Question Set 1 (Page 3)
1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 10.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?
Answer: The work done (W) by a constant force (F) acting in the direction of displacement (s) is calculated using the formula: W = F × s
Given: Force (F) = 7 N ; Displacement (s) = 8 m
Work done (W) = 7 N × 8 m = 56 J (joules).
Question Set 2 (Page 4)
1. When do we say that work is done?
Answer: In science, we say that work is done only when two conditions are met:
- A force must act on an object.
- The object must be displaced (it must move) in the direction of the force.
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 the work done (W) when a constant force (F) acts on an object in the direction of its displacement (s) is: W = F × s
3. Define 1 J of work.
Answer: 1 Joule (J) of work is the amount of work done on an object when a force of 1 Newton (N) displaces it by 1 meter (m) along the line of action of the force. 1 J = 1 N × 1 m
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: The work done (W) is calculated as: W = Force (F) × Displacement (s)
Given: Force (F) = 140 N ; Displacement (s) = 15 m
Work done (W) = 140 N × 15 m = 2100 J (joules).
Question Set 3 (Page 7)
1. What is the kinetic energy of an object?
Answer: Kinetic energy (E_k) is the energy possessed by an object due to its motion. Any moving object, like a running athlete or a speeding stone, has kinetic energy.
2. Write an expression for the kinetic energy of an object.
Answer: The expression for the kinetic energy (E_k) of an object of mass (m) moving with a uniform velocity (v) is: E_k = 1/2 mv²
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: The formula for kinetic energy is E_k = 1/2 mv².
- Initial State: Velocity is v. Kinetic energy is 25 J.
- Case 1: Velocity is Doubled (2v)
When velocity is doubled, kinetic energy increases by 2² = 4 times.
New E_k = 4 × 25 J = 100 J
- Case 2: Velocity is Increased Three Times (3v)
When velocity is tripled, kinetic energy increases by 3² = 9 times.
New E_k = 9 × 25 J = 225 J
Question Set 4 (Page 11)
1. What is power?
Answer: Power is defined as the rate of doing work or the rate of transfer of energy. It tells us how quickly (fast or slow) work is done. Power (P) = Work done (W) / Time taken (t)
2. Define 1 watt of power.
Answer: 1 watt (W) is the power of an agent that does work at the rate of 1 Joule (J) per second.
1 W = 1 J s⁻¹
3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Answer: Power (P) is calculated as:
P = Energy consumed / Time taken
Given: Energy consumed = 1000 J
Time taken = 10 s
Power (P) = 1000 J / 10 s = 100 J/s or 100 W (watts).
4. Define average power.
Answer: Average power is used when the rate of doing work changes over time. It is calculated by dividing the total energy consumed (or total work done) by the total time taken.
Average Power = Total Energy Consumed / Total Time Taken
Activity 10.1 (Page 1-2)
Activity: We have discussed in the above paragraphs a number of activities which we normally consider to be work in day-to-day life. For each of these activities, ask the following questions and answer them:
(i) What is the work being done on?
(ii) What is happening to the object?
(iii) Who (what) is doing the work?
Answer: Here are the answers for some activities, based on the scientific definition of work:
- Kamali studying hard (reading, drawing, etc.)
- (i) Work being done on: Books, pen, diagrams, brain (mental activity).
- (ii) Happening to the object: Small movements like drawing occur, but there is no large displacement of objects. Mostly, no mechanical displacement of the main objects occurs.
- (iii) Who is doing the work: Kamali. (Scientifically, very little mechanical work is done).
- You pushing a huge rock that does not move
- (i) Work being done on: The huge rock.
- (ii) Happening to the object: The rock does not move (displacement is zero).
- (iii) Who is doing the work: You (but scientifically, no work is done on the rock).
- You climbing up the steps of a staircase
- (i) Work being done on: Your body (raising your mass against gravity).
- (ii) Happening to the object: Your body is displaced vertically through a height.
- (iii) Who is doing the work: You. (Scientifically, a lot of work is done).
Activity 10.2 (Page 2)
Activity: Think of some situations from your daily life involving work. List them. Discuss with your friends whether work is being done in each situation. Try to reason out your response. If work is done, which is the force acting on the object? What is the object on which the work is done? What happens to the object on which work is done?
