11. Work and Energy Class 9 Science Chapter 11 NCERT Solutions (CBSE)

CBSE Class 9 Science Chapter 11. Work and Energy – Full NCERT Textbook Solutions

Chapter 11. Work and Energy

Internal Question and Answer:

Example 11.1:  A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force (Fig. 11.2), then find the work done .

      

Solution: Here, F = 5 N and s = 2 m

  The work done (W) = Force (F) × Displacement (s)  = 5 × 2 J = 10 J

1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 11.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?

        

Solution: Here, F = 7 N and s = 8 m

The work done (W) = Force (F) × Displacement (s) = 7 × 8 J = 56 J

Example 11.2:  A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.

Solution: Here, Mass , m = 15 kg and displacement, s = 1.5 m.

Work done,

Therefore, the work done by him on the luggage is 225 J.

Internal Question and Answer:

1. When do we say that work is done ?

Answer: There are two condition satisfied for work to be done :

 (i) a force should act on an object, and   (ii) the object must be displaced.

2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.

Answer:  Work done (W) = force (F) × displacement (S)

3. Define 1 J of work.

Answer:  1 J of work is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

4. 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?

Solution: Here , Force (F) = 140 N  and Displacement (s) = 15 m

We know that , Work done (W) = Force (F) × Displacement (s) = 140 × 15 J = 2100 J

Therefore, the work done is 2100 J .

Example 11.3 : An object of mass 15 kg is moving with a uniform velocity of 4 m/s . What is the kinetic energy possessed by the object?

Solution : Here, Mass of the object, , Velocity of the object

We know that ,

The kinetic energy of the object is 120 J .

Example 11.4:  What is the work to be done to increase the velocity of a car from 30 km/h  to 60 km/h if the mass of the car is 1500 kg?

Solution:  Mass of the car, m =1500 kg,

Initial velocity of car,  30 km/h

Therefore, the initial kinetic energy of the car, m/s

 The final velocity of the car,  60 km/h m/s

The final kinetic energy of the car,

Thus, the work done = Change in kinetic energy = 156250 J

Internal Question and Answer:

1. What is the kinetic energy of an object?

Answer: The kinetic energy is the energy possessed by an object due to its motion.

An object moving with some velocity can do work, so it has energy. The kinetic energy of an object depends on its mass and speed.

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

Answer:  An object of mass,  moving with velocity , then the kinetic energy is

3. The kinetic energy of an object of mass, m moving with a velocity of 5  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?

Solution: Here,  and

We know that, 

When the velocity is doubled : Here, m = 2 kg  ,

 

When velocity is doubled, kinetic energy becomes 100 J.

When the velocity is increased three times : Here, m = 2 kg  ,

When velocity is increased three times, kinetic energy becomes 225 J.

Example 11.5: Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8  .

Solution: Mass of the object, m = 10 kg , Displacement (height), h = 6 m, and g = 9.8

Potential energy  = 588 J.

The potential energy is 588 J.

Example 11.6 : An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. (Given, g = 10 )

Solution:  Let  be the height of the object .

Mass of the object, m = 12 kg , Potential energy,  J

We know that ,

Therefore, the object is at the height of 4 m.

Example 11.7: Two girls, each of weight 400 N climb up a rope through a height of 8 m. We name one of the girls A and the other B. Girl A takes 20 s while B takes 50 s to accomplish this task. What is the power expended by each girl?

Solution: (i) Power expended by girl A : ,    and t = 20 s

We have,  Power

(ii) Power expended by girl B:  F = mg = 400 N ,  h = 8 m ,  t = 50 s

We have,     Power = 64 W.

Power expended by girl A is 160 W.

Power expended by girl B is 64 W.

Example 11.8 : A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 m/s² .

Solution:  Here, m = 50 kg , g = 10  , Height of the staircase, and  t = 9 s

Weight of the boy, W = mg = 50 kg × 10  = 500 N

We have,   = 375 W.

Therefore, the power is 375 W.

Example 11.9 An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy consumed in one day by the bulb.

