# Work and Energy : Practice Questions

1 Mark Questions

1. Define SI unit of work.

2. A student is writing a three hours science paper. How much work is done by the student? Give reasons to your answer.

3. List two essential conditions for work to be done.

4. Give one example when work done by a body negative.

5. A 2 m high person is holding a 25 kg trunk on his head and is standing at a roadways bus-terminus. How much work is done by the person?

6. Calculate the work done when a force of 15 N moves a body by 5 m in its direction.

7. Moon is experiencing a gravitational force due to earth and is revolving around the earth in a circular orbit. How much work is done by moon?

8. State law of conservation of energy.

9. Name the term used for the sum of kinetic energy and potential energy of a body.

10. If the heart works 60 joules in one minute, what is its power?Â

11. Define 1 KWh.

12. Define 1 W of power.

13. Name the type of energy possessed by a raised hammer.

14. In an oscillating pendulum, at what position the potential and kinetic energy are maximum?

15. A coolie is walking on a railway platform with a load of 30 kg on his head. How much work is done by coolie?

16. Identify the kind of energy possessed by a running athlete.

17. At what speed a body of mass 1 kg will have a kinetic energy of 1 J.?

18. If the speed of the body is halved, what is the change in its kinetic energy?

19. A horse of mass 210 kg and a dog of mass 25 kg are running at the same speed. Which of the two possesses more kinetic energy? How?

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

21. What will cause greater change in Kinetic energy of a body. Changing its mass or changing its velocity?

22. What is power? What is its SI unit ?

23. To what height should a body of mass 5 kg be raised so that its potential energy is 490 J? [g = 9.8 m/${s^2}$]

24. On pushing a mighty stone, a child is unable to move it. If work done is zero, where is the energy, he, lost?

25. State the SI unit of

(a) work,
(b) power.

26. Relate watt to joule.

27. What is one unit of electrical energy consumed equal to?

28. Relate one horsepower to the SI unit of power?

29. A ball of mass 5 kg is dropped from a tower d, height 2 m. What is its K.E. half way down?

30. Define one joule.

31. Define one Watt.

32. In what situation(s) is work done equal to zero?

33. When a body falls freely, its potential energy

(A) .........and simultaneously,
(B) its kinetic energy...........

34. A machine of 500 W works for 2 hours. Find the number of units of electricity consumed.

35. How is energy conversion occurring in a Hydel power station?

36. If a force of 50 N moves a body with constant speed of 10 m/s, how much power is spent?

37. State the CGS unit of energy.

38. Relate the CGS unit of energy to its SI unit.

39. Derive a relation between kinetic energy of a body and its momentum.

Solutions

1. SI unit of work is Joule. 1 Joule of work is done when a force of 1 N displaces a body by 1 m.Â

2. Work done = Force Ã— displacement as displacement is zero. No work is done by the student.Â

3. (i) Force should be applied on body.

(ii) Body should move in the direction of force.Â

4. When a body is raised vertical upward, displacement and gravitation force are is in opposite direction. The work done by gravity is negative.Â

5. Zero. As displacement is zero.Â

6. Work done = 15 Ã— 5 = 75 J.Â

7. No work is done by moon as the gravity force and displacement are perpendicular to each other.Â

8. Law of conservation of energy states that energy can only be converted from one form to another, it can neither be created nor destroyed.Â

9. Mechanical Energy.Â

10. Power = ${{60J} \over {60s}}$ = 1 W. [1 min = 60 s]

11. 1 KWh is the energy consumed when power of 1000 w is consumed for 1 hour.

12. When one joule of work is done in one second, the power is said to be 1 watt.

13. Potential Energy.

14. At the highest point of the bob, potential energy is maximum, while at the lowest point kinetic energy is maximum.

15. Since force due to load is downward, and the coolie is moving in horizontal direction, no work is done by coolie.

16. Kinetic energy.

17. K.E = ${1 \over 2}m{v^2}$

$V\, = \,\sqrt {{{2KE} \over m}} \, = \sqrt {{{2 \times 1} \over 1}\,} = \,\sqrt {2\,} \,m\,/s$

18. Since $K.E\,\alpha {v^2}$

If v is halved; KE = 1/4 of the original.

