WORK, ENERGY AND POWER

Section A

One Mark Questions

1. What is work done in holding a 15kg suitcase while waiting for a bus for 15 minutes?2. Is it practically possible to have situations where (E – V) < 0?3. Can K.E. of a system be increased or decreased without applying any external force on

the system?4. Give some example where a force does work on a body but fails to change its K.E.5. Does the sun do any work on earth, when earth revolves around the sun in a perfectly

circular orbit?6. Does K.E. depend upon the direction of motion involved? Can it be negative? Does its

value depend on frame of reference? 7. Name the largest and smallest practical unit of energy.8. Is work done by a non conservative force always negative?9. Is linear momentum of a system always conserved?10. ‘The collision between two hydrogen atoms is perfectly elastic, so the momentum is

conserved’. Do you agree with this statement?11. A ball of mass m moving with vel. v strikes head on elastically with a number of balls of

same mass at rest in a line. Only one ball from other side moves with same velocity. Explain why not two balls move simultaneously, each with vel. v/2?

12. Is it possible to have a collision in which the whole of K.E. is lost?13. If two objects collide and one is initially at rest (a) is it possible for both to be at rest after

collusion? (b) is it possible for any one to be at rest after collision?14. What should be the angle between the force and the displacement for maximum and

minimum work?15. Does potential energy of a spring decrease/ increase when it is compressed or stretched?16. When a air bubble rise in water, what happens to its potential energy?17. In which, elastic or inelastic collision, the momentum of system is conserved? What

about K.E.18. In which motion, momentum changes but K.E. does not?19. A shot fired from a cannon explodes in the air. What will be the changes in momentum

and K.E.?20. Out of joule, calorie, kilowatt and electron volt, which one is not the unit of energy?21. The momentum of an object is doubled. How does its K.E. change?22. Can P.E. of an object be negative?23. Does work done in moving a body depend on how fast or how slow the body is moved?24. What type of energy is stored in the spring of a watch?25. A spring is cut in two equal halves. How is the spring constant of each half affected?26. Is it possible to exert a force which does work on a body without changing its kinetic

energy? If so, give example.

27. In case of a moving body, as force of friction is µ mg, can we regard µ mg x as potential energy similar to mgh?

28. If A⃗, B⃗ and C⃗are non zero vectors and A⃗.B⃗=0 and B⃗, C⃗ = 0, then find out the value of A⃗.C⃗.

29. The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

30. Can the scalar product of two vectors be negative?Section A(Solution)

One Mark Answer

1. Work done is zero, because displacement is zero.2. No, because (E-V) represents K.E., which cannot be negative.3. Yes, by doing work through internal forces e.g., in explosion of a bomb.4. When a body is dragged on a rough horizontal surface with a constant velocity, work is

done against friction but K.E. = constant.5. No, because angle between gravitational pull and direction of motion at any instant is 900

6. No, K.E. does not depend upon the direction of motion. No, K.E. cannot be negative. Yes, value of K.E. depends upon the frame of reference.

7. ‘Kilowatt hour’ is the largest practical unit of energy and ‘electron volt’ is the smallest practical unit of energy.

8. No, for example, work done by a non conservative force like friction is zero, so long as the body does not start moving. Again when friction causes motion, work done by friction is positive.

9. No, only when the system is isolated.10. No, because momentum is conserved even when collision is inelastic.11. When one ball of mass m moves with vel. v, both linear momentum and K.E. are

conserved. If two balls were to move simultaneously, each with velocity v/2; linear momentum will be conserved, but K.E. will not be conserved.

12. Yes, for example, in perfect inelastic collusion of two bodies moving towards each other with equal linear momenta.

13. (a) No, because momentum will not be conserved in that case. (b) Yes, when mass of two objects are equal and collision is perfectly elastic.

14. For maximum work θ = 00 and for the minimum work θ = 900

15. When a spring is compressed or stretched, potential energy of the spring increases in both the cases. This is because work is done by us in compression as well as stretching.

16. Potential energy of the bubble decreases, because work is done by up thrust on the bubble.

17. Momentum is conserved for the system in both the type of collisions, but K.E. is conserved only in elastic collisions.

18. In uniform circular motion.19. There will be no change in linear momentum, but the K.E. will increase. This is because

chemical potential energy of the explosives in the shot is converted into K.E.20. Kilowatt is not the unit of energy.