Answer: A few examples where work is scientifically done:
| Situation | Is Work Done? | Force Acting | Object on which Work is Done | What Happens to the Object? |
|---|---|---|---|---|
| A bullock pulling a cart | Yes | Force exerted by the bullock | The cart | It is displaced through a distance. |
| A girl pulling a trolley | Yes | Force exerted by the girl | The trolley | It is displaced through a distance. |
| Lifting a book | Yes | Force applied by you (against gravity) | The book | It is displaced (rises up). |
Activity 10.3 (Page 2)
Activity: Think of situations when the object is not displaced in spite of a force acting on it. Also think of situations when an object gets displaced in the absence of a force acting on it. List all the situations that you can think of for each. Discuss with your friends whether work is done in these situations.
Answer: Situations Where Force Acts But Displacement is Zero (Work Done = 0)
- Examples:
- Pushing a huge wall or a building that doesn’t move.
- Holding a heavy load stationary on your head.
- A person pressing hard on a locked car, but the car doesn’t budge.
- Discussion on Work: In all these cases, the displacement (s) is zero, so the work done (W = F × s) is zero.
Situations Where Displacement Occurs in the Absence of a Force (Work Done = 0)
- Example (Conceptual):
- An object sliding on a perfectly frictionless surface in outer space. If it was already moving, it will continue to move at a uniform velocity forever, even though no net force is acting on it.
- Discussion on Work: When there is no net force (F = 0), the work done (W = F × s) is zero, even if displacement (s) is happening. This object moves due to its inertia.
Activity 10.4 (Page 3)
Activity: Lift an object up. Work is done by the force exerted by you on the object. The object moves upwards. The force you exerted is in the direction of displacement. However, there is the force of gravity acting on the object. Which one of these forces is doing positive work? Which one is doing negative work? Give reasons.
Answer:
- Force Exerted by You: This force is doing positive work.
- Reason: The force you exert is acting upwards, and the object’s displacement is also upwards. Since the force and displacement are in the same direction, the work done is positive.
- Force of Gravity: This force is doing negative work.
- Reason: The force of gravity always acts downwards, but the object’s displacement is upwards. Since the force and displacement are in opposite directions, the work done is negative.
Activity 10.5 (Page 4)
Activity: A few sources of energy are listed above. There are many other sources of energy. List them. Discuss in small groups how certain sources of energy are due to the Sun. Are there sources of energy which are not due to the Sun?
Answer: Other Sources of Energy
- Wind energy
- Hydroelectric energy
- Biomass energy
- Chemical energy (in fuels and food)
- Electrical energy
Sources Due to the Sun : Many energy sources come from the Sun:
- Wind Energy: Caused by the uneven heating of the Earth by the Sun.
- Hydroelectric Energy: The Sun evaporates water, which rises and falls as rain, driving the water cycle.
- Biomass and Fossil Fuels (Coal, Petroleum): These get their stored chemical energy from plants that used the Sun’s light energy long ago through photosynthesis.
Sources Not Due to the Sun
- Nuclear Energy: Energy from the core of atoms.
- Geothermal Energy: Heat energy from the interior of the Earth.
- Tidal Energy: Caused primarily by the gravitational pull of the Moon (and the Sun).
Activity 10.6 (Page 5)
Activity: Take a heavy ball. Drop it on a thick bed of sand… Compare their depths. Which one of them is deepest? Which one is shallowest? Why? What has caused the ball to make a deeper dent? Discuss and analyse.
Answer:
- Depths: The depression created from the highest point (1.5 m) will be the deepest. The depression from the lowest point (25 cm) will be the shallowest.
- Why: When the ball is raised higher, more work is done on it against gravity, so it acquires more potential energy ($E_p = mgh$). As it falls, this potential energy turns into kinetic energy.
- Deeper Dent: The ball dropped from a greater height has more kinetic energy just before hitting the sand. The ability to do more work (creating a deeper dent) is due to this greater energy of motion.
Activity 10.7 (Page 5)
Activity: Set up the apparatus as shown in Fig. 10.5… From where does this energy come? Repeat this activity by increasing the mass on the pan. In which case is the displacement more? In which case is the work done more? In this activity, the moving trolley does work and hence it possesses energy.
