NCERT Solutions of Work, Energy And Power class 9th science chapter 3 with extra questions
Work, Energy, and Power
1. Work
In scientific terms, work is done when a force acts on an object and displaces it in the direction of the force. It is mathematically expressed as:
W = F × d × cos(θ)
Where:
- W = Work (Joules, J)
- F = Force (Newtons, N)
- d = Displacement (meters, m)
- θ = Angle between force and displacement
Types of Work Done
- Positive Work: When force and displacement are in the same direction (e.g., lifting a weight).
- Negative Work: When force and displacement are in opposite directions (e.g., applying brakes in a car).
- Zero Work: When displacement is zero or force is perpendicular to displacement (e.g., carrying a bag while walking on a horizontal path).
Example: Work Done by a Force
A force of 10 N moves an object 5 m in the direction of the force. Calculate the work done.
W = 10 N × 5 m × cos(0°) = 50 J
The work done is 50 Joules.
2. Energy
Energy is the ability of an object or system to do work. It exists in various forms such as kinetic energy, potential energy, thermal energy, etc. The SI unit of energy is the Joule (J).
Forms of Energy
- Kinetic Energy: Energy of motion.
- Potential Energy: Energy stored due to position or configuration.
- Thermal Energy: Energy related to temperature and heat.
- Chemical Energy: Energy stored in chemical bonds.
Kinetic Energy
Kinetic energy is the energy possessed by an object due to its motion. It is expressed as:
Kinetic Energy (KE) = ½ mv²
Where:
- m = Mass of the object (kg)
- v = Velocity of the object (m/s)
Derivation of Kinetic Energy from Equation of Motion
From the equation of motion:
v² = u² + 2as
Multiplying both sides by m/2:
½ mv² = ½ mu² + mas
Since work done (W) is F × s and force F = ma, we get:
W = ½ mv² – ½ mu²
If the object starts from rest, u = 0, so:
KE = ½ mv²
Example: Kinetic Energy of a Car
A car of mass 1000 kg is moving at a speed of 15 m/s. Calculate its kinetic energy.
KE = ½ × 1000 kg × (15 m/s)² = 112,500 J
The kinetic energy of the car is 112,500 Joules.
Potential Energy
Potential energy is the energy stored in an object due to its position or configuration. For an object at height h, the potential energy is given by:
Potential Energy (PE) = mgh
Where:
- m = Mass (kg)
- g = Acceleration due to gravity (9.8 m/s²)
- h = Height above ground (m)
Example: Potential Energy of a Book
A book of mass 2 kg is placed on a shelf 3 m high. Calculate its potential energy.
PE = 2 kg × 9.8 m/s² × 3 m = 58.8 J
The potential energy of the book is 58.8 Joules.
3. Law of Conservation of Energy
The Law of Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another. The total energy in an isolated system remains constant.
For example, when an object falls, its potential energy converts into kinetic energy, but the total energy remains the same.
4. Power
Power is the rate of doing work. It is calculated as:
Power (P) = Work Done (W) / Time Taken (t)
Where:
- P = Power (Watts, W)
- W = Work (Joules, J)
- t = Time (seconds)
Example: Power of a Machine
A machine does 5000 Joules of work in 10 seconds. Calculate its power.
P = 5000 J / 10 s = 500 W
The power of the machine is 500 Watts.
Rate of Doing Work
The rate of doing work determines the power output of a system. A higher rate of work done corresponds to higher power.
5. Commercial Unit of Energy
The commercial unit of energy is the kilowatt-hour (kWh). It is used to measure the energy consumption in homes and industries.
1 kWh is the energy consumed by a 1000 W appliance running for 1 hour.
1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
Numerical: Energy Consumption
An electrical appliance of 500 W is used for 3 hours. Calculate the energy consumed in kWh.
Energy = 500 W × 3 hours = 1.5 kWh
The energy consumed is 1.5 kWh.
Physics Questions and Answers
1. A force of 7 N acts on an object. The displacement is 8 m in the direction of the force. What is the work done in this case?
Answer: The work done is calculated using the formula:
W = F × d
Given, Force (F) = 7 N and Displacement (d) = 8 m,
W = 7 N × 8 m = 56 J
Therefore, the work done is 56 Joules.
