JKBOSE 9th Class Science Solutions Chapter 3 Work, Energy and Power

◆ All living beings need food.

◆ In order to survive all living beings have to do some basic activities for which energy is required. This energy they get from food they eat.

◆ In our daily life we consider any useful physical or mental activity as work. From science point of view for doing work two conditions must be satisfied : (1) some force must act on the object (ii) the object must be displaced in the direction of force.

◆ Work done by the force acting on a body is equal to the product of magnitude of the force the force and the displacement in the direction of force.

◆ When force acts in a direction opposite to the direction of displacement produced, then the work done is negative.

◆ When force acts in the direction of displacement then the work done is positive.

◆ For us the sun is the major natural source of energy. In addition to this, we can also get energy from nuclei of atoms, from interior of earth and tides.

◆ If a body has capacity to do work then it is said to possess energy.

◆ The object which does work loses energy and the object on which work is done gains energy.

◆ Energy is present in different forms as for example kinetic energy, potential energy, heat energy, chemical energy, electric energy and light energy.

◆ The sum total of potential and kinetic energy of the body is called mechanical energy.

◆ The energy present in the body due to its motion is called its kinetic energy.

◆ The kinetic energy of an object increases with the increase of its velocity.

◆ When an object is raised to some height above the ground, the work done against gravitational force is stored in the object as potential energy.

◆ We can transform one form of energy to another form.

◆  According to law of conservation of energy, energy can neither be created nor destroyed but it can only be transformed from one form to another form total energy before and after transformation always remains constant.

◆ The rate of doing work or transformation of energy is called power.

◆ The unit of power is watt

◆ 1 kilowatt = 1000 watt

⇒ Energy. The capacity of doing work is called energy.

⇒ Kinetic Energy. The capacity of the bodies to do work due to motion present in them is called kinetic energy.

⇒ Potential Energy. The capacity of an object to do work due to change in its position or configuration is called its potential energy.

⇒ Law of Conservation of Energy. Energy can neither be created nor destroyed but it can be changed from one form into another form.

⇒ Joule. If one Newton (N) of force acts on a body of 1 kg and displaces it through 1 m than work done on the body is one joule.

⇒ Power. The rate at which energy is supplied or consumed is called power. The unit of power is watt (W).

             Power = Energy supplied / Time

⇒ Watt. If a source supplies or consumes energy at the rate of 1 Joule (J) per second then the power of the source is said to be one watt.

⇒ Work. If force acting on a body displaces the body in the direction of force then work is said to be done by the force.

        Work = Force × Displacement

i.e.         W = F × S

Ans.— Average Power. It is defined as the ratio of total energy consumed to the total time taken.∴

∴ Average Power (P_av) = Total energy consumed / Total time taken

Ans.— (i) Suma while swimming is applying her muscular force in a particular direction and gets displaced. Therefore, work is being done by Suma.

(ii) The load being carried by donkey is acting in the downward direction perpendicular to the horizontal direction of displacement. And when the force acts perpendicular to the direction of displacement then no work is done.

Therefore, donkey is not doing any work.

(iii) Work is being done because in lifting water, the displacement as well as force are in vertically upward direction.

(iv) A green plant carrying photosynthesis does no work since neither there is force applied nor any displacement in direction of force applied.

(v) An engine pulling a train is doing work since displacement is in direction of force applied.

(vi) No work is done on food grain. However part of heat supplied coverts moisture of grains into steam which rises up increasing P.E.

(vii) Work is being done since force and displacement is there in the same direction.

Ans.—The work done by the force of gravity will be zero. This is because the displacement is in a horizontal direction while the force is acting vertically downward perpendicular to this direction of displacement.

In this situation θ = 90°

∴ cos θ = cos 90° = 0

Now work done (W) = F cos θ × S

= F × 0 × S

W = 0

Ans.— Chemical energy of the chemicals in the battery is first being converted to electric energy. Then the electric energy of the battery is converted into heat energy and light energy by the bulb.