Answer:
- Source of Energy: The energy comes from the kinetic energy possessed by the moving trolley.
- Increasing Mass: Increasing the mass on the pan makes the trolley move faster, increasing its kinetic energy.
- Displacement and Work Done:
- The displacement of the wooden block will be more when the mass on the pan is increased.
- The work done on the block will also be more because the work done is equal to the energy transferred from the trolley to the block.
Activities 10.8 – 10.10 (Page 7)
Activity 10.8: Take a rubber band. Hold it at one end and pull from the other… How did it acquire energy when stretched?
Answer: When you stretch the rubber band, you exert a force and cause a displacement, so work is done on the band. This energy is transferred and stored in the band due to the change in its shape (configuration). This stored energy is called potential energy. When you release it, this potential energy is converted back into kinetic energy, making it snap back.
Activity 10.9: Take a slinky as shown below… How did the slinky acquire energy when stretched? Would the slinky acquire energy when it is compressed?
Answer:
- Acquiring Energy when Stretched: When the slinky is stretched, work is done on it against the tension of the coils. This work is stored as potential energy due to the change in its configuration.
- Acquiring Energy when Compressed: Yes, the slinky would also acquire potential energy when it is compressed. Work is done to push the coils closer together, changing its configuration, and this energy is stored.
Activity 10.10: Take a toy car. Wind it using its key… Did it move? From where did it acquire energy? Does the energy acquired depend on the number of windings? How can you test this?
Answer:
- Did it Move: Yes, the toy car moves.
- Source of Energy: When the key is wound, work is done on the spring inside the car. This energy is stored as potential energy in the compressed spring. This potential energy then turns into the kinetic energy that makes the car move.
- Dependence on Windings: Yes, the energy acquired depends on the number of windings. More windings mean more work is done and more potential energy is stored.
- Testing: You can test this by winding the key a different number of times (e.g., 5 turns vs. 20 turns) and measuring the distance the car travels each time. The car with more windings will travel farther.
Activities 10.11 – 10.12 (Page 7)
Activity 10.11: Lift an object through a certain height… From where did it get the energy? Think and discuss.
Answer: The object got the energy from the work done by the person (or agent) who raised it. The person exerted a force (equal to the object’s weight) over a distance (the height, h) against gravity. This work done is stored in the object as gravitational potential energy because of its position above the ground.
Activity 10.12: Take a bamboo stick and make a bow… The potential energy stored in the bow due to the change of shape is thus used in the form of kinetic energy in throwing off the arrow.
Answer: This activity demonstrates energy conversion:
- Work is done to stretch the bowstring, changing the bow’s shape.
- This work is stored as potential energy in the stretched bow.
- When released, the potential energy is rapidly converted into the kinetic energy (energy of motion) of the arrow, making it fly.
Activity 10.13 (Page 9)
Activity: Discuss the various ways of energy conversion in nature… (a) How do green plants produce food? (b) Where do they get their energy from? (c) Why does the air move from place to place? (d) How are fuels, such as coal and petroleum formed? (e) What kinds of energy conversions sustain the water cycle?
Answer: (a) Green plants produce food through the process of photosynthesis.
(b) They get their energy from the Sun. They convert the Sun’s light energy into chemical energy (stored in the food).
(c) Air moves (creating wind) because the Sun heats the Earth’s surface unevenly. This difference in temperature causes air pressure differences, which moves the air (converting heat energy into kinetic energy of the wind).
(d) They are formed from the remains of ancient plants and animals buried under the Earth for millions of years. The energy stored in them is chemical energy, originally obtained from the Sun.
(e) The Sun’s heat energy causes evaporation (changing water’s state), which creates water vapor with high potential energy. As rain falls, this potential energy is converted into kinetic energy.
Activity 10.14 (Page 9)
Activity: Many of the human activities and the gadgets we use involve conversion of energy from one form to another. Make a list of such activities and gadgets. Identify in each activity/gadget the kind of energy conversion that takes place.
