In-Text Questions and Answers
Question 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:
Work done is calculated by multiplying the force by the displacement in the direction of the force. So,
Work done = Force × Displacement
Work done = 7 N × 8 m = 56 Joules
Therefore, the work done is 56 Joules.
Question 2:
- When do we say that work is done?
Answer:
We say that work is done when a force causes an object to move in the direction of the force. Both force and displacement must be present.
Question 3:
- 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:
Work done (W) = Force (F) × Displacement (s)
Question 4:
- Define 1 J of work.
Answer:
1 Joule (1 J) of work is done when a force of 1 Newton moves an object through a distance of 1 meter in the direction of the force.
Question 5:
- 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:
Work done = Force × Displacement
Work done = 140 N × 15 m = 2100 Joules
So, 2100 Joules of work is done in ploughing the field.
Question 6:
- What is the kinetic energy of an object?
Answer:
Kinetic energy is the energy that an object possesses due to its motion.
Question 7:
- Write an expression for the kinetic energy of an object.
Answer:
The expression for kinetic energy (KE) is:
Kinetic Energy (KE) = (1/2) × Mass (m) × Velocity (v)²
KE = (1/2) mv²
Question 8:
- 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:
First, find the mass:
Given KE = 25 J, v = 5 m/s
KE = (1/2) m v²
25 J = (1/2) m × (5 m/s)²
25 J = (1/2) m × 25
25 J = 12.5 m
So, m = 2 kg
When velocity is doubled (v = 10 m/s):
KE = (1/2) × 2 kg × (10 m/s)²
KE = 1 kg × 100 m²/s²
KE = 100 J
When velocity is tripled (v = 15 m/s):
KE = (1/2) × 2 kg × (15 m/s)²
KE = 1 kg × 225 m²/s²
KE = 225 J
So, when the velocity is doubled, the kinetic energy is 100 Joules, and when the velocity is tripled, it is 225 Joules.
Question 9:
- What is power?
Answer:
Power is the rate at which work is done or energy is transferred over time.
Question 10:
- Define 1 watt of power.
Answer:
1 watt (1 W) of power is defined as 1 Joule of work done or energy transferred in 1 second.
Question 11:
- A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Answer:
Power = Energy consumed / Time
Power = 1000 J / 10 s = 100 W
So, the power of the lamp is 100 Watts.
Question 12:
- Define average power.
Answer:
Average power is the total work done or energy transferred divided by the total time taken.
Exercise Questions and Answers
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 windmill 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:
- Suma is swimming in a pond.
Work is done because Suma applies force to move forward, and there is displacement in the direction of the force. - A donkey is carrying a load on its back.
No work is done on the load if the donkey moves horizontally because the force (upward) is perpendicular to the displacement (forward), so work done is zero. - A windmill is lifting water from a well.
Work is done because the windmill applies an upward force to lift water against gravity, causing displacement. - A green plant is carrying out photosynthesis.
No mechanical work is done in the scientific sense because there is no displacement caused by a force. - An engine is pulling a train.
Work is done as the engine exerts force to move the train, causing displacement. - Food grains are getting dried in the sun.
No mechanical work is done as there is no displacement due to force. - A sailboat is moving due to wind energy.
Work is done because the wind applies force to the sails, causing the boat to move.
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:
The work done by gravity depends on the vertical displacement. Since the object starts and ends at the same height, the net vertical displacement is zero. Therefore, the total work done by gravity over the entire path is zero.
Question 3:
A battery lights a bulb. Describe the energy changes involved in the process.
Answer:
- Chemical energy in the battery is converted into electrical energy.
- Electrical energy flows through the bulb.
- The bulb converts electrical energy into light energy and heat energy.
Question 4:
A 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:
First, calculate initial and final kinetic energies:
Initial KE = (1/2) × 20 kg × (5 m/s)² = 250 J
Final KE = (1/2) × 20 kg × (2 m/s)² = 40 J
Work done = Final KE – Initial KE
Work done = 40 J – 250 J = -210 J
So, the work done by the force is -210 Joules (negative because the force is reducing the kinetic energy).
Question 5:
A mass of 10 kg is at point A on a table. It is moved to 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 movement is horizontal, and gravity acts vertically, the displacement is perpendicular to the force of gravity. Therefore, the work done by gravity is:
Work done = Force × Displacement × cos(90°)
Since cos(90°) = 0,
Work done = 0
So, the work done by gravity is zero.