21. K.E. becomes four times. As K. E. = p2 / 2m22. Yes, it can be negative, when forces involved are attractive.23. No, time is not involved, in work or energy. Time is involved only in power.24. The energy stored in the spring of a watch is potential energy.25. Spring constant of each half become twice the spring constant of the original spring;26. Yes, when a spring is compressed or when a body is pulled with a constant velocity on a

rough horizontal surface.27. No, potential energy is defined only for conservative forces.28. As A⃗.B⃗=0; ⸫ AB cos θ = 0 or cos θ = 0 or θ = 900

Similarly, B⃗.C⃗=0; ⸫ BC cos θ1= 0 or cos θ1= 0 or θ1=900

i.e., A⃗ and C⃗ are parallel to each other. ⸫ A⃗.C⃗= AC cos 00 = AC

29. The sum and differences of two vectors A⃗ and B⃗ are ( A⃗+ B⃗ ) and ( A⃗−B⃗ ). If these are perpendicular to each other, then their dot product should be zero, i.e

( A⃗+ B⃗ ) . ( A⃗−B⃗ ) = 0 or A⃗. A⃗−¿ A⃗.B⃗+¿ B⃗. A⃗ - B⃗ . B⃗= 0

or A2 - B2= 0 or A2 = B2 or A = ± B

30. Yes, it will be negative if the angle between the two vectors is between 900 to 2700.Section B

2 MARKS QUESTIONS

1. Define the term work. Calculate the work done by a constant force. Is work done on a scalar or vector quantity?

2. How do you calculate the work done by a variable force?3. What is the amount of work done by

i) a weight lifter in holding a weight of 120kg on his sholder for 30s,and

ii) a locomotive against gravity, if it is travelling on a level plane?

4. What are conservative and non conservative forces? Give one example of each.5. Two bodies A and B weighting 5 kg and 6 kg respectively have equal momenta. Which

one has more kinetic energy?6. Draw a graph showing the variations potential energy and kinetic energy with respect to

height of a free fall under gravitational force.7. What is the meaning of “Collision” in physics? Differentiate between elastic and

inelastic collision. Give one example each.8. Prove that bodies of identical masses exchange their velocities after head-on elastic

collision.9. What is meant by mass energy equivalence? Find the amount of energy released by the

annihilation of 1mg matter.10. Define power and its SI unit. Power of an electric device is 40W.What does it mean?

Section C

3 MARKS QUESTIONS

11. What is meant by positive work, negative work and zero work? Give one example of each.

12. Define kinetic energy. Drive an expression for the kinetic energy of a body moving with a uniform velocity.

13. Derive an expression for the potential energy of an elastic stretched spring.14. Draw the graph of equation Fs = -km, where Fs is the spring force and x is the

displacement of block from equilibrium position. Using the graph show that maximum work done by the spring at xm isWs = -km2

m/2(k=spring constant).15. State and prove work energy theorem.16. By what factor the velocity of a body should be increased so that its kinetic energy is

increased by a factor of nine? Justify your answer. 17. Show the total mechanical energy of a body falling freely under gravity is conserved.

Discuss it graphically also.18. Prove that in case of one dimensional elastic collision of two bodies, the relative velocity

of separation after the collision is equal to the relative velocity of approach before collision.

19. Derive the equation for loss of kinetic energy during one dimensional inelastic collision. How will you account for this loss of energy?

20. Obtain the equation for final velocities of two bodies undergoing one dimensional elastic collision.

Section DValue Base Question

21. Manu went to railway station to see off his uncle. At platform, he saw that an old coolie was carrying heavy load on his head. Suddenly the coolie tripped and a baggage fell of his head. The owner of the bag started shouting at the old man. Manu didn’t tolerate this. He went to the old man, helped him in picking up the baggage and offered to carry some load for him.

a) What does this tell you about the nature of manu ?b) A man weighing 55 kg supports a body of 20 kg on his head. Calculate the work

done if he moves a distance 20m horizontally?22. Mohan was always jealous of Ravi was better in studies for which everybody praised

him. One day, Mohan challenged Ravi to defeat him in the race-uphill. They were both good runners but running uphill was difficult. Mohan ran very fast and was ahead of Ravi. After sometime, Mohan become breathless and started coughing. Ravi who was

following him saw his condition and went to help him forgetting their challenge. Then, Mohan realised why every one praised Ravi and they become the friends forever.

