Class 9 | Science | Chapter 11 |Work and Energy| NCERT Solutions
Question Answers, Page 148
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?
Work done = Force × Displacement
W= F × S
W = 7 × 8 = 56 Nm = 56 J
1. When do we say that work is done?
Work is said to be done whenever a force acts on a body and there is a displacement of the body caused by the applied force along the direction of the applied force.
2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.
W= F × S
where F is the force which displaces the body through a distance of S in the direction of force applied.
3. Define 1 J of work.
When a force of 1 newton moves a body through a distance of 1 m in its own direction, then the work done is known as 1 Joules or 1 J.
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?
Force = 140 N
Distance = 15 m
Work done= Force × Distance
Work done = 140 × 15 = 2100 J
1. What is the kinetic energy of an object?
The energy of a body due to its motion is called as its Kinetic energy.
1)A moving cricket ball can do work in pushing back the stamps.
2)Moving water can do work in turning the turbine for generating electricity.
3)Moving wind can do work in turning the blades of wind mill.
4)A moving hammer drives a nail into wood because of its kinetic energy.
5)A moving bullet can penetrate even a steel plate.
6)A moving bus,car,falling stone possesses kinetic energy.
7)A falling coconut, running athlete possesses kinetic energy.
2. Write an expression for the kinetic energy of an object.
K.E. = ½ mv2
Where K.E. is the kinetic energy
m is the mass of the body
v is the velocity with which body is moving
3. 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?
Kinetic energy of the object = 25 J
Velocity of the object = 5 m/s
K.E. = ½mv2
25= ½ × m ×(5)2
m= 2 Kg
If velocity is doubled , v = 5 × 2 = 10 m/s
K.E. = ½ × 2 × (10)2
K.E. = 100 J
If velocity is tripled , v = 5 × 3= 15 m/s
K.E. = ½ × 2 × (15)2
K.E. = 225 J
1. What is power?
Power is defined as rate of doing work .
Power = Work / Time
The S.I. unit of power is Watt.
2. Define 1 watt of power.
1 watt is the power of an appliance which does work at rate of 1 joules per second.
1 watt = 1 joule/1 second
3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Power = Work done / Time
Work done or energy consumed = 1000 J
Time = 10 s
Power = 1000/10 = 100 J/s or 100 W
4. Define average power.
Average power of an appliance is defined as the total work done by it in the total time taken.
Average power = Total work done/ total time taken
Exercises Page 158
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
1) Suma applies a force to push the water backwards.Therefore suma swims in the forward direction. Hence the force causes displacement. Hence , work is done by suma while swimming in a pond.
2)While carrying a load, the donkey has to apply a force in upward direction.But displacement of the load is in forward direction.Since , displacement is perpendicular to force, the work done is zero.
3) Wind mill is lifting water from a well and doing work against gravity.
4) In this case, there is no displacement and force, so no work is done.
5) An engine applies the force to pull the train.This allows the train to move in the direction of force.Therefore, there is displacement in the train in same direction.
6) During the drying of food grains, there is no force and displacement hence no work is done.
7) Wind energy applies a force on the sailboat to push it in forward direction.Therefore, there is a displacement in the boat in the direction of force.Hence work is done by wind.
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?
Work done by the force of gravity on the object depends only on vertical displacement.
When the object move upwards, the work done by gravity is negative and when the object move downwards, the work done by gravity is positive.
Therefore the work done by the gravity on the object is zero joules.
3. A battery lights a bulb. Describe the energy changes involved in the process.
When bulb is connected to a battery, then chemical energy of the battery is transferred into electrical energy.When the bulb receives this electrical signal , it converts it into heat and light energy.
4. Certain force acting on a 20 kg mass changes its velocity from 5 ms–1 to 2 ms–1. Calculate the work done by the force.
Mass of the body = 20 kg
Initial velocity = 5 m/s
Final velocity = 2 m/s
Work done = change in kinetic energy
Work done = ½mu2 -½mv2
Work done = ½ m(u2-v2)
Work done = ½ × 20 (52 -22)
Work done = 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.
