is given by the expression,

W = mgh

Where,

h = Vertical displacement = 5 m,

m = Mass of the body = 40 kg

g = Acceleration due to gravity = 9.8 m s−2

∴ W = 40 × 5 × 9.8 = 1960 J.

At half-way down, the mechanical energy of the item is going to be 1960/2

At this time, the item has an equal quantity of potential and K.E.

This can be due to law of conservation of energy. Hence, half-way down, the K.E. of the

item can be 980 J.

Ans 11.

Work is completed whenever the given two conditions are satisfied:

a force acts on the body.

There is a displacement of the body by the appliance of force in or opposite to the

direction of force.

If the force direction is perpendicular to the displacement, the work performed gravity on

the satellite is perpendicular to its displacement. Hence, the work done on the satellite

by the planet is zero.

We know

W = F. s cos θ

W = F. s cos 90o

W = F. s. 0 [ cos 900 = 0]

W = 0

Ans 12.

Yes, consider a uniformly moving object,

Suppose an object is moving with constant rate. The web force performing on it is zero.

But there is a displacement on the motion of the article. Hence, there will be a

displacement while not a force.

Page No. 159

Ans 13.

Work is completed whenever the given two conditions are satisfied.

(i) A force acts on the body.

(ii) There is a displacement of the body by the applying of force in or opposite to the

direction of force.

When an individual holds a bundle of fodder over his head, then there’s no displacement

within the bundle of fodder. Although, force of gravity is functioning on the bundle, the

person isn’t applying any force thereon. Hence, within the absence of force, work done

by the person on the bundle is zero.

Solution 14

With the help of the expression, energy consumed by an electric heater will be obtained,

E = P x T

Where,

P = Power rating of the heater,

P = 1500 W = 1.5 kw

Time that the heater has operated,

T= 10 h

Therefore, energy consumed = Power × Time

= 1.5 × 10 = 15 kWh = 15 unit

Hence, the energy consumed by the heater in 10h is 15 kWh or 15 unit.

Ans 15.

Consider the case of oscillation pendulum.

When the pendulum bob is pulled (say towards left), the energy supplied is stored in it is

the form

Of PE on account of its higher position. When the pendulum is released so that it starts

moving towards right, then its PE changes into KE such that in mean position, it has

maximum KE, and Zero PE. As the pendulum moves towards extreme right, its KE changes

into PE such that at the extreme position, it has maximum PE and zero KE. When it moves

from this extreme position to mean position, its PE again changes to KE. This illustrates

the law Of conservation of energy. Eventually, the bob comes to rest, because during

each oscillation a part of the energy possessed by it transferred to air and in overcoming

friction at the point of suspension. Thus, the energy of the pendulum is dissipated in air.

The law of conservation of energy is not violated because the energy merely changes its

form and is not destroyed.

Solution 16

Solution 17.

Given:

The mass of the body = 1500kg

Velocity v = 60km/hr

The work required to stop the car = kinetic energy change of the car

Ans 18.

Case I

In this case, the direction of force functioning on the block is perpendicular to the

displacement

(� = 900). Therefore, work done by force on the block are going to be zero.

Case II

In this case, the direction of force functioning on the block is within the direction of

displacement.

(� = 00). Therefore, work done by force on the block are going to be positive.

Case III

In this case, the direction of force on the block is opposite to the direction of

displacement.

(� = 1800). Therefore, work done by force on the block are going to be negative.

Ans 19.

Yes, acceleration in an object could be zero even when several forces are acting on it.

This happens when all the forces cancel out each other i.e., the net force acting on the

object is zero.

Solution 20.

Energy consumed by an electrical device will be obtained with the assistance of the

expression for power,

E = P x T

Where,

P = Power rating of the device,

P = 500 W = 0.50 kw

Time that the device runs,

T= 10 h

Energy consumed by the device

Energy = Power × Time

= 0.50kw × 10h = 5 kWh

Hence, the energy consumed by four equal rating devices in 10 h = 4 × 5 kWh

= 20 kWh = 20 Units.

Ans 21.

When the object falls freely towards the bottom, its potential energy decreases and

kinetic energy will increase, because the object touches the bottom, all its potential

energy gets reborn into kinetic energy. Because the object hits the laborious ground, all

its K.E. gets reborn into heat and sound energy.