111EquationChapter (Next) Section 1

Understanding inertia & Analysing momentum

Learning outcomes1. explain what inertia is2. relate mass to inertia3. give examples of situations involving inertia4. suggest ways to reduce the negative effects of inertia5. define the momentum of an object6. define momentum as the product of mass and velocity7. state the principle of conservation of momentum8. describe the applications of conservation of momentum9. solve problems involving momentum

Inertia

1. The inertia of an object is the tendency of the object to remain at rest, if it is at rest or of moving, to continue its uniform motion in a straight line.

2. For example,(a) In figure, when the bus moves forward suddenly, the feet of the

passenger are made to move forward. The inertia of his body tends to remain at rest. The inertia of his body tends to remain at rest. Hence, the passenger falls backward.

(b)

In figure, when the bus slows down suddenly, the feet of the passenger are brought to rest. The inertia of his body tends to continue moving forward. Hence, the passenger falls forward.

3. Newton’s first law of motion states that if the body at rest, it will remain at rest, If the body is moving, it keeps on moving at constant speed in a straight line unless acted upon by an external force.

Inertia and mass

1. When the mass of an object increases, the inertia of the object increases.2. For example,

(a) The pail with the sand is more difficult to start swigging because of its greater mass. The bigger the mass the greater its inertia. Therefore, the pail with sand tends to be at rest. (reluctance to move)

(b If both pails are swinging, the pail with sand

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Lesson 4

A

B

) will swing for a longer period of time. This is because bigger mass has bigger inertia, so the pail will continue to be in motion.reluctance to stop.

Application of Inertia

1 Drying wet umbrellaThe umbrella is rotated and stopped suddenly. Water droplets on the umbrella are removed because of the inertia of the droplets.

2 Pouring ketchup out the bottleWhen the bottle is jerked quickly and stopped suddenly, the inertia of the sauce causes the sauce to move downwards and out of the bottle.

3 Tightening the hammer head.When the wooden handle is knocked on a hard surface, the hammer head's large mass and large inertia will exhibit resistance to the change in its state of motion. Therefore, it continues to move even though the handle has stopped. In this way, the head can be tightened to the handle.

4 Running in a zig-zag pattern when chased by an elephant.The inertia of an elephant is large due to its mass. This makes it difficult for the elephant to change its direction suddenly.

5 Reducing the inertia of tankers.Tankers should be divided into smaller tanks to reduce the effects of inertia when they stop suddenly.

6 Reducing the movement of loads.A steel structure should be placed between the driver's seat and the load at the back of the lorry to prevent the load from being thrown forward.

7 Reducing injuries.Air bags prevent the driver and passenger from hitting the dashboard, steering wheel and mirrors during accidents.

Momentum

1. The momentum of an object is defined as the product of its mass and its velocity.

2. The SI unit for momentum is kg m s-1

3. Momentum is a vector quantity.4. Example

(a) What is the momentum of a 650 kg car moving at 5 m s-1?

(b) The figure below shows two objects, J and K moving towards a wall.

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C

D

Which object is easier to stop?

Principle of Conservation of Momentum

1. The principle of conservation of momentum states that the total momentum in the system is conserved provided that no external force acts on the system.

Elastic collision Inelastic collision Explosion

Two objects collide and move apart after a collision

Two object collide and move together after a collision

Two object move in opposite direction after an explosion

Kinetic energy is conserved Total kinetic energy of

objects before and after collision is equal.

Kinetic energy is not conserved

Total kinetic energy of objects before and after collision is not equal.

Kinetic energy is not conserved

Total kinetic energy of objects before and after collision is not equal.

Momentum is conserved Total momentum of objects before and after collision is equal Total energy of both objects is conservedFormula Formula Formula

Application of Principle of Conservation of Momentum

1. Rocket(a) A rocket carries fuel in the form of liquid oxygen and liquid hydrogen

which burns violently in the combustion chamber.(b) The gases produced are forced out through the exhaust at high velocity. (c) This creates a high momentum downwards and according to the principle of

conservation of momentum, the rocket gains a forward momentum, thus moving upwards with a high velocity.

2. Jet engine(a) A jet engine carries fuel in the form of kerosene and the

combustion of kerosene burns violently with compresses air in the combustion chamber.

(b) The hot gases formed are forced out of the exhaust at high velocity.

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E

F

(c) The ejected high-speed exhaust gases create a backward momentum. Based on the principle of conservation of momentum, the backward momentum creates a forward momentum for the engine. The plane thus flies forwards.

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Try it yourself1. Calculate the momentum of the following objects in kg m s-1.

(a) A tennis ball of mass 0.05 kg moving in a velocity of 90 km h-1.(b) A soccer ball of mass 400 g moving in a velocity of 12 m s-1.(c) A car of mass 900 kg moving in a velocity of 108 km h-1.(d) A bullet of mass 20 g moving in a velocity of 200 m s-1.

