## ICSE Living Science Physics for Class 8 Solutions Chapter 4 Energy

Check Your Progress

Answer the following :

Question 1.

What is the amount of work done in pushing a wall?

Answer:

The amount of work done in pushing a wall is zero as there is no displacement of the wall in pushing it.

Question 2.

State the formula used to calculate the work done.

Answer:

The formula used to calculate the work done is

Work = Force x displacement W = F x s

Question 3.

What is the SI unit of work ?

Answer:

The SI unit of work is joule (J).

Question 4.

If either of the displacement or the force applied changes, how does the amount of work done get affected ?

Answer:

Amount of work done is directly proportional to both the displacement as well as the force applied. So, work done increases if either of the displacement or the force applied increases and decreases if either of the displacement or the force applied decreases.

Question 5.

A force of 45 N displace a chair by 0.5 m. What is the amount of work done ?

Answer:

Force applied on the chair, F = 45 N

Displacement of the chair, 5 = 0.5 m

Amount of work done, W = F x s

= (45 N) x (0.5 m) = 22.5 J

Check Your Progress

A. Write true or false. Correct the false statement.

Question 1.

Mechanical energy is of two types – potential energy and kinetic energy.

Answer:

True

Question 2.

Kinetic energy of an object is the energy stored in it.

Answer:

False.

Correct : Potential energy of an object is the energy stored in it.

Question 3.

Kinetic energy of an object depends on its mass and velocity.

Answer:

True

Question 4.

The energy stored in an object due to its raised position is known as elastic potential energy.

Answer:

False.

Correct : The energy stored in an object due to its raised position is known as gravitational potential energy.

Question 5.

A ball thrown from a balcony possesses kinetic energy.

Answer:

True

B. Solve the following numericals.

Question 1.

A ball of mass 400 g is thrown at a speed of 2 m/s. Determine its kinetic energy.

Answer:

Mass of the ball, m = 4000 g

Speed of the ball, v = 2 m/s

Kinetic energy of the ball, K.E. = \(\frac {1}{2}\) mv^{2}

= \(\frac {1}{2}\) (400 g) x (2 m/s)^{2} = (200 g) x (4 m^{2}/s^{2})

= 800 J

Question 2.

A motorbike moving at a speed of 12 m/s has a kinetic energy of 3600 J. Determine its mass.

Answer:

Mass of the motorbike, m = ?

Speed of the motorbike, v = 12 m/s

Kinetic energy of the motorbike, K.E. = 3600 J

From the formula,

K.E = \(\frac {1}{2}\) mv^{2}

3600 J = \(\frac {1}{2}\) m x (12 m/s)^{2} = \(\frac {1}{2}\)m x 144 m^{2}/s^{2}

= 72 m^{2}/s^{2}

m = 50 kg

Question 3.

A child lifts a book of mass 1 kg from the table to a cupboard at a height of 2 m from the floor. What is the potential energy of the book with respect to the floor?

Answer:

Mass of the book, m = 1 kg

Height of the book with respect to the floor, h = 2m g = 10 m/s^{2}

Potential energy of the book with respect to the floor, P.E. = mgh

= (1 kg) x (10 m/s^{2}) x (2 m)

= 20 J

Question 4.

What is the speed of a runner of mass 50 kg whose kinetic energy while running is 2500 J?

Answer:

Mass of a runner, m = 50 kg

Speed of the runner, v = ?

Kinetic energy of the runner, K.E. = 2500 J

From the formula,

K.E. = \(\frac {1}{2}\) mv2

We get,

2500 J = \(\frac {1}{2}\) x (50 kg) x v^{2}

2500 J = 25 kg x v^{2}

or v^{2} = 100 m^{2}/s^{2}

or v^{2} = 100 m/s

Question 5.

A child climbs a wall of height 4 m. He now possesses a potential energy of 1600 J. What is the mass of the child?

Answer:

Mass of the child, m = ?

Height of the child, h = 4 m

g = 10 m/s^{2}

Potential energy of the book with respect to the floor, P.E. = 1600 J

From the formula,

P.E. = mgh or 1600

J = m x (10 m/s^{2}) x (4 m)

or m = 40 kg

A. Tick the most appropriate answer.

Question 1.

In which of the following situations, no work is said to be done?

a. drawing water from a well

b. kicking a ball

c. climbing up a hill

d. pushing a wall

Answer:

d. pushing a wall

Question 2.