a) What value of Ravi do you appreciate?b) If the masses of bag is 3 kg and is taken up on an inclined plane of length 10m

and height 5 m,; i) work done by gravitational force ? ii) work done by applied force on upward journey ?

c) What do you mean by positive work and negative work ? Ans; )W=- mgh = 3x10x 5= -150J 2) 150J

23. Mohan was very lazy and overweight. she didn’t do any exercise or physical work. As her weight was increasing whenever she walked she felt pain in her knees. She consulted a doctor who advised her to reduce her weight otherwise her condition would not improve. She tried to follow doctors advise and challenged her life style, she stopped eating junk food, started using stairs instead of using lift, started walking small distance instead of using cars. After sometimes, she become fit and fine again.

i. What values do you infer from this ?ii. If Mahek weighting 80 kg climbs up a staircase having vertical height of

10m, five times a day, how many calories does she burn in a day ?(1 cal. = 4.2 J)

iii. What is the largest practical unit of energy ? Ans; 80x 9.8x 10x5/4.2= 9333.3cal

24. Rohit and Suresh were going to the market when they spotted a man who left a black bag in the corner of stall and ran away. They went near it and heard some ticking sound coming from it. They immediately called police and alerted the people nearby. By their alertness, a major tragedy was averted.

i. What qualities of Rohit and Suresh do you appreciate ?ii. A bomb at rest explodes into 2 fragments of mass 3.0 kg and 1.0 kg. The total K.E

of fragments is 6 X 104 J. Calculate the K.E of bigger fragmentiii. In which type of collision, elastic or inelastic, momentum is conserved ?

Ans; E1 +E2 = 1/3iv. E1 +E2 = 6 x 104J E1= 1.5 x 10 4J

25. Ravi used to live in a remote village of Rajasthan which didn’t have electricity. He was a good student and studied very hard to become an engineer in spite of all hardships. While studying, he came to know that solar energy can be converted to electrical energy by using specially designed devices. He went to his village and discussed it with villagers. He also told them that Govt. also gives subsidy for using solar devices. All the villagers agreed and they contacted the Govt officials who obliged their request and the village became the model village which used solar energy for electricity.

i) What can you say about Ravi ?ii) If direct solar energy is incident on the horizontal surface at an average rate of

200 watt per square meter and 20% of this energy can be converted to use

electrical energy, then how much area is needed to supply 8 KW of electrical energy ?

iii) Why is solar energy a better source of energy ? Ans: El energy req= 8000w area= 8000/40 = 200sq m

Section E

5 MARKS QUESTIONS

1. a)State law of conservation of energy. Prove it for free fall. Draw a graph showing the variation of potential energy and kinetic energy with respect to height of a free fall under gravitational force.

b)The bob of a pendulum is released from a height ‘h’. Find its kinetic energy when it crosses the mean position.

2a) What is elastic collision? Write the properties. Show that in case of one dimensional elastic collision of two bodies, the relative velocity of separation after the collision is equal to the relative velocity of approach before the collision.

b) What will happen when? a. A heavy body collides with a light mass at rest.b. A light body collides with a heavy mass at rest.

3a)Derive an expression for the velocity of the two masses m1and m2 moving with speeds u1

and u2 undergoing elastic collision in one dimension.

b). A mass m moving with a speed u collides with a similar mass m at rest, elastically and obliquely. Prove that they will move in directions making an angle π2 with each other.

4 Derive the expression for the potential energy of stretched spring.c. The potential energy of a spring when stretched through a distance x is 25 J.

What is the amount of work done on the same spring so as to stretch it by an additional distance 5x ?

5 a).Draw a plot of spring force versus displacement X. Hence find an expression for the P.E of an elastic stretched spring.

b) Prove that bodies of identical masses exchange their velocities after head-on elastic collision.

6 State work-energy theorem. Prove it for a variable forceb) Two bodied m1 and m2 (m1>m2) have equal kinetic energies. Which will have more momentum?

7 What is a conservative force ? Prove that gravitational force is conservative, while frictional force is non-conservative.

b) What is the work done to change the velocity of a body of mas 2kg from 5m/s to 2m/s.8 Work done can be +ve , -ve and zero .Explain it with examples.

a. A bullet losses 19% of its kinetic energy when passes through an obstacle. What is the percentage change in its speed ?