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.
Answer: The work done is:
W = m × g × h
Given, Mass (m) = 15 kg, g = 9.8 m/s², and Height (h) = 1.5 m,
W = 15 kg × 9.8 m/s² × 1.5 m = 220.5 J
Therefore, the work done is 220.5 Joules.
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?
Answer: Kinetic energy is given by:
KE = ½ mv²
Given, m = 15 kg and v = 4 m/s,
KE = ½ × 15 kg × (4 m/s)² = 120 J
Therefore, the kinetic energy is 120 Joules.
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?
Answer: The work done is the change in kinetic energy:
ΔKE = ½ m(v² – u²)
Convert velocities to m/s: 30 km/h = 8.33 m/s, 60 km/h = 16.67 m/s,
ΔKE = ½ × 1500 kg × (16.67² – 8.33²)
ΔKE = ½ × 1500 × (278.89 – 69.39) = 157125 J
Therefore, the work done is 157,125 Joules.
5. What is the kinetic energy of an object? Write an expression for the kinetic energy of an object. The kinetic energy of an object of mass, m moving with a velocity of 5 m/s 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: Kinetic energy (KE) is the energy an object possesses due to its motion, expressed as:
KE = ½ mv²
For velocity doubled (10 m/s):
KE = ½ m × (10 m/s)² = 100 J
For velocity tripled (15 m/s):
KE = ½ m × (15 m/s)² = 225 J
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 m/s².
Answer: The potential energy is given by:
PE = mgh
Solving for height (h):
h = PE / (m × g) = 480 J / (12 kg × 10 m/s²) = 4 m
Therefore, the height is 4 meters.
7. 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 m/s².
Answer: The potential energy is given by:
PE = mgh
Given, m = 10 kg, g = 9.8 m/s², and h = 6 m,
PE = 10 kg × 9.8 m/s² × 6 m = 588 J
Therefore, the energy possessed is 588 Joules.
8. Two girls, each of weight 400 N, climb up a rope through a height of 8 m. Girl A takes 20 s while B takes 50 s. What is the power expended by each girl?
Answer: The power is given by:
Power = Work Done / Time
For both girls, Work Done (W) = 400 N × 8 m = 3200 J.
- Girl A: P = 3200 J / 20 s = 160 W
- Girl B: P = 3200 J / 50 s = 64 W
Therefore, A expends 160 W and B expends 64 W.
9. 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 m/s².
Answer: The total height (h) climbed is:
h = 45 steps × 0.15 m/step = 6.75 m
Work Done (W) = mgh = 50 kg × 10 m/s² × 6.75 m = 3375 J
Power (P) = Work Done / Time = 3375 J / 9 s = 375 W
Therefore, his power is 375 W.
10. What is power? Define 1 watt of power. A lamp consumes 1000 J of electrical energy in 10 s. What is its power? Define average power.
Answer: Power is the rate at which work is done or energy is transferred. One watt is the power when 1 joule of work is done in 1 second.
For the lamp:
P = Energy / Time = 1000 J / 10 s = 100 W
Average power is the total work done divided by the total time taken.
Frequently Asked Questions (FAQs)
A: The formula for work done is W = F × d × cosθ, where F is the force, d is the displacement, and θ is the angle between the force and displacement.
A: Kinetic energy is the energy possessed by an object due to its motion. It is given by the formula KE = ½ mv².
A: Potential energy is the energy possessed by an object due to its position or height above the ground. It is given by the formula PE = mgh.
A: Power is the rate of doing work. It is calculated as Power = Work Done / Time.
A: The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.
A: Work is the transfer of energy. When work is done on an object, its energy changes.
A: One kilowatt-hour (kWh) is the energy consumed by a 1000 W appliance running for 1 hour. 1 kWh = 3.6 × 10⁶ J.
A: Gravitational potential energy increases as height increases, and is directly proportional to the height above the ground.
A: In an elastic collision, kinetic energy is conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.
A: Work is done when a force causes an object to move in the direction of the force. The amount of work depends on the force applied and the distance moved.
