WORK AND ENERGY - Q&A
Questions on Page 1151. When do we say that work is done?
Answer: Work is said to be done when a force acts on an object and the object is displaced in the direction of the force. Mathematically, work is the product of force and displacement (W = F × s).
2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Answer: The expression for work done is:
W = F × s
Where:
W = Work done
F = Force applied
s = Displacement
3. Define 1 J of work.
Answer: 1 Joule (1 J) is the amount of work done on an object when a force of 1 Newton (1 N) displaces it by 1 meter (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?
Answer:
Given:
Force (F) = 140 N
Displacement (s) = 15 m
Work done (W) = F × s
W = 140 N × 15 m
W = 2100 J
Questions on Page 119
1. What is the kinetic energy of an object?
Answer: Kinetic energy is the energy possessed by an object due to its motion. Any moving object possesses kinetic energy.
2. Write an expression for the kinetic energy of an object.
Answer: The expression for kinetic energy (Ek) is:
Ek = ½ mv2
Where:
m = Mass of the object
v = Velocity of the object
3. The kinetic energy of an object of mass, m moving with a velocity of 5 m s-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?
Answer:
Given:
Initial velocity (v1) = 5 m s-1
Initial Kinetic Energy (Ek1) = 25 J
Formula: Ek = ½ mv2, so Ek ∝ v2 (Kinetic energy is directly proportional to the square of velocity).
Case 1: Velocity is doubled (v2 = 2v1)
New Kinetic Energy (Ek2) ∝ (2v1)2
Ek2 ∝ 4v12
Ek2 = 4 × Ek1
Ek2 = 4 × 25 J = 100 J
Case 2: Velocity is increased three times (v3 = 3v1)
New Kinetic Energy (Ek3) ∝ (3v1)2
Ek3 ∝ 9v12
Ek3 = 9 × Ek1
Ek3 = 9 × 25 J = 225 J
Questions on Page 123
1. What is power?
Answer: Power is defined as the rate of doing work or the rate of transfer of energy. It measures how fast or slow work is done.
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. (1 W = 1 J/s).
3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Answer:
Given:
Energy (E) = Work (W) = 1000 J
Time (t) = 10 s
Power (P) = Work / Time = W / t
P = 1000 J / 10 s
P = 100 W
4. Define average power.
Answer: Average power is defined as the total energy consumed divided by the total time taken. It is useful when the power of an agent varies with time.
Average Power = Total Energy Consumed / Total Time Taken
Exercises
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:
1. Suma is swimming in a pond: Work is done. Suma applies force to push the water backward, and she is displaced forward. Since there is force and displacement, work is done.
2. A donkey is carrying a load on its back: Work is not done (against gravity). The force of gravity acts downwards, while the displacement is horizontal. Since the angle between force and displacement is 90°, work done by gravity is zero. However, the donkey does work against friction.
3. A wind-mill is lifting water from a well: Work is done. The windmill exerts an upward force to lift the water, and the water is displaced upwards.
4. A green plant is carrying out photosynthesis: Work is not done. This is a biological process involving internal energy changes, but there is no external force causing physical displacement of the plant.
5. An engine is pulling a train: Work is done. The engine applies a pulling force, and the train is displaced in the direction of the force.
6. Food grains are getting dried in the sun: Work is not done. There is no force or displacement involved in the process of drying; it is just evaporation of moisture due to heat.
7. A sailboat is moving due to wind energy: Work is done. The wind exerts a force on the sail, and the boat moves (displaces) in the direction of the force.
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 is zero.
Explanation: Work done by gravity depends only on the vertical displacement (h). Since the object returns to the same horizontal level, the net vertical displacement is zero (h = 0).
W = m × g × h
W = m × g × 0 = 0 J
3. A battery lights a bulb. Describe the energy changes involved in the process.
Answer:
The energy changes are as follows:
1. Chemical Energy in the battery is converted into Electrical Energy.
2. Electrical Energy is then converted into Heat Energy and Light Energy by the bulb.
Sequence: Chemical Energy → Electrical Energy → Heat + Light Energy.
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.
Answer:
Given:
Mass (m) = 20 kg
Initial velocity (u) = 5 m s-1
Final velocity (v) = 2 m s-1
Work done is equal to the change in kinetic energy (Work-Energy Theorem).
W = ½ m (v2 - u2)
W = ½ × 20 × (22 - 52)
W = 10 × (4 - 25)
W = 10 × (-21)
W = -210 J
The negative sign indicates that the force is a retarding force (opposing motion).
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 by the gravitational force is zero.
Explanation: Gravitational force acts vertically downwards. The displacement of the object is horizontal. Since the angle between the force (gravity) and the displacement is 90° (perpendicular), the work done is zero (W = Fs cos 90° = 0). Also, there is no change in vertical height.
6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Answer:
No, this does not violate the law of conservation of energy.
Explanation: As the object falls, its potential energy decreases, but its kinetic energy increases by an equal amount. The potential energy is continuously transformed into kinetic energy. At any point during the fall, the sum of potential energy and kinetic energy (total mechanical energy) remains constant.
7. What are the various energy transformations that occur when you are riding a bicycle?
Answer:
1. Chemical Energy (from food) in your body is converted into Muscular Energy.
2. Muscular Energy is converted into Mechanical (Kinetic) Energy to move the bicycle.
3. Some energy is also converted into Heat Energy due to friction between tires and road, and within body muscles.
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:
Work done on the rock is zero because there is no displacement. However, energy transfer does take place.