No work is said to be done if the angle between the directions of force and displacement is

a. 0°.

b. 90°.

c. between 0° and 90°.

d. 180°.

Answer:

b. 90°.

Question 3.

If the force applied on a body decreases, then the work done on it will

a. decrease.

b. increase,

c. remain the same.

d. be zero.

Answer:

a. decrease.

Question 4.

When a ball is thrown vertically upwards, the gravitational potential energy of the ball

a. increases.

b. decreases.

c. remains the same.

d. becomes zero.

Answer:

a. increases.

Question 5.

Which form of energy is possessed by a stretched spring?

a. chemical

b. elastic potential

c. kinetic

d. heat

Answer:

b. elastic potential

Question 6.

Which of the following is an example of stored energy?

a. light energy

b. sound energy

c. electrical energy

d. chemical energy

Answer:

d. chemical energy

Question 7.

If the velocity of an object increases, then its kinetic energy

a. increases.

b. decreases,

c. remains the same.

d. becomes zero.

Answer:

a. increases.

Question 8.

What is the SI unit of power?

a. J

b. J/s

c. J.s

d. s

Answer:

b. J/s

B. Fill in the blanks.

- The energy possessed by a moving train is in the form of …………..
- The work done by the force of gravity on a child walking horizontally with a bag in his hand is …………..
- The kinetic energy of an object of mass 10 kg is ………….. than that of an object of mass 2 kg, if both are moving with the same velocity.
- The potential energy of raindrops …………… when they fall down.
- A hydroelectric power plant uses the transformation of ………….. energy to ………… energy to generate electricity.
- Power is ………….. if more work is done in less interval of time.

Answer:

- The energy possessed by a moving train is in the form of kinetic energy.
- The work done by the force of gravity on a child walking horizontally with a bag in his hand is zero.
- The kinetic energy of an object of mass 10 kg is more than that of an object of mass 2 kg, if both are moving with the same velocity.
- The potential energy of raindrops decreases when they fall down.
- A hydroelectric power plant uses the transformation of potential energy to kinetic energy to generate electricity.
- Power is greater if more work is done in less interval of time.

C. Match the columns.

1. Work done | a. sound energy |

2. Simple pendulum | b. capacity to do work |

3. Coiled spring in a watch | c. transformation of energy |

4. Vibrating bodies | d. force x displacement |

5. Energy | e. elastic potential energy |

Answer:

1. Work done | d. force x displacement |

2. Simple pendulum | c. transformation of energy |

3. Coiled spring in a watch | e. elastic potential energy |

4. Vibrating bodies | a. sound energy |

5. Energy | b. capacity to do work |

D. Write true or false. Correct the false statements.

Question 1.

Work is said to be done only if a force is applied on a body.

Answer:

False.

Correct : Work is said to be done only if a force is applied on a body displaces it.

Question 2.

If a car and a motorcycle are running at the same speed, then both will have the same kinetic energy.

Answer:

False.

Correct : If a car and a motorcycle are running at the same speed, then both will have different energy because they have different mass.

Question 3.

When you climb up the stairs, your potential energy increases.

Answer:

True

Question 4.

Energy can easily be created.

Answer:

False.

Correct : Energy can neither be created nor be destroyed.

Question 5.

The sum of potential and kinetic energy keeps changing for any system.

Answer:

False.

Correct : The sum of potential and kinetic energy remains the same for any system.

Question 6.

Roller coaster ride is an example of transformation of energy between potential and kinetic energy.

Answer:

True

Question 7.

Electrical energy can be considered as a type of kinetic energy.

Answer:

True

Question 8.

Power and energy means the same.

Answer:

False.

Correct : Energy is the capacity to do work whereas power is the rate of doing work.

E. Answer the following in a word or two or in a sentence.

Question 1.

What will be the work done by a force acting on a body if the displacement of the body is zero?

Answer:

The work done by a force acting on a body is zero is the rate of doing work.

Question 2.

Give an example in which potential energy gets converted into kinetic energy.

Answer:

A stone dropped from a building is an example in which potential energy gets converted to kinetic energy.

Question 3.

Name the energy possessed by a flowerpot placed at the rooftop of a building.

Answer:

A flowerpot placed at the rooftop of a building possesses gravitational potential energy.

Question 4.

What are the two factors on which kinetic energy of an object depends?

Answer:

Kinetic energy of an object depends on its mass and velocity.

Question 5.

Name the energy stored in a compressed spring.

Answer:

Elastic potential energy is stored in a compressed spring.