Answer: Here are some examples of energy transformation:
| Activity/Gadget | Energy Conversion |
|---|---|
| Electric Bulb | Electrical energy to Light energy + Heat energy |
| Loudspeaker | Electrical energy to Sound energy + Heat energy |
| Burning a Matchstick | Chemical energy to Heat energy + Light energy |
| A Car Engine | Chemical energy (fuel) to Heat energy to Mechanical energy (motion) |
| A Cell Phone (using battery) | Chemical energy to Electrical energy to Light energy, Sound energy, etc. |
Activity 10.15 (Page 10)
Activity: An object of mass 20 kg is dropped from a height of 4 m. Fill in the blanks in the following table by computing the potential energy and kinetic energy in each case. For simplifying the calculations, take the value of g as 10 m s⁻².
- Mass (m) = 20 kg; Total Height (h_total) = 4 m; g = 10 m s⁻²
- Total Energy = m g h = 20 × 10 × 4 = 800 J (This stays constant)
| Height at which object is located (m) | Potential Energy (E_p = mgh) (J) | Kinetic Energy (E_k = Total Energy – E_p) (J) | E_p + E_k (J) |
|---|---|---|---|
| 4 | 20 × 10 × 4 = 800 | 800 – 800 = 0 | 800 |
| 3 | 20 × 10 × 3 = 600 | 800 – 600 = 200 | 800 |
| 2 | 20 × 10 × 2 = 400 | 800 – 400 = 400 | 800 |
| 1 | 20 × 10 × 1 = 200 | 800 – 200 = 600 | 800 |
| Just above the ground (h ≈ 0) | 0 | 800 – 0 = 800 | 800 |
Activity 10.16 (Page 10)
Activity: Consider two children, say A and B. Let us say they weigh the same. Both start climbing up a rope separately. Both reach a height of 8 m. Let us say A takes 15 s while B takes 20 s to accomplish the task. What is the work done by each? The work done is the same. However, A has taken less time than B to do the work. Who has done more work in a given time, say in 1 s?
Answer:
- Work Done by Each: The work done by both A and B is the same. This is because they have the same weight (force) and climbed the same height (displacement).
- Work Done in 1 s (Power): Child A has done more work in 1 s.
- Reason: Power is the rate of doing work (Work/Time). Since A took less time (15 s) than B (20 s) to do the same work, A has a higher power.
Activity 10.17 (Page 11)
Activity: Take a close look at the electric meter installed in your house… How many ‘units’ are consumed during day time? How many ‘units’ are used during night? Tabulate your observations. Draw inferences from the data…
Answer: This activity helps you understand how the rate of energy consumption (power) and the total time of use determine the total energy used, which is measured in ‘units’ (kilowatt-hour, kWh).
- Observation: You would find the readings different between day and night, depending on when high-power appliances (like air conditioners, water heaters, or washing machines) are used.
- Inference: If the night usage is higher, it suggests high-power appliances are running more during that time. This demonstrates practically that energy consumption depends on both the appliance’s power and how long it is switched on.
Exercises : Question Set 1 (Page 12)
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’.
Answer:
- Suma is swimming in a pond.
- Work is done. Suma exerts a force, and her body is displaced forward.
- A donkey is carrying a load on its back.
- Work is not done on the load by the force supporting it if the donkey walks horizontally. The force on the load is upward (against gravity), but the displacement is forward. Since the force is perpendicular to the displacement, work done is zero.
- A wind-mill is lifting water from a well.
- Work is done. The wind-mill mechanism exerts an upward force on the water, displacing it vertically through a height.
- A green plant is carrying out photosynthesis.
- Work is not done in the mechanical sense. This is energy conversion (light to chemical), not mechanical force causing displacement.
- An engine is pulling a train.
- Work is done. The engine exerts a pulling force, and the train is displaced over a distance.
- Food grains are getting dried in the sun.
- Work is not done in the mechanical sense. This involves heat transfer, not mechanical force causing displacement.
- A sailboat is moving due to wind energy.
- Work is done. The wind exerts a force on the sails, and the boat is displaced over a distance.
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.
Reason: The work done by gravity only depends on the vertical displacement (change in height). Since the starting point and the ending point are on the same horizontal line, the net vertical displacement is zero.