19. $K.E\,\alpha \,Mass$.

Since mass of horse is greater than that of dog, the horse will posses greater kinetic energy.

20. A freely falling body loses potential energy , but it gains equal amount of kinetic energy such that the sum total of energy remains constant. Hence , this does not violate the law of conservation of energy.

21. Changing velocity of a body will cause greater change in the kinetic energy of the body.

22. Power is the rate of doing work. Its unit is watt.

1 Watt = 1 Joule/s.

23. P.E = mg.h

$\,h\, = \,{{P.E} \over {mg\,}}\, = \,{{490} \over {5 \times \,9.8}}\, = \,10\,m.$

24. The energy is lost in the form of heat energy.

25. (a) SI unit of work is Joule.

(b) SI unit of power is Watt

26. 1 watt = 1 Joule / 1 sec

27. 1 unit of electrical energy = $3.6\, \times \,{10^6}\,$ Joule

28. 1 horse power = 746 Watts

29. A ball is dropped from 2 m. The halfway point is when it has moved through 1m.

By III equation of motion
${v^2}\, - \,{\mu ^{2\,}}\, = \,2 gh$
$\,{v^2}\, = \,2\, \times \,10\, \times \,1$
K.E = ${1 \over 2}m{v^2}\, = \,{1 \over 2}\, \times \,2\, \times 10\, \times \,1\, = \,1\,J.$

30. 1 Joule of work is said to be done when a body is displaced by 1m due to a force of 1N

31. 1 watt is the power of an object which does work at the rate of 1 Joule per second

32. Work is equal to zero when-

(i) Force is zero
(ii) Displacement is zero
(iii) Displacement is perpendicular to the direction of force.

33. (A) decreases, (B) increases

34. Work done 500 Ã— 2 = 1000 Wh

= 1 KWh.
unit of electricity consumed = 1.

35. Potential Energy of water in dam $\to$ Kinetic energy of water passing through gates $\to$ Kinetic energy of turbines $\to$ Electrical Energy.

36. Power = ${{Work\,done} \over {Time}} = {{F \times d} \over t}$ = F Ã— V.

= 50 Ã— 10 = 500 W

37. CGS unit of energy is ergs

38. 1 Joule = ${10^7}$ ergs

39. Kinetic energy = ${1 \over 2}m{v^2}$

= ${1 \over 2}{{{m^2}{v^2}} \over m}\, = {{{p^2}} \over {2m}}$ , where p is the momentum.

2 Marks Questions

1. List two conditions which need to be satisfied for the work to be done on an object?

2. Define energy and define its SI unit.

3. An archer stretches a bow to release an arrow to hit the target at a distance of 10 m. Explain who does the work,in which form is the energy possessed the bow and the arrow.

4. Write the form of energy possessed by the body in the following situations:

(a) a coconut falling from tree.
(b) an object raised to a certain height
(c) blowing wind
(d) A child driving a bicycle on road

5. Given below are a few situations, study them and state in which of the given cases work is said to be done. Give reason for your answer.

(a) A person pushing hard a huge rock but the rock does not move.
(b) A bullock pulling a cart up to 1 km on road.
(c) A girl pulling a trolley for about 2 m distance.
(d) A person standing with a heavy bag on his head.

6. 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.

7. A ball of mass 2 kg is dropped from a height. What is the work done by its weight in two seconds after the ball is dropped?

8. A bag of wheat weighs 60 kg. Find the height to which it is lifted so that its potential energy is 3000 J. (g = 10 m${s^{ - 2}}$)

9. A body of mass 2 kg is thrown up with a speed of 25 m/s. Find its maximum potential energy.

10. (a) Define 1 Watt.

(b) An electric bulb of 60W (sixty watt) is used for 6 (six) hours per day. Calculate the units of energy consumed in one day by the bulb.

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

12. A man of mass 60 kg runs up a flight of 30 steps in 40 s. If each step is 20 cm high, calculate his power.

13. (a) What is meant by potential energy of a body?

(b) A body of mass 'm' is raised to a vertical height. 'h' through two different paths A and B. What will be the potential energy of the body in the two cases? Give reason for your answer.