Sol.— Here mass (m) = 20 kg

Initial velocity (u) = 5 m s^-1

Final velocity (v) = 2 m s^-1

Initial kinetic energy of the body (E_k1) = 1/2 mu²

= 1/2 × 20 × (5)²

= 1/2 × 20 × 5 × 5

= 250 J

Final kinetic energy of the body (E_k2) = 1/2 mv²

= 1/2 × 20 × (2)²

= 1/2 × 20 × 2 × 2

= 40 J

∴ Work done by the force = Change in kinetic energy

= Final kinetic Energy – Initial kinetic energy

= 40 J – 250 J

Negative sign shows that there is decrease in velocity due to opposing force which is doing work.

Solution.— An object of mass 10 kg is displaced in the horizontal direction from point A to point B but the gravitational force is acting vertically downward which makes an angle of 90° with the direction of displacement.

∴ Work done by the gravitational force (W) = F cos θ × S

= F cos 90° × S

= F × 0 × S

= 0 Ans.

Ans.— It does not violate the law of conservation of energy. When the height of freely falling body decreases, its potential energy decreases but kinetic energy increases. Kinetic energy increases by the same amount as potential energy has decreased. At any time the sum of kinetic energy and potential energy remains conserved.

Ans.— When we are riding a bicycle and pedalling it, the energy of our muscles gets transformed into heat energy and kinetic energy. This kinetic energy is used in doing work against the frictional energy offered by the road.

Ans.— Although you have not been able to move the heavy rock, you are very much tired and this has reduced your energy. Since we have failed to move the heavy rock, work appears to be zero.

While pushing the stone, you had to stretch your muscles, heart had to pump more blood and in making these changes, your energy is definitely lost. The work done by you on your body is not zero. You may have to eat some food to compensate for the work done by your muscles and heart.

Sol.— We know, 1 unit of energy =  1 kilowatt hour (1kWh)

= 1 kW x 1h

= (1 x 1000 watt) × (1 x 60 × 60 s)

= 36 × 10⁵ J

= 3.6 × 10⁶ J

∴ 250 units of energy = 250 × 3.6 x 10⁶ J

= 900 × 10⁶ J

= 9 × 10⁸ J Ans.

Q. 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.

Sol.— Here mass of the object (m) = 40 kg

Height above the ground (h) = 5 m

Acceleration due to gravity (g) = 10 m s^-2

Potential energy of the object at a height of 5 m (E_p) = m × g × h

= 40 × 10 × 5 J

= 2000 J Ans.

Let v be the velocity of the object when it has come halfway down

Distance moved by the object (S) = 5/2 = 2.5 m

Using,   v²– u² = 2gS

v² – (0)² = 2 × 10 × 2.5

v² = 2 × 25

or, v² = 50

Kinetic energy of the object on reaching half way down (E_k) = 1/2 mv²

= 1/2 × 40 × 50

= 1000 J Ans.

Ans.— When a satellite moves around the earth the force of gravity is directed inward along the radius of the circular path while the direction of motion is along the tangent which is perpendicular to the radius. In this way force of gravity and displacement are mutually at right angle en to each other as a result of which the work done on the satellite is zero.

We know,  work done (W) = F cos θ × S

= F cos 90° × S

= F × 0 × S

= 0

Ans.— In the absence of any external force the displacement of the object is possible if the object is moving with a uniform velocity. And if the object is in the state of rest then the displacement is not possible in the absence of external force.

Ans.— A person holds a bundle of hay over his head for 30 minutes and got tired but the force of gravity acting on the bundle did not displace the bundle of hay in the direction of force of gravity. Since there is no displacement in the direction of force, therefore, no work is said to be done by him.

Sol.— Given, Power of the heater (P) = 1500 W

Time for which heater is used (t) = 10 hr

Energy used by the heater in 10 hours (E) = ?

We know, energy used = Power × Time

= 1500 Watt × 10 hrs

= 15000 Wh

= 15000 / 1000 kWh

= 15 kWh Ans.

= 15 units Ans.

Ans.— Energy transformation in oscilated pendulum :

Initially bob is at rest at its mean position, thus in kinetic energy is zero. We can consider its potential energy equal to zero in this position.

