Exercises on Chapter 11 of Science Class 9

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’.

(a) Suma is swimming in a pond.

(b) A donkey is carrying a load on its back.

(c) A wind-mill 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.

Solution:

Work is finished whenever the given 2 conditions are satisfied:

(i) A force acts on the body.

(ii) There’s a displacement of the body [not by itself but] by virtue of the application of force in the direction of force or in the opposite direction of the force applied.

(a) While swimming, Suma applies a force to push the water backwards.  This creates a forward reaction, by water pushing her forwards. Here application of force results in displacement hence work is done.

(b) [Although donkey is doing work in when it is moving but here the carrying of load is asked]  While carrying the load, the donkey should applies a force in upward direction to balance the force of gravity. But, displacement of the load is within the forward direction – Not in the direction of force.  So, the work done is zero.

(c) A wind mill works against the gravity to elevate water. Hence, work is done by the wind mill in lifting water from the well.

(d) During this case, there’s no displacement of the leaves of the plant. Therefore, the work done is zero.

(e) An engine is to tugged to the train. This permits the train to maneuver within the direction of force. Therefore, there’s a displacement within the train in the same direction in which the engine applies force. Hence, work is done.

(f) Although Sun applies energy on the grains but the food grains don’t move. Hence, the work done is zero.

(g) A sailing ship is displaced and the displacement is due to adjustment of the sails which collect the force of Wind energy. Hence, work is done by wind on the boat.

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?

Solution:

Work done on an object depends solely on vertical displacement. Vertical displacement in this  case is zero.

So, work done,  W= m g h  = 0 since h is zero.

Consequently, the work done on the given object by gravity is zero joule.

3. A battery lights a bulb. Describe the energy changes involved in the process.

Solution:

When a bulb is connected to a battery, the chemical energy of the battery is transferred into electrical energy. Once the bulb receives it, it converts it into light and warmth. Hence, the transformation of energy within the given situation may be shown as:

Chemical Energy → Electrical Energy → Light Energy + Heat Energy.

4. Certain force acting on a 20 kg mass changes its velocity from 5 ms^-1 to 2 ms^-1. Calculate the work done by the force.

Solution:

Given:

Initial velocity u = 5 ms^-1

Final velocity v = 2 ms^-1

Mass of the body = 20kg

The initial kinetic energy, E_ki = (1/2) mu² = (1/2) x 20 x (5)² = 250kgms^-2 = 250Nm = 250J

Final kinetic energy E_kf = (1/2) mv² = (1/2) x 20 x (2)² =40 kgms^-2  = 40 Nm = 40J

Therefore,

Work done = Change in kinetic energy

Work done = E_kf – E_ki

Work done =40J – 250J

Work done = -210J

Where negative sign indicates that force acts contrary to motion direction.

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 why.

Solution:

Work done by gravity depends solely on the vertical displacement of the body. It doesn’t rely on the trail of the body. Displacement here is zero.  Therefore, work done, W = mgh, is also zero.

6. The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?

Solution:

No.  It doesn’t violate the law of conservation of energy. This is because once the body falls from a height, its potential energy keeps on changing into kinetic energy increasingly.  So the decreasing potential energy is compensated by rising kinetic energy. Throughout, the total energy of the body remains conserved. Therefore, the law of conservation of energy isn’t violate.

7. What are the various energy transformations that occur when you are riding a bicycle?

Solution:

During riding a bicycle, the chemical energy stored in the muscles also known as the muscular energy of the rider is converted into heat and mechanical energy.  The potential energy gets converted into the Kinetic energy as the bicycle speeds up; and the heat energy provides warmth to the body.

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?

Solution:

When we push a large rock which does not get displaced, work is not done & there’s no transfer of muscular energy to the stationary rock.  The loss of energy occurs as the muscle fibers keep on working which in turn heats up our body.

[If the rock had shifted a bit but not moved owing to the resistance of the surface then there also some energy had got transferred. Also when 2 surfaces rub against each other some compression occurs, so does on the rock surface also but that is so negligible that the energy transferred there is not accounted for.]

9. A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Solution:

1 unit = one kWh

1 kWh = 3.6 x 10⁶ J

Therefore, 250 units of energy = 250 × 3.6 × 10⁶

= 9 × 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.