F. Answer the following in short.

Question 1.

State the factors responsible for the work done by a body.

Answer:

The factors responsible for work done by a body are force and displacement.

Question 2.

Define kinetic energy and give an example of a body possessing kinetic energy.

Answer:

Kinetic energy of a body is the energy possessed by it due to its motion. A moving car is an example of a body possessing kinetic energy.

Question 3.

State two differences between power and energy.

Answer:

Energy

- It is the capacity to do work.
- It doesn’t depend on time.

Power:

- It is the amount of energy transferred in unit time.
- It depends on time.

Question 4.

List two situations where no work is done.

Answer:

No work is done in reading a book and pushing a wall.

Question 5.

How can you measure the gravitational potential energy of an object?

Answer:

The gravitational potential energy of an object can be measured by the expression P.E. = mgh

where, m = the mass of the object

g = acceleration due to gravity

h = height at which the object is placed above the reference level.

Question 6.

State the law of conservation of energy.

Answer:

The law of conservation of energy states that energy can neither be created nor be destroyed but it can be converted from one form to another.

G Answer the following in detail.

Question 1.

Explain why water stored in a dam has potential energy.

Answer:

The water is stored in a reservoir at a certain height above a dam. As gravitational potential energy is the possessed by an object due to its raised position, therefore, water in a dam possesses gravitational potential energy.

Question 2.

What is meant by mechanical energy? Explain in detail.

Answer:

The energy possessed by a body due to the work done on it is known as mechanical energy. When work is done on a body, another body supplies the force to do the work. For example, when you lift a stone from the ground, your body supplies the force which raises the height of the stone from the ground (work done). In doing the work, your body spends some energy. As energy is neither created nor destroyed, some of the energy spent by your body is gained by the stone. This energy is the mechanical energy.

Work is done on a body when the body is displaced. So, the energy gained by a body due to its state of motion or due to its position is known as mechanical energy. Mechanical energy is of two types — kinetic energy or energy in action and potential energy or stored energy. These two forms of energy are readily changeable from one form to the other.

Question 3.

Describe the work-energy relationship by giving a suitable example.

Answer:

Energy is the ability of a body to do work. So, there is a direct relationship between energy and work. For example, when an object is at a height from the ground, it has a certain amount of potential energy. When you drop the object, it falls down because of the force of gravity. So, work is being done on the body.

While falling down, its potential energy is gradually used up until it becomes zero (just when the object touches the ground). At any point during its fall, the amount of potential energy which is used up by the body is equal to the distance, the body has travelled (work done). So, work done by a body = energy change in the body.

Question 4.

Describe the energy transformation taking place in an oscillating pendulum.

Answer:

When a pendulum swings to-and-fro, its energy is constantly from potential to kinetic and vice-versa. Let us consider the energy transformation in the pendulum at its different positions. At position B, when the bob is raised from position A to position B, the work is done on it against the force of gravity. This work done gets stored in it in the form of gravitational potential energy. At this position, the pendulum has only potential energy but no kinetic energy.

At position A, when the bob starts moving down from position B to position A, its potential energy goes on decreasing but its kinetic energy goes on increasing. When the bob reaches the mean position A, it has only kinetic energy but no potential energy.

At position C, as the bob goes from position A towards C, its kinetic energy goes on decreasing but its potential energy goes on increasing. On reaching the extreme position C, the bob has only potential energy but no kinetic energy.

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H. Solve the following numerical problems.

Question 1.

Calculate the work done in pushing a cart through a distance of 10 m when the force applied on it is equal to 120 N.

Answer:

Force applied on the cart,F = 1230 N

Displacement of the car, s = 10 m

Amount of work done, W = F x s

= (120 N) x (10 m)

= 1200 J

Question 2.

If 1000 J of work is done by a machine to move a body through a distance of 20 m, then find the force applied on the body.

Answer:

Work done by a machine on a body, W = 1000 J

Displacement of the body, s = 20 m

Force applied on the body, F = ?

Using the formula,

W = F x s

1000 J = F x 20 m

F = \(\frac {1000J}{20m}\) = 50 N

Question 3.

Calculate the kinetic energy of an object weighing 600 kg moving at a velocity of 30 m/s.

Answer:

Mass of the object, m = 600 kg

Velocity of the object, v = 30 m/s

Kinetic energy of the object, K.E. = \(\frac {1}{2}\) mv^{2}

= \(\frac {1}{2}\) x (600 kg) x (30 m/s)^{2}

= 270000 J

Question 4.