When we take the bob of the pendulum to one side its height goes on increasing and we have to do some work against the force of gravity. This work is stored in the bob as its potential energy. Thus, when a bob is released from one of its extreme position, i.e. state of maximum displacement B at this position its kinetic energy is zero and potential energy is maximum. Now, the bob is in motion and is moving towards its mean position A its height goes on decreasing that means its potential energy also goes on decreasing whereas its velocity goes on increasing and hence, its kinetic energy increases. Because bob is moving through the air, thus, some energy is consumed against the force of friction due to air. This causes increase in speed of molecules of air and thus, kinetic energy of the molecules increase. At the mean position, kinetic energy of the bob becomes maximum and potential energy becomes minimum. Due to inertia of motion bob does not stop here but it moves to the other side of its mean position.

Its height again starts increasing so that potential energy also increases, but kinetic energy continues to decrease. When bob reaches at the extreme position ‘O’ its potential energy becomes maximum and kinetic energy becomes zero. Bob does not stop here it tev comes back towards its mean position ‘A’. At every point of its motio point of its motion, sum of kinetic energy and potential energy of the bob along with energy of air molecules remains constant. Thus, during oscillation of the bob of a simple pendulum total energy remains conserved.

Amplitude of the simple pendulum depends on the total energy of the bob. The energy transfered to the molecules of the air by the oscillating bob can never be recovered. Thus total energy of the bob goes on decreasing. When, the bob transfers whole of its energy to the molecules of the air then its total energy becomes zero and it comes to rest at its mean position.

Thus there is no violation of the law of conservation of energy.

Ans.— Potential Energy. It is the energy possessed by an object when it is raised above or below the surface of earth.

Mathematical Expression. Consider a body of mass ‘m’ raised to a height ‘h’ above the surface of earth to a position ‘B’. In order to lift the body to this height we have to apply minimum force equal to mg, the weight of the body in the upward direction from position ‘A’.

∴ Work done on the body against the

force of gravity (W) = Force × Displacement

W = F × S

But mg and S = h

W = mg x h

= mgh

The work done (W = mgh) on the body is

against the force of gravity

∴ E_p = W = mgh

Since this work done is against the force of gravity, so this energy is called gravitational potential energy. This potential energy does not depend on the path along which the body is moved.

Practical Examples. (i) In olden days there were no digital watches and the watches used to be wound up. When its spring is open then the watch does not work. When its spring is wound up then it starts working.

As is shown in Fig. on winding the spring closes and potential energy is stored up. This potential energy due to change in size and shape of the spring helps to move the hands of watch.

(ii) Try to open a spring with your both hands. Work is, therefore, being done by your hands. By doing this the spring extends in its length and as such potential energy is stored in it.

Ans.— Kinetic Energy. It is defined as the energy possessed by a body due to velocity. if body

is not in motion then it does not possess kinetic energy.

Potential Energy. Refer Q. No. 1 under Long Answer Type Quesitons on.

Mathematical Expression. Suppose a football of mass ‘m’ is at rest and force ‘F’ is applied. Due to the force acting on it, the football covers a distance ‘S’ in ‘t’ seconds and attains a velocity v. Thus, acceleration produced in the football is ‘a’

Work done on the football W = F × S

According to Newton’s second law of motion,

F = m × a

Equation (8) proves that the work done on the football is stored in it as kinetic enegry.∴

∴ Work done = kinetic energy stored = 1/2 mv²

Ans.— Law of conservation of energy. According to this law total energy always remain constant or total energy always remains the same. Though one form of energy can be transformed to some other form of energy but total but total energy stil still remains constant.

Explanation with example. Throw a ball vertically upwards from the surface of earth. You do some work on the ball. This work gets stored in the form of potential energy. This is called gravitational potential energy. As the ball moves up and up its velocity continue to decreaes and its kinetic energy continue to decrease and potential energy goes on increasing. When ball reaches the maximum height its kinetic energy becomes minimum i.e. zero but potential energy becomes maximum. We can prove mathematically that at any position in the path of motion of the ball. Sum of potential energy and kinetic energy remains same.

Consider a ball of mass m situated at maximum height above the earth surface. Let this ball be dropped from the point A as shown in fig. to reach the position C on the earth surface.