Question 6:
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
Answer:
No, it does not violate the law of conservation of energy. As the object falls, its potential energy decreases, but its kinetic energy increases by the same amount. The total mechanical energy remains constant (ignoring air resistance).
Question 7:
What are the various energy transformations that occur when you are riding a bicycle?
Answer:
- Chemical energy in your body (from food) is converted into muscular energy.
- Muscular energy is converted into mechanical (kinetic) energy as the bicycle moves.
- Some energy is also converted into heat due to friction.
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:
Yes, energy transfer takes place. Your muscles expend energy, which is converted into heat within your body. Although no work is done on the rock, energy is used up by your body.
Question 9:
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 kilowatt-hour (kWh)
1 kWh = 3.6 million joules (3.6 × 10⁶ J)
Energy consumed = 250 units × 3.6 × 10⁶ J/unit = 900,000,000 J
So, the household consumed 900 million Joules of energy.
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:
Potential Energy (PE) = m × g × h
PE = 40 kg × 10 m/s² × 5 m = 2000 J
At half-way down (height = 2.5 m),
Potential Energy = 40 kg × 10 m/s² × 2.5 m = 1000 J
Total energy remains 2000 J, so
Kinetic Energy (KE) at half-way = Total energy – Potential Energy
KE = 2000 J – 1000 J = 1000 J
So, the kinetic energy half-way down is 1000 Joules.
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 gravity is zero because gravity acts towards the center of the Earth (centripetal force), and the satellite moves perpendicular to this force in its orbit. Since the force and displacement are perpendicular, no work is done.
Question 12:
Can there be displacement of an object in the absence of any force acting on it?
Answer:
Yes, if an object is already in motion, it will continue to move with constant velocity (Newton’s first law) even if no force acts on it, resulting in displacement.
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.
Answer:
In terms of physics, no work is done on the hay because there is no displacement. The person gets tired due to internal energy expenditure, but mechanically, no work is done on the object.
Question 14:
An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Answer:
Energy used = Power × Time
Energy = 1500 W × 10 h × 3600 s/h
Energy = 1500 W × 36,000 s = 54,000,000 J
So, the heater uses 54 million Joules of energy.
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?
Answer:
- When the pendulum bob is pulled to one side, it gains potential energy.
- As it swings down, potential energy is converted to kinetic energy.
- At the lowest point, kinetic energy is maximum.
- As it swings up on the other side, kinetic energy converts back to potential energy.
- Due to air resistance and friction, some mechanical energy converts to heat.
- The bob eventually stops because all its mechanical energy is converted to heat.
- This is not a violation of the law of conservation of energy because the total energy remains constant; it has just transformed into other forms.
Question 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:
Work done = Change in kinetic energy
Initial KE = (1/2) mv²
Final KE = 0 (since velocity is zero)
Work done = Final KE – Initial KE
Work done = 0 – (1/2) mv² = – (1/2) mv²
So, -(1/2) mv² of work should be done (negative sign indicates work is done against the motion).
Question 17:
Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h.
Answer:
First, convert velocity to m/s:
60 km/h = 16.67 m/s
Initial KE = (1/2) × 1500 kg × (16.67 m/s)²
Initial KE ≈ 0.5 × 1500 kg × 277.8 m²/s²
Initial KE ≈ 208,350 J
Work required = – Initial KE = -208,350 J
So, -208,350 Joules of work is required to stop the car.
Question 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:
- If the force is in the same direction as displacement (east), work is positive.
- If the force is opposite to displacement (west), work is negative.
- If the force is perpendicular to displacement (north or south), work is zero.
Question 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. If the forces acting on an object are balanced (net force is zero), then the acceleration is zero even though multiple forces are acting.
Question 20:
Find the energy in joules consumed in 10 hours by four devices of power 500 W each.
Answer:
Total power = 4 × 500 W = 2000 W
Energy = Power × Time
Time = 10 h × 3600 s/h = 36,000 s
Energy = 2000 W × 36,000 s = 72,000,000 J
So, the devices consume 72 million Joules of energy.
Question 21:
A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?
Answer:
The kinetic energy is transformed into other forms of energy upon impact:
- Sound energy (noise when it hits the ground)
- Heat energy (slight warming at the point of impact)
- Deformation energy (if the object or ground deforms)
Energy is conserved; it is not lost but converted to other forms.