14. What is the amount of work done in the following cases? Justify your answer by giving the appropriate reason.

(a)By an electron revolving in a circular orbit of radius around a nucleus.
(b)By the force of gravity, when a stone of mass 'm' is dropped from the top of a multi- stored building of height 'h'.

15. An electric bulb of 100 W works for 4 hours a day. Calculate the units of energy consumed in 15 days.

16. 16 bulbs of 40 W are used for 6 hours a day along with one 100 W bulb for 2 hours. Calculate the `units' of energy consumed in one day by all bulbs.

17. (a) Define kinetic energy.

(b) Write an expression for kinetic energy of an object and also give its SI unit.

18. Find the power of human heart, which beats 72 times per minutes, if it does 1.5 J of work every beat.

19. The momentum of a body is increased four times. What is its final kinetic energy?

20. A ball of mass 0.5 kg is thrown up with a velocity of 15 m/s. Find its potential energy at the highest point. [Take g = 10 m/${s^2}$]

21. State energy conversion occurring in

(a) pendulum (b) bulb.

22. A bulb/machine becomes hot after working for some time. Why?

23. A boy of mass 80 kg is running at 10 m/s. Find the work done by him.

24. Give one example of

(a) positive work
(b) zero work done.

25. A man rotates the wheel of an amusement slide in a fair. How much work is done by him if he rotates the wheel 40 times in 1 minute?

26. How is energy conserved in a simple pendulum?

27. What is the power of a pump if it pulls 200 kg water from a 20 m deep well in 30 s?[g = 10 m/${s^2}$]

28. Define (a) kinetic energy (b) potential energy.

29. Derive an expression for kinetic energy of a body of mass m, moving with velocity v.

30. Sun is the ultimate source of energy. How does it provide energy of flowing water?

31. If energy of universe is constant, why are we facing energy crisis?

32. State the commercial unit of energy and its relation with joule.

33. In what form is energy possessed by:

(a) Water stored in a dam
(b) A stretched bow
(c) A raised bat
(d) A running horse?

34. Derive an expression for potential energy of a body.

35. Fill in the blanks:

(a) 1 MW = ? W
(b) 1 J = ? KJ

Solutions

1. (i) Force should be applied on body.

(ii) Body should move in the direction of force.

2. Energy is the capacity to do work. The unit of energy of an object is joule. 1 Joule = 1N Ã— 1m

3. The archer does the work in pulling the bow string taut. The muscular energy of archer arm a $\to$ potential energy of taut string $\to$ kinetic energy of arrow.

4. (a) Kinetic energy + potential energy (when at a height)

(b) Potential energy.

(c) Kinetic energy.

(d) Kinetic energy.

5. (a) No work is done as there is no displacement.

(b) Work done as there is displacement.

(c) Work done as there is displacement when force is applied.

(d) No work done as displacement is zero.

6. Work done = Force Ã— displacement

= mg Ã— h

= 15 Ã— 10 Ã— 1.5

= 225 J.

7. Work done = increase in K.E

Now, v = u + at

= 0 + 10 Ã— 2 = 20 m/s.

$\,K.E\, = \,{1 \over 2}m{v^2}\, = \,{1 \over 2}\, \times \,2\, \times \,{(20)^2}\, = \,400 J.$

8. P.E = mgh.

$\,h = {{P.E} \over {mg}}\, = \,{{3000} \over {60 \times 10}}\, = \,5 m.$

9. Max. P.E = Max. K.E

= ${1 \over 2}m{v^2}$

= ${1 \over 2}\, \times \,2\, \times \,{(25)^2}\, = \,625 J.$

10. (a) When one joule of work is done in one second, the power is said to be 1 watt.

(b) Energy consumed = power Ã— time

= 60 W Ã— 6 h.

= 360 Wh =0.36 KWh = 0.36 Units.

11. Work done = ${1 \over 2}m{v^2}$.

= ${1 \over 2}\, \times \,1500\, \times \,{(60\, \times \,{5 \over {18}})^2}$

= $20.83\,\, \times \,{10^4}J.$

(should be equal and opposite to the K.E)

12. Total height reached by man = 30 Ã— ${{20} \over {100}}m$ = 6 m

Power = work done/time = mgh/time = ${{1500 \times 10 \times 6} \over {40}}\, = \,90 W$

13. (a) Potential energy is defined as the energy possessed by a body due to its position or configuration.