W = 50 kg × 10 m/s² × 6.75 m = 3375 J
Power = Work Done / Time = 3375 J / 9 s = 375 W
Therefore, the boy’s power is 375 Watts.
10. What is power? Define 1 watt of power. A lamp consumes 1000 J of electrical energy in 10 s. What is its power? Define average power.
Answer: Power is the rate at which work is done or energy is transferred. It is expressed as:
Power = Work Done / Time
1 Watt: The power expended when 1 joule of work is done in 1 second (1 W = 1 J/s).
Given, Energy = 1000 J, Time = 10 s,
Power = 1000 J / 10 s = 100 W
Average Power: The total energy consumed divided by the total time.
11. An electric bulb of 60 W is used for 6 hours per day. Calculate the ‘units’ of energy consumed in one day by the bulb.
Answer: Energy consumed is given by:
Energy = Power × Time
Given, Power = 60 W = 0.06 kW, Time = 6 hours,
Energy = 0.06 kW × 6 hours = 0.36 kWh
Therefore, the energy consumed in one day is 0.36 units.
12. Reason out whether or not work is done in the following activities: (a) Suma is swimming in a pond, (b) A donkey is carrying a load on its back, (c) A windmill is lifting water from a well, (d) A green plant is carrying out photosynthesis, (e) An engine is pulling a train, (f) Food grains are getting dried in the sun, (g) A sailboat is moving due to wind energy.
Answer:
- (a) Work is done as there is displacement in the direction of the applied force.
- (b) No work is done as there is no displacement in the vertical direction of the force applied by the donkey.
- (c) Work is done as the windmill lifts water, and displacement occurs in the direction of the force.
- (d) No work is done since there is no displacement of an object by a force.
- (e) Work is done as the engine pulls the train, causing displacement.
- (f) No work is done as there is no displacement in the direction of any force.
- (g) Work is done as the sailboat moves, and there is displacement in the direction of the wind force.
13. 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 gravity depends on the vertical displacement of the object. Since the object returns to the same height, the vertical displacement is zero. Therefore, the work done by gravity is zero.
14. A battery lights a bulb. Describe the energy changes involved in the process.
Answer: In this process, the chemical energy in the battery is first converted into electrical energy. The electrical energy is then converted into light and heat energy when it reaches the bulb.
15. 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.
Answer: The work done is the change in kinetic energy:
W = ΔKE = ½ m(v² – u²)
Given, m = 20 kg, u = 5 m/s, v = 2 m/s,
W = ½ × 20 kg × (2² – 5²)
W = 10 × (4 – 25) = -210 J
Therefore, the work done by the force is -210 Joules (negative because the velocity decreases).
16. 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: Since the object is moved horizontally, there is no vertical displacement. Gravitational force acts vertically, so no work is done in the horizontal direction.
Therefore, the work done by gravity is zero.
17. 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. As the object falls, its potential energy is converted into kinetic energy. The total mechanical energy (potential + kinetic) remains constant throughout the fall.
18. What are the various energy transformations that occur when you are riding a bicycle?
Answer: While riding a bicycle, the muscular energy of the rider is transformed into mechanical energy, which moves the bicycle. Some of this mechanical energy is converted into heat due to friction between the tires and the road, as well as between the moving parts of the bicycle.
19. 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, energy is expended, but since there is no displacement, no work is done on the rock. The energy spent by your muscles is converted into heat and dissipated in your body, causing fatigue.
20. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
Answer: 1 unit of energy = 1 kWh = 3.6 × 10⁶ J. Therefore,
Energy = 250 units × 3.6 × 10⁶ J = 9 × 10⁸ J
Therefore, the household has consumed 9 × 10⁸ Joules of energy.
21. 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 halfway down.
Answer: The potential energy at a height of 5 m is:
PE = mgh = 40 kg × 9.8 m/s² × 5 m = 1960 J
At halfway down (2.5 m), the potential energy will be:
PE_half = mgh = 40 kg × 9.8 m/s² × 2.5 m = 980 J
The kinetic energy halfway down will be the difference between the total potential energy and the remaining potential energy:
KE_half = PE – PE_half = 1960 J – 980 J = 980 J
Therefore, the kinetic energy when the object is halfway down is 980 Joules.
