Chapter 11 . Work and Energy

Class 9 Science Chapter 11 Work and Energy Internal / Example Questions and Answers :

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

Internal Questions :

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,

Work done is 225 J.

Internal Questions :

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, 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

m/s

m/s

Therefore, the initial kinetic energy of the car,

J

J

J

 The final velocity of the car,  60 km/h

m/s

The final kinetic energy of the car,

J

J

J

Thus, the work done = Change in kinetic energy

J

J

= 156250 J

Internal Questions :

1. What is the kinetic energy of an object?

Answer: The kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases with its speed. An object of mass,  moving with velocity  has a kinetic energy of .

The kinetic energy of an object moving with a certain velocity is equal to the work done on it to make it acquire that velocity.
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, J and

We know that ,

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

   

J

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

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

Acceleration due to gravity, 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 ,

 

m

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 : Weight of the girl,  

and Displacement (height),  

Time taken

Power

w

(ii) Power expended by girl B:

Weight of the girl, mg = 400 N

Displacement (height), h = 8 m

Time taken, t = 50 s

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  .

Solution:  Here, m = 50 kg , g = 10  ,

Height of the staircase,

Time taken to climb, t = 9 s

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

Power,

W

= 375 W.

Power is 375 W.

Internal Questions :

1. What is power ?

Answer: Power is the rate of doing work or the rate of transfer of energy .The unit of power is watt (W) .
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 W

4. Define average power .

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

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,  Power of electric bulb = 60 W = 0.06 kW ,  Time , t = 6 h

Energy = Power × time taken

= 0.06 kW × 6 h

= 0.36 kW h

= 0.36 units.

The energy consumed by the bulb is 0.36 units .

Class 9 Science Chapter 11 Work and Energy Exercise Questions and Answers :

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’.
• Suma is swimming in a pond.
• A donkey is carrying a load on its back.
• A wind-mill is lifting water from a well.
• A green plant is carrying out photosynthesis.
• An engine is pulling a train.
• Food grains are getting dried in the sun.
• A sailboat is moving due to wind energy.

Answer:  (i) Suma is swimming in a pond.

No work is being done because swimming is a physical activity, but it does not involve the transfer of energy or the displacement of an object.

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

Work is being done because the donkey is exerting a force to lift and carry the load, resulting in the displacement of the load.

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

Work is being done because the windmill is using the wind's energy to lift water, causing a displacement of the water.

(iv) A green plant is carrying out photosynthesis.

No work is being done because photosynthesis is a chemical process that occurs within the plant. It does not involve the transfer of energy or the displacement of an object.

(v) An engine is pulling a train.

Work is being done because the engine is exerting a force to move the train, resulting in the displacement of the train.

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

No work is being done because the drying process is a result of natural heat and evaporation. It does not involve the transfer of energy or the displacement of an object.

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

Work is being done because the wind is exerting a force on the sail, causing the sailboat to move and resulting in the displacement of the sailboat.

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: The work done by the force of gravity on the object is zero.
3. A battery lights a bulb. Describe the energy changes involved in the process.

Answer: Chemical energy in the battery is converted to electrical energy, which is then transformed into heat energy due to resistance in the bulb's filament. Finally, the heat energy is converted into light energy emitted by the bulb.
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 ,

J

J

J

J

Therefore, the work done by the force is - 210 J .

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 gravitational force is acting vertically downward, while the displacement of the object is horizontally along the table. Since the displacement is perpendicular to the direction of the gravitational force, there is no component of the displacement in the direction of the force. So, the work done by the gravitational force is zero.

Therefore, when the mass is moved horizontally on the table from point A to point B, the gravitational force does not perform any work on the object.

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

Answer: No, it does not violate the law of conservation of energy. The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In the case of a freely falling object, as it falls, its potential energy decreases, but its kinetic energy increases. The decrease in potential energy is balanced by an increase in kinetic energy, maintaining the total energy of the system constant. Therefore, the law of conservation of energy is still upheld, as the total energy remains conserved throughout the process.
7. What are the various energy transformations that occur when you are riding a bicycle?