(b) The potential energy in both the cases will be mgh. This is so as the P.E depends on the vertical height, not the path aken.

14. (a) No work is done as the electrostatic force is perpendicular to the displacement.

(b) Work done = mgh (Force Ã— displacement)

15. Energy consumed = Power Ã— Time

= 100 Ã— 4 Ã— 15

= 6000 Wh

= 6 KWh = 6 units

16. Total energy consumed

= Energy consumed by (16 bulbs of 40w + 1 bulb of 100w)

= (16 Ã— 40 Ã— 6) + 100 Ã— 2

= 4040 Wh

= 4.040 KWh = 4.04 units

17. The energy possessed by an object due to its motion is the kinetic energy of an object.

K.E = ${1 \over 2}m{v^2}$ where m is mass and v is velocity of object.

18. Power of human heart

= Work done in each beat Ã— no. of beats in 1 s.

= $1.5 \times {{72} \over {60}}\, = \,1.8 W.$

19. K.E = ${{{p^2}} \over {2m}}$. If momentum is increased 4 times , K.E will become

${{{{(4P)}^2}} \over{2m}}\, = 16{{{P^2}} \over {2m}}$ i.e 16 times.

20. u = 15 m/s : v=0, g= 10 $m/{s^2}$

$\Rightarrow$${v^2} - {u^2} = \,2gh$

$\Rightarrow$$gh = {1 \over 2}({v^2} - {u^2}) = \,{1 \over 2}\,{u^2}$

P.E = mgh =${1 \over 2}m{u^2} = \,{1 \over 2}\, \times 0.5 \times 15 \times 15 = 56.25 J$

21. (a) K.E $\to$ P.E $\to$ K.E $\to$ P.E

(b) Electrical energy $\to$ Heat energy $\to$ Light.

22. A bulb/machine gets hot after sometime as some of its energy is converted into heat energy. In bulb this is due to the resistance of wires, in machine this is due to friction between body parts.

23. Work done = Force Ã— displacement

= mg Ã— distance moved in 1 s.

= 80 Ã— 10 Ã— 10

= 8000J in 1 sec.

24. (a) When an object falls under gravitational attraction, positive work is done by gravity.

(b) If an object does not move when force is applied, zero work is done.

25. Since the net displacement of wheel is zero, no work is done by the man.

26.

In a simple pendulum, work is done when the bob is raised. This is its P.E .When the bob is released, it moves down, its P.E decreases, but K.E increases. At the lowest point K.E is maximum, P.E is zero.
The bob rises to the other side. K.E decreases P.E increases. The total energy remains constant or we can say its energy is conserved.

27. Power of pump = ${{Work done} \over {Time}} = {{mgh} \over {Time}}$

= ${{200 \times 10 \times 20} \over {30}}$

= 1333.3 W.

28. (a) The energy possessed by an object due to its motion is the kinetic energy of an object.

(b) Potential energy is defined as the energy possessed by a body due to its position or configuration.

29. Work done = F Ã— d.

= m Ã— a Ã— d -------(1)

By Newton's III equation of motion.

${v^2} - {u^2}$ = 2ad , where d is the displacement

Therefore, $\,ad\, = {{{v^2} - {u^2}} \over 2}$ -------------(2).

Substituting (2) in (1), we have

Work done = ${1 \over 2}m({v^2} - {u^2})$

If the initial velocity is zero, then work done = ${1 \over 2}m{v^2}$

This is the K.E of the body.

30. A part of sun's energy is in the form of heat energy. Due to the heat energy, water evaporates from seas and oceans and fall as rain fall in the mountains, This water comes down the plains and create flowing rivers. Thus sun's energy is converted into kinetic energy of the flowing water.

31. We are facing energy crisis because the energy consumed is from fossil fuels.The reserve of fossil fuel is limited and will get exhausted in some years.

32. Commercial unit of energy is KWh .

1 KWh = $3.6\, \times \,{10^6}J.$

33. (a) Potential Energy.

