Work and Energy

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Q1: A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force
acts on the object through the displacement. What is the work done in this case?

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Q1. When do we say that work is done?
Work is said to be done when a force causes displacement of an object in the direction of applied force.

Q2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Work done = Force x Displacement

Q3. Define 1J of work.

When a force of IN causes a displacement of 1m, in its own direction the work done is said to be one joule.

Q4. A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing
the length of the field?
Work done = Force x Displacement = 140 x 15 = 2,100 J

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Q1. What is the kinetic energy of an object?
The energy possessed by a body by virtue of its motion is called kinetic energy.

Q2. Write an expression for the kinetic energy of an object.

Q3. The kinetic energy of an object of mass, m moving with a velocity of 5 ms -1 is 25 J. What will be its kinetic energy when its velocity is
doubled? What will be its kinetic energy when its velocity is increased three times?

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Q1. What is power?

Power is defined as the rate of doing work.

Q2. Define 1 watt of power.

When a work of 1 joule is done in 1 s, the power is said to be one watt.
Q3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Given W = 1000J, t = 10s, P =?
We know, P = W/t = 1000/10 = 100W.

Q4. Define average power.

When a machine or person does different amounts of work or uses energy in different intervals of time, the ratio between the total work
or energy consumed to the total time is average power.

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Q1. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term
‘work’.
(a) Suma is swimming in a pond.
(b) A donkey is carrying a load on its back.
(c) A wind mill is lifting water from a well.
(d) A green plant is carrying out photosynthesis.
(e) An engine is pulling a train.
(f) Food grains are getting dried in the sun.
(g) A sailboat is moving due to wind energy.

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.

Q2. An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the
final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the
object?
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.

Q3. A battery lights a bulb. Describe the energy changes involved in the process.
Within the electric cell of the battery the chemical energy changes into electrical energy. The electric
energy on flowing through the filament of the bulb, first changes into heat energy and then into the light energy.
Q4. Certain force acting on a 20 kg mass changes its velocity from 5 m s -1 to 2 m s-1. Calculate the work done by the force.

Q5. A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work
done on the object by the gravitational force? Explain your answer.
The work done is zero. This is because the gravitational force and displacement are perpendicular to each other.

Q6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of
energy? Why?
It does not violate the law Of conservation of energy. Whatever, is the decrease in PE due to loss of height, same is the increase in the
KE due to increase in velocity of the body.

Q7. What are the various energy transformations that occur when you are riding a bicycle?
The chemical energy of the food changes into heat and then to muscular energy. On paddling, the muscular energy changes into
mechanical energy

Q8. Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the
energy you spend going?
Energy transfer does not take place as no displacement takes place in the direction of applied force. The energy spent is used to
overcome inertia of rest of the rock.

Q9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
1 unit of energy = 1kWh

Given

Energy (E) = 250 units

1 unit = 1 kWh

1 kWh = 3.6 x 106 J

Therefore, 250 units of energy = 250 × 3.6 × 10 6

= 9 × 108 J.

Q10. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy?
If the object is allowed to fall, find its kinetic energy when it is half-way down.

Q11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.
When a satellite moves round the Earth, then at each point of its path, the direction of force of gravity on the satellite (along the radius)
is perpendicular to the direction of its displacement (along the tangent). Hence, the work done on the satellite by the force of gravity is
zero.

Q12. Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your
friends and teacher.
The answer is both Yes and No. Yes because when an object moves in deep space from one point to another point in a straight line,
the displacement takes place, without the application of force. No, because force cannot be zero for displacement on the surface of
earth. Some force is essential.
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Q13. A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your
answer.
The person does not do work because no displacement takes place in the direction of applied force as the force acts in the vertically
upward direction.

Q14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Energy consumed by an electric heater can be obtained with the help of the expression,
P=W/t
where,
Power rating of the heater, P = 1500 W = 1.5 kW
Time for which the heater has operated, t = 10 h
Work done = Energy consumed by the heater
Therefore, energy consumed = Power × Time
= 1.5 × 10 = 15 kWh
Hence, the energy consumed by the heater in 10 h is 15 kWh or 15 units.

Q15. Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum
bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is
it a violation of the law of conservation of energy?
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.

Q16. An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to
bring the object to rest?
Kinetic energy of an object of mass m moving with a velocity v is given by the expression 1/2mv². To bring the object to rest, an equal
amount of work i.e. 1/2mv² is required to be done on the object.

17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h.

Solution:

Given data:

The mass of the body = 1500kg

Velocity v = 60km/hr

The work required to stop the moving car = change in kinetic energy

=1/2 mv2

=1/2 * 5000 * (50/3)2

= -208333.3 J

18. In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east
shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive
or zero.

Case I

In this case, the direction of force functioning on the block is perpendicular to the displacement. Therefore, work done by force on the
block will be zero.

Case II
In this case, the direction of force functioning on the block is in the direction of displacement. Therefore, work done by force on the block
will be positive.

Case III

In this case, the direction of force functioning on the block is contrary to the direction of displacement. Therefore, work done by force on
the block will be negative.

19. Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with
her? Why?

Solution:

Acceleration in an object could be zero even when many forces work on it. This happens when all the forces get rid of one another, i.e.,
the online force working on the object is zero. For a uniformly moving object, the online force working on the it is zero. Hence, the
acceleration of the thing is zero. Hence, Soni is correct.

20. Find the energy in kW h consumed in 10 hours by four devices of power 500 W each.

Solution:

Given,

Power rating of the device (P) = 500 W = 0.50 kW

Time for which the device runs (T) = 10 h

Energy consumed by an electric device can be obtained by the expression

Power = Energy consumed/Time taken

∴ Energy consumed = Power × Time

Energy consumed = 0.50 × 10

Energy consumed = 5 kWh

Thus, the energy consumed by four equal rating devices in 10 h will be

⇒ 4 × 5 kWh

= 20 kWh

21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?

Solution:

When an object falls freely towards the ground, its potential energy decreases, and kinetic energy increases; as the object touches the
ground, all its potential energy becomes kinetic energy. Since the object hits the ground, all its kinetic energy becomes heat energy and
sound energy. It can also deform the ground depending upon the ground’s nature and the amount of kinetic energy possessed by the
object.