During the downward journey of the ball imagine that it is in position B and has travelled distance x. Let, v be the velocity of the ball when it reaches the position B.

Finally the ball strikes the earth surface at point C. Let v’ be the final velocity of ball at C.

Thus we find that each of positions A, B and C of the ball, total energy remains the same (= mgh) i.e., energy remains conserved.

On striking the earth surface the energy of the ball appears as sound and heat energy If by some means we are able to measure these forms of energy it would be found to be the same as at A or B or C. This proves the law of conservation of Energy.

Ans.— When the force acting on the object is not in the direction of motion. A gardener pushes the lawn mower in the forward direction. He applies force F on the handle HH’ facing the ground.

As is clear from the figure, the gardener is not applying force in the horizontal direction but applies force in a direction making angle θ with the direction of force. In such situation the force acting on the machine drives the roller in the horizontal direction from A to B.

Here the effective force is F cos θ and not F and the vertical component F sin θ balances the weight of the lawn mower.

∴ Work done by the lawn mower (W) = Component of Force × Displacement

= F cos θ × S

(i) When the force acts along the direction of displacement then θ = 0º and cos θ = cos 0º = 1

W = F cos θ × S

=F × 1 × S

W = F × S

This time the work done will be maximum.

(ii) When the force acting on the object is in a direction perpendicular to the direction of motion then θ = 90° and cos θ = cos 90º = θ W = F cos θ × S

∴ W = F cos θ 90º × S

= F cos 90° × S

=  F × 0 × S

⇒ W = 0

This time the work done is minimum.

Ans.— Work. Work done by a force or by an object in the product of applied force and the displacement taking place in the direction of applied force.

If  F = force acting on the body

S = displacement of the body in the direction of force

work done by force,  W = F × S    ….(i)

we know, when a force acts on a body acceleration is produced in the body.

Thus,   if m = mass of body

a = acceleration produced in the body then

from, Newton’s second law of motion

F = m × a ….(ii)

Using (i) and (ii),

W = m × a × S  ….(iii)

Unit of work. When force is measured in Newton (N) and displacement in metre (m), the

Work = Newton × Metre

W = N × m

W = Joule (J)

∴ S.I. unit of work is Joule (J) and C.G.S. unit is erg.

1 Joule 10⁷ erg.

Ans.— This statement can be understood by the following example. If a child tries to push a car by applying his, maximum force but the car does not displace even through 1 centimeter, then in the language of physics we can say that the child has done no work.

In this situation suppose the child applies force F and displacement S = 0 then

∴ Work done by the child, W = F × S

= F × 0

⇒ W = 0

Ans.— A stone is made to move in a circle as shown the fig. then the finger with which you hold the string will experience some force. The force acting on the moving stone is known as centripetal force.

This force acts radially inwards towards the centre of the circle. If in this situation the stone gets detached then it will fly off in the direction tangential along AT or BT as shown in fig. 3.13 Now, the centripetal force acts perpendicular to the direction of motion, thus no work is done by the centripetal force.

Ans.— Power. Harish and Karan climbed up a tree to pluck 60 mangoes each. They started climbing at the same moment of time. Harish got his 60 mangoes in 30 minutes whereas Karan got his 60 mangoes in 60 minutes. That means Karan took more time to do the same work. Both did the same work, both had same energy but their power was 30. not same i.e. Power of Harish is more than that of Karan.

Power. Power of an object or a machine is its time rate of doing work i.e. Power is defined as rate of doing work with time.

∴ Power = Work done /  time taken

or, P = W / t

If work is measured in joule and time in second then unit of power is ‘watt’.

1 watt = 1 Joule / 1 second

commercial unit of power is kilowatt.

1 kilowatt = 1000 watt = 1000 joule/second

Ans.—Place a nail on a wooden block and hammer it, some part of the nail goes into the wooden block, when nail is completely into the block due to hammering, when nail in further hammered then nail, hammer and block all gets heated up. When hammer is lifted up for hammering, its potential energy increases due to its position. When it falls on the nail then its whole energy is transformed into kinetic energy of the nail and the nail goes into the wooden block. When nail is completely embedded into the block then mechanical energy of the hammer converts into heat energy of the nail, block and hammer meaning thereby that mechanical energy gets converted or transformed into heat energy.