Answer:  When riding a bicycle, the energy transformations that occur are as follows:

(i) Muscular energy (chemical energy in the body) is converted to mechanical energy to pedal the bike.

(ii) Mechanical energy is transformed into kinetic energy as the bicycle moves forward.

(iii) Kinetic energy can be converted to potential energy when going uphill, and vice versa when going downhill.

Friction and air resistance transform some of the energy into heat energy.

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:  Yes, the transfer of energy still takes place when you push a huge rock with all your might and fail to move it. The energy you spend is primarily going into overcoming the static friction between the rock and the surface. This energy is converted into heat, resulting in an increase in the temperature of the rock and the surrounding area.
9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Solution: We know that ,

1 unit  = 1 kilowatt-hour (kWh)

= 1000 × 60 × 60 J

= 3600000 J

250 unit = 250 × 3600000 J

               J

               J

              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 ms-2

  Potential energy EP=mgh

=40×9.8×5 J

=1960  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,

 

 

Kinetic energy

J

Joules

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 around the Earth is zero. This is because the force of gravity is acting perpendicular to the satellite's motion, and work is only done when a force acts in the direction of an object's motion. Since the satellite's path is a circular orbit, and gravity is always directed toward the center of the Earth, there is no work done by gravity on the satellite.
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: No, there cannot be displacement of an object in the absence of any force acting on it. According to Newton's first law of motion, an object at rest will remain at rest and an object in motion will continue moving with a constant velocity in a straight line, unless acted upon by an external force. In the absence of any force, there would be no cause for the object to undergo any change in its state of motion or position. Therefore, the object would not experience any displacement.

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: A person holding the bundle of hay over his head for 30 minutes has not done any work in the physics sense. Work done is defined as the product of force and displacement in the direction of the force. Since the person is not displacing the hay vertically, no work is being done.
14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Solution:  Given,  W = 1500 watts and Time = 10 hours

We know that , Energy = Power × Time

Energy = 1500 W × 10 hours

Energy = 15,000 watt-hours (Wh)

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

Energy kWh

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 lift a pendulum bob, it gains potential energy. As it swings, this potential energy is converted into kinetic energy. However, due to friction and air resistance, some energy is lost as heat and sound, causing the bob to eventually stop. This doesn't violate the law of conservation of energy; instead, it demonstrates energy transformation. The total energy is conserved, but it changes from potential to kinetic to other forms.

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: In order to bring an object of mass () moving with a constant velocity() to rest, the work done on the object would be equal to the change in its kinetic energy.

The kinetic energy of an object is

Since the object is initially moving with a constant velocity, its kinetic energy is non-zero. To bring it to rest, the final kinetic energy would be zero. Therefore, the change in kinetic energy is equal to the negative of the initial kinetic energy.

Hence, the work done on the object to bring it to rest would be

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

The initial kinetic energy of the car : 

Initial Kinetic Energy

J

J

J

Since the car needs to be brought to rest, its final kinetic energy will be zero.

Work = Final Kinetic Energy  –  Initial Kinetic Energy

Work done

J

Therefore, the work required to stop the car is – 208,437.5 Joules.

The negative sign indicates that work is done against the motion of the car, reducing its kinetic energy to zero.

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 (at a 90-degree angle), 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, it is possible for the acceleration of an object to be zero even when several forces are acting on it. This can occur when the forces acting on the object are balanced and cancel each other out, resulting in a net force of zero and no 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

Number of devices = 4

Total power = Power of one device × Number of devices

Total power = 500 W × 4 = 2000 W

Next, convert the total power to kilowatts:

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 eventually stops upon reaching the ground, its kinetic energy is fully converted into other forms of energy, such as sound and heat. The object loses all its initial kinetic energy during the impact and comes to rest.