(b) Potential Energy.

(c) Potential Energy.

(d) Kinetic Energy.

34. Potential energy is the energy stored in a body when work is done on it.

Work done = Force Ã— displacement

= mg Ã— h (distance moved)

= mgh

35. (a) 1 Mw = ${10^6} W.$

(b) 1 J = ${10^{ - 3}} KJ.$

3 Marks Questions

1. Water is falling on the blades of a turbine at the rate of 800 kg per minute, height of fall is 50 m. Calculate the power given to turbine.(g = 10 m/${s^2}$)

2. A force of 10 N acts on a body of 2 kg for 3 seconds. Find the kinetic energy acquired by the body in 3 seconds.

3. State Law of conservation of energy and express it in the form of an equation for a body of mass m falling from a point A at height h', above the ground at
(a) A
(b) C at a height h from ground
(c) B.

4. Mention the commercial unit of energy. Express it in terms of joules. Calculate the energy in joule consumed by a device of 60 W in 1 hour."

5. (a) When is the work done by a body said to be negative?

(b) An object of mass 5 kg is dropped from a height of 10 M. Find its kinetic energy, when it is half way down.

6. A body of mass 5 kg is thrown vertically upwards with a speed of 10 m/s. What is its kinetic energy when it is thrown? Find its potential energy when it reaches at the highest point.Also find the maximum height attained by the body.(g = 10 m/${s^2}$).

7. Calculate the electricity bill amount for a month of April, if 4 bulbs of 40 W for 5 hrs, 4 tube lights of 60 W for 5 hrs, a T.V of 100 W for 6 hrs, a washing machine of 400 W for 3 hrs are used per day. The cost per unit is Rs. 1.80.

8. A force applied on a body of mass 4 kg for 5 seconds changes its velocity from 10 m/s to 20 m/s. Find the power required.

9. A car weighing 1200 kg is uniformly accelerated from rest and covers a distance of 40 m in 5 seconds. Calculate the work done by the engine of car during this time. What is the final kinetic energy of car?

10. (a) An object of mass 'm' is moving with a constant velocity V. How much work should be done on the object to bring it to rest?

(b) Earth is revolving round the sun. What is the work done by the gravitational force exerted by the sun on earth? Justify your answer.

11. (a) Give one situation where force is applied but no work is done. Explain why.

(b) A pump is used to raise water to a height of 20 m. It transfers 2000 kg of water in 15 minutes. Calculate power of the pump. [g = 10 m${s^2}$]

12. (a) The potential energy of a freely falling object decreases progressively.

(i) What happens to its kinetic energy.

(ii) Total mechanical energy? State the law on which your answer is based.

(b) A household consumes 1 kWh of energy per day. How much energy is this in joules?

13. (a) State and define SI unit of power.

(b) A person carrying 10 bricks each of mass 2.5 kg on his head moves to a height 20 m in 50 s. Calculate power spent in carrying bricks by the person.
(g = 10 m/${s^2}$)

14. Give an example in each case where work done by a force is :
(a) zero
(b) positive
(c) negative

15. A student lifts an object in the upward direction. In doing so, he applies the force on the object in the upward direction and displaces it in that direction:
(However, the force of gravity is also acting on the object.)
(a) State the direction in which force of gravity is acting on it.
(b) Which one of these forces is doing positive work? Give reason.
(c) Which one of these forces is doing negative work? Give reason.

16. Define kinetic energy.
A stone of mass 2 kg is falling from rest from the top of a steep hill. What will be its kinetic energy after 5 s? (g = 10 m${s^{ - 2}}$)

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

18. Two women Shanti and Kamla each of mass 50 kg and 60 kg respectively climb up through a height of 10 m. Shanti takes 20 s while Kamla takes 40 s to reach.Calculate the difference in the power expended by Shanti and Kamla.(Assuming g = 10 m${s^{ - 2}}$)

19. (a) Define Potential energy.

(b) Give an example where potential energy is acquired by a body due to change in its shape.

(c) A skier of mass 50 kg stands at 'A' at the top of a ski jump. He takes off at 'A' for his jump to 'B'.

Calculate the change in his gravitational potential energy between 'A' and 'B'. Where height of A is 75 m and height of B is 60 m.