2. The following diagrams show several collisions. In each case, determine the unknown values.

(a)

(b)

(c)

(d)

(e)

3. An object of 4 kg, which is moving with a velocity of 5 m s-1, collides with another object of mass

, moving with a velocity of 2 m s-1 in the opposite direction. After the collision, the two objects coalesce and move in the same direction. What is the final velocity of the two objects?

4. An object with a mass of 2 kg, moving with a velocity of 5 m s -1 collides with another object

of mass 3 kg which is moving with a velocity of 2 m s-1 in the same direction as . After

collision, moves with a velocity of 3 m s-1 in its original direction. What is the velocity of , after collision?

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5. Trolley P has a mass of 2 kg and trolley Q has a mass of 3 kg. Both trolleys are placed on a horizontal surface. P is moving towards Q, which is at rest, with a constant velocity of v m s-1. After collision, P and Q stick together and move together. What is the final velocity of the two trolleys after collision in terms of v?

6. A bullet of 20 g is being fired from a rifle which weighs 3 kg. The rifle moves backwards with a velocity of 0.2 m s-1, while the bullet moves with 30 m s-1 away from the rifle. What is the total momentum of the rifle and the bullet (in kg m s-1) after the bullet is fired?

7. A girl of mass 30 kg and a boy of mass 50 kg stand on a smooth surface on a movable track. The boy pushes the girl and the girl moves with a velocity of 0.5 m s -1. How fast does the boy travel in the opposite direction?

8. A bullet of mass 20 g hits a target of mass 980 g and penetrates through it. At the time the bullet hits the target, the two of them move with a velocity of 4.0 m s -1. Calculate the velocity of the bullet before collision.

9. A bullet of mass 50 g is being fired from a rifle of mass M kg. After the shot is fired, the bullet travels in a velocity of 50 m s-1 while the rifle moves backwards with a velocity of 1.0 m s -1. What is the value of M?

10. A particle, P of mass 50 g moves in a velocity of v m s-1 collides with a particle, Q of mass 450 g. Particle Q is initially at rest. After collision, both particles stick together and move with the same velocity of 2.0 m s-1. What is the velocity, v before collision?

11. Diagram 1 shows a section of ticker tape when the tape is being pulled by a trolley of mass M. The trolley moves and collides with another trolley which is at rest and has a mass of 1.5 kg. Both trolleys stick together and move in the same velocity after collision.

Diagram 1

Determine the value of M.

12. A fisherman of mass 60 kg jump out from his little boat of mass 200 kg which is parked at a jetty. If the fisherman jumps up out with a velocity of 3 m s-1, calculate the velocity of the boat.

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13. A boy of mass 50 kg runs with a velocity of 5 m s-1 and jumps onto a trolley which is moving with a velocity of 1.5 m s-1 in the same direction as the boy. If the mass of the trolley is 20 kg, what is the final velocity of the trolley and the boy?

14. Diagram 2 shows a “trolley explosion” experiment. When the vertical pin is hammered, an “explosion” occurs and both trolleys move in the opposite direction towards the wall. Both trolleys hit the stopper at the same time.

Diagram 2

If the m ass of trolley A is 2 kg, what is the mass of trolley B?

15. Tick () the correct answer. (a) In an elastic collision:

¨ Total energy is conserved¨ Total momentum is conserved¨ Total kinetic energy is conserved

(b) In an inelastic collision¨ Total energy is conserved¨ Total momentum is conserved¨ Total kinetic energy is conserved

(c) In an explosion¨ Total energy is conserved¨ Total momentum is conserved¨ Total kinetic energy is conserved

16. When the mass of an object decreases,

A the energy of the object increases C the velocity of the object decreasesB the acceleration of the object increases D the inertia of the object decreases

17. The figure at the right shows an oil tanker in motion. The tanker takes five to ten kilometres to stop in an emergency.This situation happens due toA low resistance between the tanker and sea waterB strong currentC inertia of the tankerD large force acting on the tanker

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18. The figure shows two boys playing on swings. The mass of the first boy is 50 kg and the second is 30 kg.If the same magnitude of force is applied on both boys, which of them will be able to swing easily from rest? A The 30 kg boyB The 50 kg boyC No difference between two

19. The figure below shows the conditions of a boy carry two different pails. The boy can carry and move an empty pail easily. When the pail is fully filled with water, he faces difficulty to carry and move the pail.This is because the empty pail hasA a smaller inertiaB a smaller resistanceC a smaller friction to the surfaceD a smaller momentum

20. If you are sitting in a car, what will happen to you if the car suddenly accelerates?

A Remain stationary B Move up vertically C Surge forward D Fall backward

21. Momentum can be defined as

A mass displacement C mass accelerationB mass velocity D weight displacement

22. In an elastic collision, the following is conserved except

A total energy C total momentumB total potential energy D total kinetic energy

23. Calculate the momentum of a 20 000 kg aeroplane moving with velocity of 200 m s-1.

A 40 000 kg m s-1 C 400 000 kg m s-1

B 80 000 kg m s-1 D 4 000 000 kg m s-1

24. A bullet with mass of 20 g is fired from a 3 kg rifle with a velocity of 250 m s-1. What is the total momentum of the bullet and the rifle after explosion?