Solution: Here, P = 60 W = 0.06 kW , t = 6 h

Energy = power × time

= 0.06 kW × 6 h = 0.36 kW h = 0.36 units.

Therefore, the energy consumed by the bulb is 0.36 units .

Internal Question and Answer:

1. What is power?

Answer: Power is the rate of doing work or the rate of transfer of energy .

2. Define 1 watt of power.

Answer:  1 watt is the power of an agent, which does work at the rate of 1 joule per second.

3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?

Solution :  Here, W = 1000 J  and t = 10 s

We know that , Power

4. Define average power.

Answer:  The average power is the ratio of the total energy and the total time taken.

Exercises of Chapter 11. Work and Energy

1. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.

(i) Suma is swimming in a pond.

(ii) A donkey is carrying a load on its back.

(iii) A wind-mill is lifting water from a well.

(iv) A green plant is carrying out photosynthesis.

(v) An engine is pulling a train.

(vi) Food grains are getting dried in the sun.

(vii) A sailboat is moving due to wind energy.

Answer:  (i) Suma is swimming in a pond. → Work is done.
Suma applies force with her arms and legs to push water backwards, and she moves forward . Hence, force causes displacement.

(ii) A donkey is carrying a load on its back. → Work is not done .
The donkey applies force vertically upward to balance the load, but the displacement is horizontal. Since displacement is not in the direction of force, no work is done by the donkey on the load.

(iii) A wind-mill is lifting water from a well. → Work is done.
The wind-mill applies force on the rope/bucket to lift water upward and water moves upward. Hence, work is done.

(iv) A green plant is carrying out photosynthesis. → Work is not done .
No force is causing any displacement of the plant as a whole. Photosynthesis is a chemical process, not mechanical work.

(v) An engine is pulling a train. → Work is done.
The engine applies force on the train through the coupling and the train moves forward . Hence, work is done.

(vi) Food grains are getting dried in the sun. → Work is not done (in scientific sense).
No force causes displacement. The grains remain in place; drying is due to heat energy, not mechanical work.

(vii) A sailboat is moving due to wind energy. → Work is done.
Wind applies force on the sails, causing the boat to move . Hence, work is done.

2. 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?

Answer: Work done by gravity depends only on the vertical height change. Since the object returns to the same horizontal level, the net change in height is zero. Hence, work done by gravity is zero.

3. A battery lights a bulb. Describe the energy changes involved in the process.

Answer: When a battery lights a bulb, the following energy changes take place:

(i) Chemical energy stored in the battery is converted into electrical energy.

(ii) The electrical energy is then converted into light energy and heat energy .

4. Certain force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.

Solution: Here, m = 20 kg ,  and

We know that ,

5. 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.

Answer : The work done on the object by the gravitational force is zero. The gravitational force acts vertically downward, but the displacement from A to B is horizontal. Since the force and displacement are perpendicular to each other, no work is done by gravity.

6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?

Answer: No. When potential energy decreases, kinetic energy increases by an equal amount. Total mechanical energy remains constant. Energy is only converted from potential to kinetic, not destroyed. Hence, the law of conservation of energy is not violated.

7. What are the various energy transformations that occur when you are riding a bicycle?

Answer:  When you ride a bicycle, muscular energy is converted into mechanical energy to move the pedals. This mechanical energy is then converted into kinetic energy and some heat energy. Thus, energy changes from one form to another, but the total energy remains conserved.

8. 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?

Answer: No, no energy transfer happens to the rock because the rock does not move. But the energy you spend is not lost. It gets converted mostly into heat energy and some into sound energy. Also, a part of it is used in the tension and contraction of your muscles. So, energy is still conserved; it just changes into other forms instead of moving the rock.

9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Solution: We have,  1 unit  = 1 kilowatt-hour (kWh) = 1000 × 60 × 60 J = 3600000 J

250 unit = 250 × 3600000 J  J  J J = 900000000 J

So, 250 units of energy is equal to 900,000,000 joules.

10. 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.