Where the energy goes: The energy you spend is used up by your muscles (Muscular Energy) to sustain the force. This energy is dissipated as Heat Energy (making you feel hot) and is also used for internal bodily functions, causing fatigue. It does not transfer to the rock as mechanical work.
9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer:
Given: Energy consumed = 250 units.
1 Unit = 1 kWh (Kilowatt-hour)
1 kWh = 3.6 × 106 J
Total Energy in Joules = 250 × 3.6 × 106 J
E = 900 × 106 J
E = 9.0 × 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.
Answer:
Given:
Mass (m) = 40 kg
Height (h) = 5 m
g = 10 m/s2 (approx)
Potential Energy (PE) at height 5 m:
PE = mgh
PE = 40 × 10 × 5 = 2000 J
Kinetic Energy (KE) at half-way down:
At half-way, height = 2.5 m.
Potential Energy at half-way = mghhalf = 40 × 10 × 2.5 = 1000 J.
According to Law of Conservation of Energy:
Total Energy at top = Total Energy at half-way
PEtop = PEhalf + KEhalf
2000 J = 1000 J + KEhalf
KEhalf = 2000 - 1000 = 1000 J
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 is zero.
Justification: The gravitational force acts towards the center of the earth (centripetal force). The satellite moves tangentially to the orbit. At any instant, the direction of motion (displacement) is perpendicular (90°) to the direction of the force.
W = Fs cos 90° = 0.
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, there can be displacement in the absence of a net force.
Explanation: According to Newton's First Law of Motion, an object moving with uniform velocity in a straight line will continue to move with the same velocity (and hence have displacement) if no net external force acts on it. So, if an object is already in motion in a frictionless environment (like deep space), it will continue to displace without any force.
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:
The person has done no work on the bundle of hay.
Justification: Work is defined as W = F × s. Although the person applies an upward force to hold the bundle, there is no displacement (s = 0) of the bundle. Since displacement is zero, the work done is zero. He gets tired due to muscle fatigue (internal energy usage), not mechanical work.
14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Answer:
Given:
Power (P) = 1500 W = 1.5 kW
Time (t) = 10 hours
Energy (E) = Power × Time
E = 1.5 kW × 10 h
E = 15 kWh
(Note: 15 kWh = 15 units)
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:
Law of Conservation in Pendulum:
- At the extreme position (highest point), the bob has maximum Potential Energy (PE) and zero Kinetic Energy (KE).
- As it moves towards the mean position (lowest point), PE converts into KE.
- At the mean position, KE is maximum and PE is minimum.
- As it swings to the other side, KE converts back to PE. The total mechanical energy (PE + KE) remains constant at all points (ideally).
Why it comes to rest: The bob eventually comes to rest due to air resistance and friction at the support. These resistive forces oppose the motion.
What happens to the energy: The mechanical energy of the pendulum is dissipated into Heat Energy (warming the air and support) and Sound Energy.
Violation of Law: No, it is not a violation. The energy is not destroyed; it is merely transformed from mechanical energy into heat and sound, which dissipate into the surroundings.
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?
Answer:
Initial Kinetic Energy = ½ mv2
Final Kinetic Energy = 0 (since it comes to rest)
Work done = Change in Kinetic Energy
W = Final KE - Initial KE
W = 0 - ½ mv2
W = -½ mv2
The magnitude of work required is ½ mv2. The negative sign indicates it is retarding work.
17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
Answer:
Given:
Mass (m) = 1500 kg
Velocity (v) = 60 km/h = 60 × (5/18) = 50/3 m/s
Work done to stop the car = Kinetic Energy of the car
W = ½ mv2
W = ½ × 1500 × (50/3)2
W = 750 × (2500/9)
W = 1875000 / 9
W ≈ 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: Force is perpendicular to displacement.
Case II: Force is in the same direction as displacement.
Case III: Force is in the opposite direction to displacement.
Answer:
Case I: Zero Work. The force is perpendicular (90°) to the displacement. (W = Fs cos 90° = 0).
Case II: Positive Work. The force and displacement are in the same direction. (W = Fs cos 0° = +Fs).
Case III: Negative Work. The force acts opposite to the direction of displacement. (W = Fs cos 180° = -Fs).
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.
Reason: Acceleration depends on the net force acting on an object (Fnet = ma). If several forces act on an object such that they balance each other (i.e., the vector sum of all forces is zero), then the net force is zero. Consequently, the acceleration will be zero.
20. Find the energy in joules consumed in 10 hours by four devices of power 500 W each.
Answer:
Given:
Power of one device = 500 W
Number of devices = 4
Total Power (P) = 4 × 500 = 2000 W = 2 kW
Time (t) = 10 hours
Energy (E) in kWh = P × t = 2 kW × 10 h = 20 kWh
Converting to Joules (1 kWh = 3.6 × 106 J):
E = 20 × 3.6 × 106 J
E = 72 × 106 J
E = 7.2 × 107 J
21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?
Answer:
When a freely falling object hits the ground and stops, its kinetic energy is converted into other forms of energy:
1. Heat Energy: Generated due to the collision/impact with the ground.
2. Sound Energy: Produced as a thud or crash sound upon impact.
3. Deformation Energy: Used to change the shape of the object or the ground (creating a dent).