20. Two bulbs of 40W each are lighted for eight hours daily. Find the cost of electrical energy consumed by them in one week at Rs. 3 per unit.

21. Find the change in momentum of a body when its kinetic energy becomes four times the original value.

Solutions

1. Power = Work done/time

= ${{mgh} \over t} = {{800 \times 10 \times 50} \over {60}} = 6670 W.$

2. Velocity acquired v = u + at

= $0{\mkern 1mu} + {\mkern 1mu} {{10} \over 2} \times 3$ as a $a = {F \over m} = {{10} \over 2}$

= 15 m/s.

K.E = ${1 \over 2}m{v^2} = \,{1 \over 2} \times 2 \times {(15)^2} = 225J.$

3. Law of conservation of energy states that energy can only be converted from one form to another, it can neither be created nor destroyed.

(a) T.E at A = mgh' (P.E = mgh' , K.E = 0).

(b) Velocity at C is found by

${v^2} - {u^2} = 2g(h' - h)$

$\,{v^2} = 2g(h' - h)$

$\,K.E = {1 \over 2}m{v^2} = mg(h' - h)$

at C, P.E = mgh'

T.E at C = P.E + K.E = mg(h â€“ h') + mgh' = mgh

(c) At B; P.E = 0.

K.E = ${1 \over 2}m{v^2}$ = mgh'Â

Total energy is the same at all points.

4. Commercial unit of energy = KWh

1kWh = $3.6 \times {10^6}J$

Energy consumed = 60 Wh, time = 1 hr = 60 Ã— 60 s.

= 60 Ã— 60 Ã— 60 J

= $1.08 \times {10^5}J$

5. (a) Work done is said to be negative if force and displacement are in opposite directions.

(b) When body falls 5m, its velocity v can be found by

${v^2} - {u^2} = 2gh$

${v^2} = \,2 \times \,10 \times \,5$

K.E = ${1 \over 2}m{v^2} = {1 \over 2} \times \,5 \times 2 \times 10 \times 5$ = 250 J.

6. K.E= ${1 \over 2}m{v^2} = {1 \over 2} \times \,5 \times 2 \times {(10)^2} = 250J$ (m = 5 kg)

At the highest point P.E = 250 J. (as it is equal to K.E maximum)mgh = 250

$\,h = {{250} \over {5 \times 10}}$ = 5 M.

7. In one day energy consumed by

(i) 4 balls = 4 Ã— 40 Ã— 5 = 800 Wh.

(ii) 4 tube light = 4 Ã— 60 Ã— 5 = 1200 Wh.

(iii) T.V = 100 Ã— 6 = 600 Wh.

(iv) washing machine = 400 Ã— 3 = 1200 Wh.

$\,$ Total energy consumed in 1 day = 3800 Wh.

$\,$ Total energy consumed in 30 days = 114000 Wh.

= 114000 KWh/1000 = 114 units.

Total cost = 114 Ã— 1.80 = Rs. 205.20.

8. Power = Change in ${{K.E} \over {Time}}$

= ${1 \over 2} \times \,{{4 \times ({{20}^2} - {{10}^2})} \over 5}$

= 120 W.

9. Distance covered S = $ut\, + \,{1 \over 2}a{t^2}$

40 = ${1 \over 2} \times a \times {5^2}$

$\,$ a = ${{40 \times 2} \over {25}}$

$\,$ = ${{16} \over {5}}m/{s^2}$

Work done = F Ã— d

= m Ã— aÃ— d

= 1200 Ã— 16/5 Ã— 40 = 153600 J.

10. (a) Work done should be equal to the energy possessed by the body that is ${1 \over 2}m{v^2}$ .

(b) Zero work is done as net displacement in the direction of force is zero.

11. (a) You push a heavy box , but it does not move. Then work done is zero as d = 0.

(b) Power of pump = Work done / time = mgh / t.

= ${{2000 \times 10 \times 20} \over {15 \times 60}}$

= 444.4 Watts.

12. (a) (i) K.E increases.

(ii) Total mechanical energy remains constant. Law of conservation of energy.