Work done on the object by the gravitational force depends only on the vertical displacement of the body and does not depend on the path followed. Therefore the work done on the object by the gravitational force is zero because direction of force is vertically downwards and displacement is horizontal.
6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Law of conservation of energy states that whenever energy gets transformed, the total energy remains unchanged.When the body falls from a height , then its potential energy changes into kinetic energy. A decrease in potential energy is equal to increase in kinetic energy of the body.Thus during the process total mechanical energy of the body remains conserved. Therefore law of conservation of energy is not violated.
7. What are the various energy transformations that occur when you are riding a bicycle?
The muscular energy of the rider gets transferred into heat energy and kinetic energy of the bicycle.Heat energy heat’s the riders body whereas Kinetic energy provides a velocity to the bicycle.
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?
When we push a huge rock there is no transfer of muscular energy to the stationary rock.
9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
1 unit = 3600000 J
250 units = 250 × 3600000 =9 × 108 J
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.
m= 40 kg
g= 9.8 m/s2
P.E. = mgh
P.E. = 40 ×9.8 ×5
P.E. = 1960 J
When the object is half-way down, its potential energy becomes half the original energy and remaining half converted into kinetic energy.
At way down , the potential energy of the object = 1960 /2 = 980 J
11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.
When a satellite moves around the earth , then the direction of force of gravity on the satellite is perpendicular to its displacement.Hence the work done by the force of gravity on a satellite moving round the earth is zero.
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.
Yes, there may be displacement in the absence of force.
In the absence of force , F= 0
then ma=0 , a=o but m≠0
If a= o means object is at rest or in a state of uniform motion in straight line.Thus there can be displacement of an object in the absence of any force acting on it.
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.
Work is said to be done whenever a force acts on a body and there is displacement by the application of force in or opposite to the direction of force. When a person holds a bundle of hay over his head, then there will be no displacement in the bundle of hay.Hence in the absence of force, work done by the person is zero.
14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Power = work done/ Time taken
Work done or energy
Energy = Power × Time taken
Energy = 1500 × 10
Energy = 15000 KWh
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?
When the pendulum moves from it mean position A to either of its extreme position B or C, then at this position its kinetic energy is zero and its potential energy is maximum.In this way total mechanical energy remains conserved.As it moves towards point A, its potential energy decreases and kinetic energy increases.As it reaches point A, its kinetic energy is maximum and potential energy is minimum.Again total mechanical energy remains conserved.
The bob comes to rest because of air resistance which resist its motion.The pendulum loses its kinetic energy to overcome this friction and stops after some time.The law of conservation is not violated.
16. 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?
The object in motion = Kinetic energy = ½mv2
The kinetic energy of the object when it comes to rest= 0
Work done on object = Change in kinetic energy
= ½mv2 – 0
17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
Kinetic energy = ½mv2
mass of the car = 1500 kg
velocity of the car= 60 km/hr = 50/3 m/s
K.E. = ½ × 1500 × (50/3)2
K.E. = 20.8 × 104 J
Work done on object= change in k.E.
W.D. = 20.8 × 104 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.
a) In case 1 , the force and displacement are perpendicular to each other , so work done is zero.
b) In case 2, the force and displacement are in same direction, so the work done is positive.
c) In case 3 , the force and displacement are in opposite direction, so the work done is 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?
When all the force acting on an object cancel out each other i.e. the net force acting on the object is zero then the acceleration in an object could be zero even when several forces are acting on it.
20. Find the energy in kW h consumed in 10 hours by four devices of power 500 W each.
Power = work done/Time taken
Power of four devices = 4 × 500 = 2000 W
Time = 10 hr
Energy consumed = power × time
= 2000 × 10
= 20 units
21. A freely falling object eventually stops on reaching the ground. What happenes to its kinetic energy?
When an object fall freely towards the ground, its potential energy decreases and kinetic energy increases.As the object reaches the ground , all its potential energy gets converted into kinetic energy.As the object touches the ground , all its kinetic energy gets converted into heat energy and sound energy.