Ans.— Difference between Potential energy (P.E.) and Kinetic energy (K.E.)

Potential Energy	Kinetic Energy
The potential energy of an object depends upon its position and size.	The kinetic energy of an object is due to its motion or velocity.
Potential energy (P.E) = m × g × h	Kinetic energy (K.E.) = 1 / 2 mv²
Potential energy of an object depends upon its height above the ground or its depth below the ground surface.	The kinetic energy of an object depends upon its velocity.

Ans.— Kinetic energy. It is defined as the energy possessed by a body due to its velocity (motion).

Kinetic energy = 1/2  mv², where ‘m’ is the mass of the body and ‘v’ its velocity.

Example. 1. The bullet fired from the gun possesses kinetic energy due to its motion.

2. When an archer stretches the string of the bow then he does work which gets stood in the bow and arrow system as potential energy and when he releases the string, then this energy gets converted into kinetic energy of the arrow.

Potential energy. It is defined as the energy possessed by a body due to its raised position above the surface of earth or changed configurations.

Example. 1. The wound up spring of the watch possesses potential energy which when unwinds makes the various parts to the machinery to move.

2. A stone lying at the top of the rock possesses potential energy.

Ans.— Energy. Energy is the ability to do work and is equal to the magnitude of total work which could be done by the energy. It has no relation with the time.

Power. It is the rate of doing work. It has no relation with the magnitude of total work.

Example. A worker taken one hour to complete a piece of work, whereas the other worker takes 2 hours to complete the same piece of work. In this case, both the workers are doing the same work i.e. both are consuming same amount of energy. But first worker did the same work in half the time as compared to other worker thus. First worker has doubled the power than the other worker.

Sol.— Potential energy (P.E) – 1 J

Mass of the box (m) = 0.5 kg

Acceleration due to gravity, (g) = 10 m/s²

Ans.— 1 commercial unit of energy (or 1 kWh) = 3.6 × 10⁶ Joule.

Ans.— Work done is zero.

Ans.— The SI unit of power is Watt.

Ans.— The kinetic energy of the body changes into its potential energy.

Ans.— Kilowatt hour. It is defined as the work done or energy consumed when power of 1 kilowatt is consumed in 1 hour.

Ans.— Mechanical energy.

Ans.— 1 kilowatt hour = 3.6 × 106 J.

Ans.— The velocity of the body should doubled at constant mass.

Ans.— When displacement is in a direction perpendicular to the applied force.

Sol.—  Power of a machine = Work done / time

= 2000 J / 10 s

= 200 Ans.

Ans.— Joule.

Ans.—  Potential energy of water will decrease. It will change to kinetic energy of water.

(A) remains same

(B) is doubled

(C is 4 times

(D) is 1/4th.

Ans.— (B) is doubled

(A) power

(B) force.

(C) electric energy

(D) pressure.

Ans.—  (C) electric energy

(A) kilocalorie

(B) kWh

(C) erg

(D) watt.

Ans.— (D) watt.

(A) acceleration is doubled

(B) weight is doubled

(C) kinetic energy is doubled

(D) kinetic energy increases 4 times.

(A) 20 J

(B) 40 J

(C) zero

(D) None of three is correct.

Ans.— (C) zero

(A) J

(B) W

(C) N

(D) horse power.

Ans.— (B) W

(A) a scalar quantity

(B) a vector quantity

(C) neither scalar nor vector quantity

(D) scalar under one condition and vector under other state.

Ans.— (A) a scalar quantity

Ans.— (A)

(A) remains unchanged

(B) increases

(C) increases

(D) becomes zero.

Ans.— (B) increases

(A) standing

(B) sitting on the ground

(C) sleeping on the ground

(D) siting in a chair.

Ans.— (A) standing

(A) 1/2 mv²  

(B) zero

(C) 2{1/2 mv²}

(D) 2mgh.

Ans.— (B) zero

(A) zero

(B) positive

(C) negative

(D) none of these.

Ans.— (B) positive

(A) positive an

(B) zero

(C) negative

(D) none of these.

Ans.— (C) negative