(b) 1 kWh = $3.6 \times {10^6}J.$

13. (a) 1 Watt is the power of an object which does work at the rate of 1 Joule per second.

(b) Power = ${{mgh} \over t} = {{10 \times 2.5 \times 10 \times 20} \over {50}}$ = 100 W.

14. (a) Since W = F Ã— d , W is zero , if d= 0 i.e if a body does not move when force is applied.

(b) Work is positive if F and d are in the same direction e.g. a ball falls, work done by gravity is positive.

(c) If a body is raised , work done by gravity is negative.

15. (a) Downwards

(b) The student is doing positive work as the displacement is in the direction of force applied by him.

(c) Gravitational force does negative work as the displacement is upward and gravity is downwards.

16. (a) The energy possessed by an object due to its motion is the kinetic energy of an object.

(b) v = u + at

= 0 + 10 Ã— 5

= 50 m/s.

$\,$ K.E = ${1 \over 2}m{v^2} = {1 \over 2} \times \,2 \times 50 \times 50.$

= 2500 J.

17. A freely falling body loses potential energy , but it gains equal amount of kinetic energy such that the sum total of energy remains constant. Hence , this does not violate the law of conservation of energy.

18. Power expended by Shanti = ${{mgh} \over t} = {{50 \times 60 \times 10} \over {20}}$. = 250 w.

Power expended by Kamla = ${{60 \times 10 \times 10} \over {40}}$ = 150 W.

Difference in power expended = 100 W.

19. (a) Potential energy is defined as the energy possessed by a body due to its position or configuration.

(b) If a spring is compressed , it acquires potential energy.

(c) Change in gravitational potential energy.

= P.E at A - P.E at B

= $mg{h_2} - mg{h_1} = mg({h_2} - {h_1})$

= 50 Ã— 10 Ã— (75-60) = 7500 J.

20. Energy consumed = 2 Ã— (40 Ã— 8) Ã— 7

= 4480 Wh = 4.48 KWh = 448 Units

Cost = 4.48 Ã— 3 = Rs. 13.44.

21. Momentum P = $\sqrt {2mK.E}$ (as K.E = ${{{p^2}} \over {2m}}$ )

If $P_1$= $\sqrt {2mK.E}$

then $P_2$= $\sqrt {2m.4KE}= 2\sqrt {2mK.E}= 2{P_1}$

Change in momentum ${P_2} - {P_1} = 2{P_1} - {P_1} = {P_1}$

5 marks Questions

1. (a) Justify that "a body at a greater height has larger energy".

(b) A body of mass 2 kg is thrown up at a velocity of 10 m/s. Find the kinetic energy of the body at the time of throw. Also, find the potential energy of the body at the highest point.

The value of g = 10m/${s^2}$.

2. (a) State the principle of conservation of energy. What are the various energy transformations that occur when you are riding a bicycle?

(b) A body of mass 25 g has a momentum of 0.40 kg m/s. Find its kinetic energy.

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

(b) Define Power. An electric heater is rated 1500 W. How much energy does it use in 10 h? Express your answer in (i) kWh (ii) joules

4. What do you mean by work? Give an example of negative work done. What is the work to be done to increase the velocity of a car from 18 km/h to 90 km/h if the mass of the car is 2000 kg?

5. (a) Define kinetic energy of an object. Can kinetic energy of an object be negative? Give reason.

(b) A car weighing 1200 kg is uniformly accelerated from rest and covers a distance of 40 m in 5 seconds. Calculate the work, the car engine had to do during this time.

6. (a) A ball thrown vertically upwards returns to the thrower. How do the kinetic and potential energies of the ball change?

(b) Calculate the power of a pump which lifts 100 kg of water to a water tank placed at a height of 20 m in 10 s.(Given = 10 m${s^{ - 2}}$)

7. (a) A battery lights a bulb. Describe the energy changes involved in the process.

(b) Calculate the amount of work needed to stop a car of 500 kg, moving at a speed of 36 Km/h.

8. (a) Give reason for the following:

(i) The kinetic energy of a freely falling object increases, yet it holds law of conservation of energy.

(ii) A girl fills up 10 pages of a notebook in order to practice sums, yet she has not done 'work' in terms of Science/Scientific concept.

