class-ix physics chapter-11 work and energy
TRANSCRIPT
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.