Solution: Here, m = 40 kg , h = 5 m and g = 9.8

  Potential energy  J  Joules

Therefore, the potential energy of the object when it is raised to a height of 5 m above the ground is 1960 joules.

When the object is halfway down, it has fallen a distance of 2.5 m. At this point, the potential energy is converted into kinetic energy.

Here, , ,  

We have,

 

And   Kinetic energy J J

Therefore, when the object is halfway down, its kinetic energy is 980 joules

11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Answer: The work done by the force of gravity on a satellite moving round the Earth is zero.

The gravitational force acting on the satellite is directed towards the centre of the Earth, while the satellite moves along its circular path. Thus, the direction of motion of the satellite is perpendicular to the gravitational force at every point.

12. 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.

Answer:  Yes, an object can have displacement even in the absence of any force acting on it.

According to Newton’s first law of motion, if no external force acts on an object, it continues to move with uniform velocity in a straight line. So, an already moving object can keep changing its position, which means displacement occurs.

For example, a spacecraft moving in outer space can continue moving for a long distance without any force acting on it. Hence, displacement is possible without force, provided the object is already in motion.

13. 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.

Answer: No, no work is done on the bundle of hay because there is no displacement of the object. In physics, work is done only when a force causes displacement. However, the person gets tired because his muscles use energy to hold the bundle.

14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Solution:  Given,  W = 1500 w  and t = 10 hours

We know that,  Energy = Power × Time

Energy = 1500 W × 10 hours = 15,000 watt-hours (Wh)

Since 1 kilowatt-hour (kWh) = 1000 watt-hours (Wh)

Energy = 15 kWh

Therefore, the electric heater uses 15 kilowatt-hours (kWh) of energy in 10 hours.

15. 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?

Answer: When we draw a pendulum bob to one side, it gains potential energy. When released, this potential energy converts into kinetic energy at the lowest point. As it rises to the other side, kinetic energy converts back to potential energy. Thus, total energy remains constant.

The bob eventually comes to rest due to air resistance and friction at the pivot. Its energy is slowly converted into heat and sound energy.

This is not a violation of the law of conservation of energy because energy is only transformed into other forms, not destroyed.

16. An object of mass,  is moving with a constant velocity, . How much work should be done on the object in order to bring the object to rest?

Answer:  The work required to bring the object to rest is equal to its initial kinetic energy.

Initial kinetic energy, 
Final kinetic energy,  (since object is at rest)

We have, Work done = Change in kinetic energy

The negative sign indicates that work is done against the motion (by an opposing force).
So, the magnitude of work required is .

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

Solution:  Here, m = 1500 kg  , and  

Work done = Change in kinetic energy

J = 208,333.33 J = 208.33 kJ

Therefore, the work required to stop the car is  208.3 kJ .

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.

         

Answer: To determine whether the work done by the force is negative, positive, or zero, we need to consider the angle between the force and the direction of displacement.

(i) If the force and displacement are in the same direction, the work done is positive.

(ii) If the force and displacement are in opposite directions, the work done is negative.

(iii) If the force and displacement are perpendicular , the work done is zero.

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?

Answer: Yes, I agree with Soni.

Acceleration can be zero even when several forces act on an object if all the forces balance each other. In this case, the net force becomes zero. According to Newton’s first law, when the net force is zero, the object remains at rest or moves with uniform velocity without acceleration.

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

Solution: Given, Power of each device = 500 W , Time duration of usage = 10 hours and Number of devices = 4

Total power = Power of one device × Number of devices

Total power = 500 W × 4 = 2000 W

We have,

Total power in kilowatts

Energy consumed = Total power in kilowatts × Time duration of usage

Energy consumed = 2 kW × 10 hours = 20 kWh

Therefore, the energy consumed by the four devices in 10 hours is 20 kilowatt-hours (kWh)

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

Answer: When a freely falling object reaches the ground, its kinetic energy does not disappear. It gets converted into other forms of energy such as heat energy, sound energy and deformation energy due to the impact with the ground. Thus, energy is conserved.

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