Ans.: Reduced by 10%9 A) Define Power? Show that power is the dot product of force and velocity.

B) What should be the power of an engine required to lift 90metric tonnes of coal per hour from a depth of 200m?Ans.: 5000 J/s

10 Explain the difference between conservative and non conservative forces.a. Show that gravitational force is a conservative force

1. Useful power = Wt = mgh

t = 1000 x 9.8 x1003600 = 272.22 W

Η = Useful powerActual power OR 0.9 = 272.22

Actual power

Actual power = 272.22 x10

9 = 302.47 W

Section E

MARKS QUESTIONS

25. a)State law of conservation of energy. Prove it for free fall. Draw a graph showing the variation of potential energy and kinetic energy with respect to height of a free fall under gravitational force.

b)The bob of a pendulum is released from a height ‘h’. Find its kinetic energy when it crosses the mean position.

26. a) What is elastic collision? Write the properties. Show that in case of one dimensional elastic collision of two bodies, the relative velocity of separation after the collision is equal to the relative velocity of approach before the collision.b) What will happen when?

a. A heavy body collides with a light mass at rest.b. A light body collides with a heavy mass at rest.

27. a)Derive an expression for the velocity of the two masses m1and m2 moving with speeds u1 and u2 undergoing elastic collision in one dimension.

b). A mass m moving with a speed u collides with a similar mass m at rest, elastically and obliquely. Prove that they will move in directions making an angle π2 with each other.

28. Derive the expression for the potential energy of stretched spring.a. The potential energy of a spring when stretched through a distance x is 25 J. What

is the amount of work done on the same spring so as to stretch it by an additional distance 5x ?

29. a).Draw a plot of spring force versus displacement X. Hence find an expression for the P.E of an elastic stretched spring.

c) Prove that bodies of identical masses exchange their velocities after head-on elastic collision.

30. State work-energy theorem. Prove it for a variable forceb) Two bodied m1 and m2 (m1>m2) have equal kinetic energies. Which will have more momentum?

31. What is a conservative force ? Prove that gravitational force is conservative, while frictional force is non-conservative.b) What is the work done to change the velocity of a body of mas 2kg from 5m/s to 2m/s.

32. Work done can be +ve , -ve and zero .Explain it with examples.a. A bullet losses 19% of its kinetic energy when passes through an obstacle. What

is the percentage change in its speed ? Ans.: Reduced by 10%

33. A) Define Power? Show that power is the dot product of force and velocity.B) What should be the power of an engine required to lift 90metric tonnes of coal per hour from a depth of 200m?Ans.: 5000 J/s

34. Explain the difference between conservative and non conservative forces.

Show that gravitational force is a conservative force

HOT’s

Q1.A light rod of length L can revolve in a vertical circle around point .The rod carries two equal masses of mass ‘m’ each such that one mass is connected at the one end of the rod and the second mass is secured at the middle of the rods’’ is the velocity imparted to the end P to deflect the rod to the horizontal position. Again mass ‘m’ in the middle of the rod is removed and mass at end P is doubled. Now ‘V’ is the Velocity imparted t end P to deflect it to the horizontal position. Find the ratio V/u .

According to principle of conservation of energy.

First case, 1/2mu2 + ½ m(u/2)2 = mgL + mg L/2

U = (12 gL/5)1/2

Second case, ½(2m)v2 = 2mgL

V = (2gL)1/2

V/u = (5/6)1/2

Q2.A stone is tied to a string of length L is whirled in a vertical circle with the other end of string at the centre .At a certain instant of time the stone is at its lowest position and has a speed u .Find the magnitude of change in velocity as it reaches a position where string is horizontal.

According t principle of conservation of energy,

1/2mv 2 + mgL = 1/2mu2

v = (u2 – 2gL)1/2

Q3.Abus is moving along a straight horizontal road with as peed v. If the coefficient of friction between the tyres and the road is μ ,find the shortest distance in which the car can be stopped.