Work done = Force x vertical displacement = mg x 0 = 0 J.
3. A battery lights a bulb. Describe the energy changes involved in the process.
Answer: The energy changes are:
- Chemical Energy (stored in the battery) is converted into Electrical Energy.
- The Electrical Energy flows to the bulb and is converted into Light Energy (what we see) and Heat Energy (what we feel).
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: Work done (W) = Change in Kinetic Energy.
- Mass (m) = 20 kg
- Initial velocity (u) = 5 m s⁻¹
- Final velocity (v) = 2 m s⁻¹
- Initial Kinetic Energy (E_k,i):
- E_k,i = 1/2 m u² = 1/2 × 20 kg × (5 m s⁻¹)²
- E_k,i = 10 kg × 25 m² s⁻² = 250 J
- Final Kinetic Energy (E_k,f):
- E_k,f = 1/2 m v² = 1/2 × 20 kg × (2 m s⁻¹)²
- E_k,f = 10 kg × 4 m² s⁻² = 40 J
- Work Done (W):
- W = E_k,f – E_k,i = 40 J – 250 J = -210 J
(The work done is negative, meaning the force was applied opposite to the direction of motion to slow the object down.)
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 on the object is zero.
Explanation: The gravitational force acts vertically downwards. Since the object is moved along a horizontal line (A to B), the displacement is perpendicular to the gravitational force. When force and displacement are perpendicular (at 90°), the work done is zero.
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.
Reason: The Law of Conservation of Energy says that the total energy must remain constant. As the potential energy (E_p) decreases because the height decreases, an equal amount of energy is converted into kinetic energy (E_k) because the speed increases. The sum of the potential energy and kinetic energy (total mechanical energy) stays the same at all times.
7. What are the various energy transformations that occur when you are riding a bicycle?
Answer: The main energy transformations are:
- Chemical Energy (from food) => Muscular Energy (in your body).
- Muscular Energy => Mechanical Energy (work on pedals).
- Mechanical Energy => Kinetic Energy (motion of the bicycle).
Some energy is lost as Heat Energy (due to friction) and Sound 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: Transfer of Energy on the Rock: No mechanical energy is transferred to the rock. Since the rock does not move, the displacement is zero, and thus the work done on the rock is zero. Where Energy Goes: The energy you spend is consumed by your body’s muscles for the effort of contraction. This energy is converted into Heat Energy inside your body, which is why you feel tired and warm.
9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer: The commercial ‘unit’ of energy is the kilowatt-hour (kWh).
- 1 unit = 1 kWh = 3.6 × 10⁶ J
- Energy consumed = 250 units
Energy in joules = 250 x 3,600,000 J = 900,000,000 J or 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. Take g = 10 m s⁻² (for simplifying the calculations).
Answer: Mass (m) = 40 kg ; Total Height (h_total) = 5 m ; g = 10 m s⁻²
- Potential Energy (E_p) at 5 m: E_p = m g h = 40 kg x 10 m s⁻² x 5 m = 2000 J
(This is the total mechanical energy.)
- Kinetic Energy (E_k) Half-way Down (at 2.5 m):
- Half-way height (h’) = 5 m / 2 = 2.5 m.
- Potential Energy at 2.5 m (E_p’):
- E_p’ = m g h’ = 40 kg x 10 m s⁻² x 2.5 m = 1000 J
- By conservation of energy (Total Energy = E_p’ + E_k’):
- E_k’ = Total Energy – E_p’ = 2000 J – 1000 J
- E_k’ = 1000 J
(The object’s kinetic energy halfway down is 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 on a satellite moving in a circular orbit around the Earth is zero.
Justification: The force of gravity (which keeps the satellite in orbit) is always directed inwards (towards the Earth). The satellite’s displacement at any instant is always tangential (perpendicular) to the force. Since the force and displacement are perpendicular, the work done 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.
Answer: Yes, an object can experience displacement (motion) in the absence of any net force acting on it.
Reason: According to Newton’s First Law of Motion, if an object is already moving, it will continue to move at a constant velocity (meaning displacement occurs) if there is no net external force acting on it. If force (F) is zero, the work done (W = F x s) is zero, even though displacement (s) is happening.