Calculate the potential energy of a stone weighing 2.5 kg placed at a height of 6 m.

Answer:

Mass of the stone, m = 2.5 kg

Height of the stone, h = 6 m

g = 10 m/s^{2}

Potential energy of the stone, P.E. = mgh

= (2.5 kg) x (10 m/s^{2}) x (6 m)

= 150 J

Question 5.

Calculate the work done by a boy in lifting a to kg laptop from the ground and keeping it on a shelf 1.5 m high.

Answer:

Mass of the laptop, m – 10 kg

Height of the shelf where laptop is placed, h – 1.5 m

g = 10 m/s^{2}

Potential energy of the laptop, P.E. = mgh

= (10 kg) x (10 m/s^{2}) x (1.5 m)

= 150 J

From work-energy relationship, we can deduce that the work done by the boy in lifting the laptop gets stored in it as gravitational potential energy. Hence, Work done in lifting the laptop = Energy change in the laptop = 150 J

Question 6.

A person does 5000 J of work in climbing a tree of height 5 m. Calculate the mass of the person.

Answer:

Mass of the person, m = ?

Height of the tree, h = 5 m

Work done by the person, W = 5000 J

From work-energy relationship, we can say that the work done by the person in climbing the tree against gravity gets stored in him as gravitational potential energy.

Potential energy of the person, P.E. = W = 5000 J

From the formula, P.E. = mgh

we get, 5000 J = m x (10 m/s^{2}) x (5 m)

or m = 100 kg

Question 7.

A 900 kg compact car is moving at a certain speed. If its kinetic energy is 3,20,000 J, find the velocity at which the car is travelling.

Answer:

Mass of the car, m = 900 kg

Velocity of the car, v = ?

Kinetic energy of the car, K.E. = 3,20,000 J

From the formula, K.E. = \(\frac {1}{2}\) mv^{2}

We get, 3,20,000 J = \(\frac {1}{2}\) x (900 kg) v^{2}

v^{2} = 711.11 m^{2}/s^{2}

or v = 26.67 m/s

Question 8.

Two bodies of equal masses move with uniform velocities v and 3 v, respectively. Find the ratio of their kinetic energies.

Answer:

For body 1,

Mass = m

Velocity = v

Kinetic energy, (K.E.)_{1} = \(\frac {1}{2}\) mv^{2}

For body 2, Mass = m

Velocity = 3v

Kinetic energy, (K.E.)_{2} = \(\frac {1}{2}\) m x (3v)^{2} = \(\frac {9}{2}\) mv^{2}

Ratio of their kinetic energies = \(\frac{(\mathrm{K} . \mathrm{E})_{1}}{(\mathrm{~K} . \mathrm{E})_{2}}\) = \(\frac{1 / 2 m v^{2}}{1 / 9 m v^{2}}\) = \(\frac {1}{9}\)

Think and answer:

Question 1.

A man is walking with a suitcase held in his hand.

a. Why is no work done on the suitcase if the man is walking on a horizontal platform?

Answer:

If a man carrying a suitcase is walking on a horizontal platform, the suitcase moves. But the force applied (force of gravity) on the suitcase is in the vertically downwards direction, whereas, its displacement is in the horizontal direction. A vertical force can never cause a horizontal displacement. So the displacement of the suitcase is not due to the force of gravity acting on it. Therefore, no work is done by the force of gravity in this case.

b. Why is work said to be done if the man is climbing a staircase?

Answer:

if a man carrying a suitcase climbs up a staircase, then work is done to carry the suitcase against the force of gravity.

Question 2.

How does an archer use the law of conservation of energy to hit his target?

Answer:

An archer draws back the arrow against the bowstring, the work done in stretching the string gets stored in it as elastic potential energy. When the bowstring is released, the stored potential energy is transformed into the kinetic energy of the string. The motion of the string launches the arrow on to the target.

Question 3.

Which factor will have a greater effect on the kinetic energy of an object, doubling its mass or doubling its velocity?

Answer:

Let mass of an object be m and its velocity be v.

Kinetic energy of the object, K.E. = \(\frac {1}{2}\)mv^{2}

When the mass is doubled, kinetic energy = \(\frac {1}{2}\) (2m) v^{2} = mv^{2}

When the velocity is doubled, kinetic energy = \(\frac {1}{2}\) m (2v)^{2} = 2mv^{2}

Doubling the velocity of an object will have greater effect on its kinetic energy than doubling its mass.