Work and Energy NCERT solutions
Table of Contents
Question 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:
| Question condition | Work status | Reason |
|---|---|---|
| • Suma is swimming in a pond. | work is done |  |
| • A donkey is carrying a load on its back. | work is not done | θ = 90˚ |
| • A wind-mill is lifting water from a well. | work is done | |
| • A green plant is carrying out photosynthesis. | work is not done | F = 0 d = 0 |
| • An engine is pulling a train. | work is done | |
| • Food grains are getting dried in the sun. | work is not done | F = 0 d = 0 |
| • A sailboat is moving due to wind energy. | work is done | |
Question 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: If an object is thrown at a certain angle from the ground and it moves in a curved path and falls back to the ground, then the work done by the force of gravity will be zero. Since the initial and final points of the path of the object lie on the same horizontal line, the vertical displacement is zero in the direction in which gravitational force acts.
W = F d cosθ
Since, displacement in direction of force is zero. d = 0
So, W = 0
Question 3:
A battery lights a bulb. Describe the energy changes involved in the process.
Ans: When a battery lights up a bulb, chemical energy stored in the battery is converted into electrical energy, and the bulb further converts this energy into light energy and heat energy.
Question 4:
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.
Ans: Given: Mass m = 20 kg initial velocity u = 5 m s–1 final velocity v = 2 m s–1
Formula / Concept: Work done = change in kinetic energy
W = 1/2 × 20 (2)2 – 1/2 × 20 (5)2
W = – 210 J
Here, negative sign indicate that work is done by resistive force.
Question 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: W = F d cosθ
Since, Angle between Gravitational force and displacement is 90˚. cosθ = cos90˚ = 0
So, W = 0
Question 6:
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Answer: The potential energy of a freely falling object decreases progressively; however, it does not violate the law of conservation of energy because potential energy is converted into kinetic energy.
Question 7:
What are the various energy transformations that occur when you are riding a bicycle?
Energy transformations that occur when you are riding a bicycle: mechanical energy is converted into kinetic energy and heat energy (riders body temperature increases).
Question 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: When you push a huge rock with all your might and fail to move it, the energy you spend is converted into heat energy.
Question 9:
A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer: Total energy consumed = 250 units = 250 kWh
Since, 1 kW h = 3.6 × 106 J
So, 250 units = 250 kWh = 250 × 3.6 × 106 J = 9 × 108 J
Question 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.
Answer: Given: m = 40 kg h = 5 m
Potential energy of object at ‘h’ height = m g h
Potential energy = m g h = 40 × 9.8 × 5 = 1960 J
If the object is allowed to fall, its kinetic energy when it is half-way down,
From energy conservation,
Total energy at highest point (at point A) = Total energy at mid point (at point C)
(KE + PE)A = (KE + PE)C
(0 + m g h)A = (KE + m g h/2)C
(KE)C = m g h – m g h/2 = m g h/2 = 40 × 9.8 × 5 / 2 = 980 J
Question 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, as the gravitational force acting on the satellite and the displacement travelled by it are perpendicular to each other.
W = F d cosθ
Since, Angle between Gravitational force and displacement is 90˚. cosθ = cos90˚ = 0 so, W = 0
Question 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.
Ans: Yes. In the absence of any force acting on it, an object can be displaced.
From Newton’s second law, F = ma = m (v-u)/t
If the external force is zero, F = 0 = m (v-u)/t
v-u = 0
v = u, means the body will maintain its state of motion or rest.
Question 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.
Ans: When a person holds a bundle of hay over his head for 30 minutes and gets tired. He does not do any work because displacement is zero.
Work = Force × Displacement
If displacement = 0 W = 0
Question 14:
An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Ans: P = 1500W t = 10 h
Energy used = power × time = 1500 × 10 = 15000 Wh = 15 kWh
Question 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?
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?
17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
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.
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?
20. Find the energy in kW h consumed in 10 hours by four devices of power 500 W each.
21. A freely falling object eventually stops on reaching the ground. What happenes to its kinetic energy?
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