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: In the scientific sense, the person has not done any work on the bundle of hay.
Justification:
Work requires displacement. Since the bundle of hay is held stationary, its displacement (s) is zero. Therefore, the work done on the hay is zero. The person gets tired because their muscles use up chemical energy, which is converted into heat, but this energy is not transferred as mechanical work to the hay.
14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Answer: Power (P) = 1500 W ; Time (t) = 10 hours
- Calculate Energy in Joules (J):
- Time in seconds (t) = 10 h x 3600 s/h = 36,000 s
- Energy (W) = Power x Time
- W = 1500 W x 36,000 s = 54,000,000 J or 4 × 10⁷ J
- Calculate Energy in Commercial Units (kWh):
- Power in kW = 1500 W / 1000 = 1.5 kW
- Energy = 1.5 kW x 10 h = 15 kWh (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: Energy Changes in a Simple Pendulum
The pendulum illustrates how energy is converted back and forth:
- Extreme Ends: At the highest points (A and C), the speed is zero, so Kinetic Energy (E_k) is zero. The height is maximum, so Potential Energy (E_p) is maximum.
- Mean Position: At the lowest point (B), the speed is maximum, so E_k is maximum. The height is minimum, so E_p is minimum.
- Throughout: As the bob swings, E_p changes into E_k, and E_k changes back into E_p. The total energy (E_p + E_k) remains constant.
Why the Bob Stops and Energy Transformation
- Why it Stops: The bob eventually comes to rest due to opposing forces like air resistance and friction at the point of suspension. These forces do work against the motion.
- What Happens to Energy: The mechanical energy (E_p + E_k) is converted into non-mechanical forms: Heat Energy (due to friction) and Sound Energy. This heat and sound dissipate into the surroundings.
- Violation: No, this is not a violation of the law of conservation of energy. The total energy of the entire system (pendulum + air + surroundings) is still conserved; it has simply changed form from useful mechanical energy to unusable heat and sound 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?
Answer: The work done to bring the object to rest must be equal to the magnitude of the object’s initial kinetic energy.
- Initial Kinetic Energy = 1/2 m v²
- Final Kinetic Energy = 0 (since it is at rest)
- Work Done (W) = Final E_k – Initial E_k = 0 – 1/2 m v²
- The magnitude of the work required is 1/2 m v².
17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?
Answer: Mass (m) = 1500 kg ; Initial velocity (v) = 60 km/h ; Final velocity (u) = 0 m/s
- Convert velocity to m s⁻¹: v = 60 km/h x (1000 m / 3600 s) = 50/3 m s⁻¹
- Calculate Initial Kinetic Energy (Work Required): 1/2 m v²
- Work = 1/2 x 1500 kg x (50/3 m s⁻¹)²
- Work = 750 kg x (2500 / 9) m² s⁻²
- Work = 1,875,000 / 9 J = 208,333.33 J
The work required to stop the car is approximately 208,333 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.
Answer:
- Diagram 1 (Force F is vertical, Displacement is horizontal):
- Work Done: Zero (Force is perpendicular to displacement.)
- Diagram 2 (Force F is east, Displacement is east):
- Work Done: Positive (Force is in the same direction as the displacement.)
- Diagram 3 (Force F is west, Displacement is east):
- Work Done: Negative (Force is opposite to the direction of displacement.)
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 is zero when the net force (or resultant force) acting on the object is zero. If several forces are acting on an object but they are balanced (they cancel each other out), the object’s velocity won’t change, and thus its acceleration will be zero.
20. Find the energy in joules consumed in 10 hours by four devices of power 500 W each.
Answer:
- Total Power (P_total): P_total = 4 x 500 W = 2000 W
- Time (t) in seconds: t = 10 hours x 3600 s/h = 36,000 s
- Energy Consumed : Energy = Power x Time = 2000 x 36,000 = 72,000,000 J or 2 × 10⁷ J
21. A freely falling object stops on reaching the ground. What happens to its kinetic energy?
Answer: When the object hits the ground and stops, its kinetic energy (energy of motion) is transformed into other forms of energy:
- Heat Energy (due to the impact and friction).
- Sound Energy (the sound of the collision).
- Energy used to deform the object and the ground.