Solution:

Gravitational mechanical energy is given by the expression,

E_p = mgh

Where,

h = Vertical displacement = 5 m, m = Mass of the item = 40 kg

g = Acceleration because of gravity = 9.8 m s−2

∴ E_p = 40 × 5 × 9.8 = 1960 J.

At half-way down, the mechanical energy of the item is going to be 1960/2 [Since height is divided by 2]

Applying the law of conservation of energy, hence, the K.E. half-way down, shall be the difference of the two i.e. 1960 – 980  =   980 J.

Ans.  The initial Potential Energy is 1960 J & The K.E. half-way down is 980 J

11. What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Solution:

Work is completed whenever the given 2 conditions are satisfied:

→ a force acts on the body.

→ there’s a displacement of the body by the appliance of force in or opposite to the direction of force.

If the direction of Force is perpendicular to the displacement, the work performed is zero. When a satellite moves round the Earth, then the direction of force of gravity on the satellite is perpendicular to its displacement. Hence, the work done on the satellite by the planet 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

Solution:

Yes, consider a uniformly moving object,

Suppose an object is moving with constant rate. The net force acting on it zero. But, there is a displacement or the motion of the article. Hence, there will be a displacement even without application of a 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.

Solution:

Work is completed whenever the given 2 conditions are satisfied.

(i) A force acts on the body.

(ii) There’s a displacement of the body by the applying of force in or opposite to the direction of force.

When an individual holds a bundle of hay over his head, then there’s no displacement.  So no work is done.

14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Solution:

Power rating of the heater, P = 1500 Watts = 1.5 kilo Watt

Time, T = ten hours of Work done

Therefore, Energy consumed by the heater = Power × Time

= 1.5 × 10 = 15 kWh

Hence, the energy consumed by the heater in 10h is 15 kWh.

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?

Solution:

Consider the case of oscillating pendulum.

When the bob moves from its mean position to either of its extreme positions, it rises through a height h. At this time, the K.E. of the bob changes fully into P.E. The K.E. becomes zero, and also the bob possesses solely P.E. When the bob moves towards the mean position  – bottom, its P.E. decreases increasingly and the Kinetic energy increases constantly. As the bob reaches its mean position, its P.E. becomes zero and also the bob possesses solely K.E. This change of energy keeps on going as long as the bob oscillates.

The bob doesn’t oscillate forever. It comes to rest as a result of air resistance which resists its motion.

The bob loses its K.E. to beat this friction and stops once a while. The law of conservation of energy isn’t violated because the energy lost by the apparatus as friction is gained by its surroundings. Hence, the overall energy of the apparatus and also the encompassing system stay preserved.

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?

Solution:

The force required to stop it should be equal to the kinetic energy of the object.  It is ½mv²

17. Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?

Solution:

The mass of the body = 1500kg

Velocity v = 60km/hr = 60,000 / 3600 m/s  =  16.67 m/s

The work required to stop the car = kinetic energy change of the car  = ½ x 1500 x (16.67)²

= 208,375 J  (app)

18. In each of the following a force, F is acting on an object with mass m, tell whether the work done by the force is negative, positive or zero.

Solution:

Case I

In this case, the direction of force functioning on the block is perpendicular to the displacement. Therefore, work done by force on the block are going to be zero.

Case II

In this case, the direction of force functioning on the block is within the direction of displacement. Therefore, work done by force on the block are going to be positive.

Case III

In this case, the direction of force on the block is contrary to the direction of displacement. Therefore, work done by force on the block are going to be negative.

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?

Solution:

Acceleration in an object might be zero even if many forces are working on it. This happens once all the forces nullify each other.  Hence, Soni is correct.

20. Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.

Solution:

Energy consumed by an electrical device, E = P x T

4 devices each of 500 W makes the total Power = 4 x 500 watts = 2 kW

Hence, the energy consumed by four equal rating devices in 10 hours is

= 2 x 10 = 20 kWh = 20 Units.

21. A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?

Solution:

When the object falls freely towards the bottom, its  kinetic energy keeps on increasing.  As the object hits the ground, all its kinetic energy gets converted into heat energy and sound energy. If the surface is soft like sand, some energy shall be used to make its way inside.