(iii) Work done by gravitational force on an object moved along a horizontal path, is zero.

(b) Find the energy in kWh consumed in 24 hours by two electric devices, one of 100 W and other of 500 W.

9. What is meant by energy? How is energy related to work done? A person pushes a wall and fails to move it. What is the work done? Why does he get tired?

Solutions

1. (a) Consider two bodies A and B having same mass m places that $h_A> h_{B.}$

Then P.E at A = $mgh_A$

P.E at B = $mgh_{B.}$

Hence P.E at A > P.E at B.

(b) K.E = ${1 \over 2}mv^2= {1 \over 2} \times 2 \times (10)^2= 100 J.$

Since initial velocity = 10, as $v^2- u^2= 2 gh.$

h = ${{ - 10^2 } \over { - 2 \times 10}} = 5 m.$

P.E = mgh = 2 Ã— 10 Ã— 5 =100 J.

2. (a) Law of conservation of energy states that energy can only be converted from one form to another, it can neither be created nor destroyed.

Muscular energy $\to$ Kinetic energy $\to$ Heat energy.

(b) K.E = ${{p^2 } \over {2m}} = {{(0.40)^2 } \over {2 \times {{25} \over {1000}}}} = 3.2 J$

3. (a) K.E $\propto v^2$

${{K.E(1)} \over {K.E(2)}} = {{v^2 } \over {(3v)^2 }} = {1 \over 9}$

(b) Power is rate of doing work.

Energy = P Ã— t = 1500 Ã— 10 = 15 kwh.

= $15 \times 3.6 \times 10^6 J\, = 5.4 \times 10^7 J.$

4. When a body is displaced in the direction of force applied, work is said to be done.

Friction always opposes motion. So work done by friction is negative.

Work done = Increase in K.E

= ${1 \over 2}mv^2 _f- {1 \over 2}mv^2 _i$

= ${1 \over 2} \times 2000 \times [(90 \times {5 \over {18}})^2- (18 \times {5 \over {18}})^2 ]$

= $6 \times 10^5 J.$

5. (a) The energy possessed by an object due to its motion is the kinetic energy of an object.

K.E can never be negative

K.E = ${1 \over 2}mv^2$. All the terms are positive. further , K.E is a scalar quantity.

(b) S = $ut\, + \,{1 \over 2}at^2$

40 = 0 + 1/2 Ã— a Ã— 25.

a = ${{80} \over {25}}m/s^2$

Work done = m Ã— a Ã— s

= 1200 Ã— 80/25 Ã— 40 = 1536000 J

= 153.600 kJ

6. (a) When a ball is thrown up , it has K.E. As it moves up, its K.E. decreases and P.E energy increases. At the highest point its P.E is maximum , K.E is zero .As the ball moves down P.E decreases and K.E increases.

(b) Power = ${{Work\,done} \over {Time}} = {{mgh} \over t} = {{100 \times 10 \times 20} \over {10}} = 2000 W.$

7. (a) Chemical Energy $\to$ Electrical Energy $\to$ Heat Energy $\to$ Light Energy.

(b) Velocity of car = 36 km/h.= $36 \times {5 \over {18}}\,m/s = 10\,m/s$ .The work done to stop the car should be qual to the K.E possessed by the car.

${1 \over 2}mv^2= {1 \over 2} \times 500 \times (10)^2= 25000 J.$

8. (a) (i) The K.E of a freely falling body increases, but its P.E. decreases such that its total energy remains constant. Hence, law of conservation of energy holds.

(ii) In terms of Science, work is done if a force is applied and causes displacement. In this work, since displacement is zero, So work done is zero.

(iii) Since gravitational force is downward, and displacement is horizontal, there is no displacement in the direction of force. So work done is zero.

(b) Energy consumed = P Ã— t

= (100 + 500) 24 = 600 Ã— 24 Wh

= 14400 Wh = 14.4 KWh.

9. Energy is the capacity to do work.

Work can only be done, if a body has energy. e.g. if a body has K.E, it can move another body or if a body has P.E., it can move from one place to another.

Work done by person is zero as there is no displacement.

He gets tired as his energy is spent is muscular contraction which gets transformed to heat energy.

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