Let distance = s

Frictional force = μmg

Work done against frictional force = w

W = (μmg)s

Initial KE of bus = 1/2mv2

From conservation of energy,W = KE

(μmg)s= 1/2mv2

s = v2/2 μg

Q4.Partocle A makes perfectly elastic collision with another particle B at rest at rest. They fly apart in opposite direction with equal speeds. Find the ratio of their masses mA/mB

(mA-mB) u1 /mA + mB = - 2mAu1/(mA +mB)

mA/mB = 1/3

Q5.What are the essential conditions required to transfer maximum Kinetic energy during collision?

1.Perfect elastic collision

2.masses of both the particles undergoing collision must be equal

3.collision should be on a rest body

4.head on collision.

Q6.A ball of 0.2kg makes an elastic head on collision with a ball of unknown mass that is initially at rest. If the 0.2 kg ball rebounds at one forth of its original speed what is the mass of the other ball?

According t law of conservation of momentum,

m1u1 = m1v1 + m2v2

m2v2 =m1(u1 – v1)--------------(1)

According to law of conservation of energy,

1/2 m1u12 = 1/2m1v1

2+1/2 m2v22

m2v22 =m1(u1

2 – v12)---------(2)

squaring (1) and dividing by(2)

m2v22 / m2v2

2 = m1(u1 – v1) / m1(u12 – v1

2)

m2 = m1(u1 – v1)2 / m1(u12 – v1

2)

m2 = m1 (u1 – v1)/(u1+v1)

=0.2 x (5u1/4)/(3u1/4)

=0.2 x5/3

=1/3 kg

Q7. Find the useful power of the engine which is used in pumping 24000litres of water per minute from a well 15 m deep to the surface. If 40% of the power is wasted , find the total power of the engine. If density of water is 1kg/litre. 3

Volume of water to be lifted = 24000 litre/min

=24000lr/60 s = 400 li/s

mass of water lifted per second = volume x density

=400x 1 = 400 kg

Distance S = 15 m

Useful power of engine = W/t = mg S/t =400 x 9.8 x 15/1= 58800 watts

Power wasted = 40%

Useful power = 60%

Total power required for engine = 58800 x 100/60

=98000 watt

=98K watts.

Q8.Find the power of an engine which can travel at the rate of 36 km/hr up an incline of 1 in 100,the mass of the engine and the load being 100 tonnes and the resistance due to friction being 100N per tones. 3

Given m = 100tonnes =100 x 1000kg

V = 36 km/hr = 10m/s

Resistance of motion = (mgsinθ + f)

=100 x 1000 x 9.8 x 1/100 + 100 x 1000 N

= 19800N

power of the engine = total resistance overcome x speed

=19800 x10 = 198KW

Q9.A light rigid rod of length L has a bob of mass M attached to one of its end just like a simple pendulum. Find the speed at the lowest point when it is inverted and released.

2

Potential energy with respect to lowest point = Mg(2L)

From conservation of energy,1/2 Mv2 = 2MgL

V = 2 √gL

Q10.A vehicle of mass ’m’ is accelerated on a horizontal frictionless road under a force changing its velocity from u to v in distance s. if a constant power P is given by the engine of the vehicle, find the value of v.

P = f x v = m (dv/dt) v

V2 dv = p/m vdt = p/m ds

Integrate,

v3 – u3 = 3ps/m

v = (3ps/m - u3) 1/3

NUMERICALS( LEVEL 1)

2. A body of mass 10 kg is released from a height 10m above the ground. What is its kinetic energy and potential energy at a point when it completes half way. Ans; KE =PE=10X 5X10 =500J

3. The linear momentum of a body is increased by 10%.what is the percentage change in kinetic energy? Ans:21%

4. A body of mass 2kg is thrown upward with a velocity 10m/s.a. 1.Is it possible for the body to have potential energy 150J?Justifyb. 2.How high it will rise?

AnsS; NO, H=U2/2g=100/2X10=5m

5. A body ‘A’ of mass m moving with a velocity v hits a body ‘B’ of mass m at rest. Find the velocity of A and B after collision? Ans; vel of A=0 vel of B =v

6. Two springs A and B with cnstants kA and kB (kA >kB)are given.In which of the springs more work is to be done if

a) They are stretched by the same amountb) They are stretched by the same force.

Ans: 1. W= ½ kx2

WA

/WB

= kA/kB

F = _kx WA/WB=kB/kA

NUMERICALS( LEVEL 2)

7. A body of mass 10 kg is released from a height 10m above the ground. What is its kinetic energy and potential energy at a point when it completes half way. Ans; KE =PE=10X 5X10 =500J

8. The linear momentum of a body is increased by 10%.what is the percentage change in kinetic energy? Ans:21%

9. A body of mass 2kg is thrown upward with a velocity 10m/s.a. 1.Is it possible for the body to have potential energy 150J?Justifyb. 2.How high it will rise?

Ans ; NO, H=U2/2g=100/2X10=5m10. A body ‘A’ of mass m moving with a velocity v hits a body ‘B’ of mass m at rest. Find

the velocity of A and B after collision? Ans; vel of A=0 vel of B =v

11. Two springs A and B with cnstants kA and kB (kA >kB)are given.In which of the springs more work is to be done if

c) They are stretched by the same amountd) They are stretched by the same force.

Ans: 1. W= ½ kx2

WA

/WB

= kA/kB

F = _kx WA/WB=kB/kA

12. A bullet of mass 20g moving with a velocity200m/s can penetrate into a fixed block of wood through a distance of 2cm.What is the resistance offered by the block to the bullet?

½ mv2 = R x d R –resistance and d- distanceR= mv2/2d = 2 X 10 4 N

13. 2.A boy of mass 50 Kg climbs with constant speed, a vertical rope 6m in 10 seconds. How much work does the boy perform? What is his power output during the climb?

W = F X d = 50 X 10 x 6 = 3.0 x 103 JP = w/t = 3 x 10 3/10 = 300W

14. A running man has half the kinetic energy that a boy of half his mass has.the man speeds up by 1m/s and then has the same kinetic energy on the boy. What were the original speeds of the man and the boy?

½ m v2 = ½ x1/2 xm/2 vb2

½ m (v +1) 2=1/2 m/2 vb2

V = 2.41m/s , vb = 4.82m/s15. a)Can a body have momentum without energy. Justify

b .Can body have energy without momentum. Justify Ans:a) No b) Yes eg: a body having potential energy alone

16. 5.A cord is used to lower vertically a block of mass m ,a distance d with a constant downward acceleration of g/4.Calculate the work done by the cord on the block.

Mg – T = maT = 3mg/4W = F X d xcos 180 = - 3mgd/4

LEVEL 3

Q1.A man of mass ’M’ is standing at a height ‘h’ throws a ball of mass ‘m’

vertically down with a speed ‘v’. Assuming no gravity, what is the distance

of man above the ground when mass reaches the floor?

Using law of conservation of momentum velocity of man is given by

MV = mv

V = mv/M

Time taken by ball to reach ground is t = h/v

Change in the distance of man = v t

= (mv/M) x h/v

=mh/M

Total distance of man from ground = h + mh/M

= h(1 + m/M)

=h ( M+m)/M

Q2.An object of mass 40 kg and having velocity 4m/s collides with another object of mass 60 kg having velocity 2m/s. Since the collision is perfectly inelastic ,what is the loss of energy?

Let v = (m1u1 + m2u2)/(m1+m2)

=(40x4 + 60x2)/(40+60)

=2.8 m/s

Loss of Kinetic Energy = Initial KE – Final KE

= ½ (m1u12 + m2 u2

2) – ½ (m1 +m2) v2

=1/2(40 x 16 + 60x4)-1/2(100)2.8x2.8

=48 J

Q3.A car of mass M is running with an acceleration ‘a’ along a straight

road If velocity of car was ‘v’ and frictional force is ‘f’ find the rate of

work done? 1

P = F x v = (M a + f) v

Q4.A car drives along smooth straight level road by an engine giving constant power. How is the velocity of car related to time?

P = F x v = ma x v = m dv/dt v

v dv= P/m dt

Integrate, v2 = P/m t

v2 α t

v α √ t

Q5.A screw jack of pitch 5mm is used to lift the tyre of a vehicle of load 200 kg with the help of a handle of useful length 1/2m.Neglecting the frictional force between screw and nut of the jack find the least force required to raise the load.

According to principle of conservation of energy,

Work done in one rotation = work done against gravity

F x 2п r = 200 x 10 x 5 x 10-3

( Fx2 п xl = mg x pitch)

F = 200 x10 x 5 x 10-3 x 2 /2 п

= 10 /3.14 = 3.18 N

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