A 750 kg m s-1 B 60 kg m s-1 C 0 kg m s-1 D -5 kg m s-1

25. A 1000 kg car travelling at 15 m s-1 collides with a 100 kg motorcycle which is at rest. After the collision, both the car and motorcycle move together. What is their velocity after the collision?

A 1.50 m s-1 B 13.64 m s-1 C 136.30 m s-1 D 150.00 m s-1

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26. Car A of mass 600 kg moving at 10 m s-1 collides with car B of mass 1000 kg moving in the opposite direction. If both car move together after the accident at 4 m s-1 in the direction of car B, find the initial velocity of car B.

A 7.0m s-1 B -10.0 m s-1 C -12.4 m s-1 D 14.8 m s-1

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Past year question1. MRSM 2009 Paper 1 Question 5

Diagram 1.1 shows a frog of mass 200 g on a leaf of mass 50 g on the surface of a pond.Diagram 1.2 shows the frog leaping way from the leaf with a velocity of 5 m s-1.

Diagram 1.1 Diagram 1.2What is the recoil velocity of the leaf?

A - 0.05 m s-1 B - 0.20 m s-1 C - 5.00 m s-1 D - 20.00 m s-1

2. MRSM 2009 Paper 1 Question 6Which of the following statements will not reduce the negative effect of inertia for a car?A Using the air bag systemB Using bumpers of hard materialC Fixing a headrest at the seatD Wearing a seatbelt

3. MRSM 2010 Paper 1 Question 5Diagram 3 shows a Sumo wrestler with a mass of 350 kg.

Diagram 3What is the advantage of the wrestler being heavy?A He is more stableB He has a large gravityC He has a large momentumD He will exert a large impulsive force on impact

4. MRSM 2011 Paper 1 Question 5Diagram 4 shows two cars colliding

Diagram 4Which of following concepts explains the situation above?A Principle of conservation of momentumB Principle of conservation of energyC Equilibrium of Forces

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D Inertia5. MRSM 2012 Paper 1 Question 5

Diagram 5 shows two cars colliding

Diagram 5Which physical quantity is conserved after collision?

A Velocity B Momentum C Kinetic energy D Impulsive force

6. MRSM 2013 Paper 1 Question 7Which of the following vehicles takes the longest time to start moving?

Amass = 750 kg

Cmass = 250 kg

Bmass = 12 000 kg

Dmass = 5 000 kg

7. MRSM 2014 Paper 1 Question 8Diagram 7.1 shows a toy car A moving at velocity, u while toy car B is at rest. After collision both toy cars move together at velocity, v as shown in Diagram 7.2 Both car have the same mass.

u v

Toy car A Toy car B Toy car A Toy car BDiagram 7.1 Diagram 7.2

Which statement is correct?A The collision is an elastic collisionB The total momentum before and after collision are the sameC The total kinetic energy before and after the collision are the sameD The momentum of each toy car before and after collision are the same.

8. SBP 2009 Paper 1 Question 5Diagram 8 shows trolley A and B of the same mass on a frictionless plane. Trolley A moves and collides with the stationary trolley B.

Diagram 8Which of the following statements is true?A The collision is an elastic collisionB Both trolleys do not undergo changes in momentumC The total momentum before and after the collision is the same

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D The total kinetic energy before and after the collision is conserved

9. SBP 2010 Paper 1 Question 7Diagram 9 shows a ticker tape that was obtained from an experiment by using trolley A of mass 2 kg and a trolley B. Trolley A was released from one end of platform so that it moves downwards and collides with the stationary trolley B. After the collision they stick and move together. What is the mass of trolley B?

Diagram 9

A 0.5 kg B 1.0 kg C 1.5 kg D 2.0 kg

10. SBP 2011 Paper 1 Question 8Diagram 10 shows two trolleys, M and N of the same mass before and after collision.

Diagram 10Which is true about u and v?

A B C D

11. SBP 2011 Paper 1 Question 11Diagram 11 shows two students skating towards P.

Diagram 11What happens to the girl when the boy releases her hand?

A Stays stationary B Moves towards P C Moves towards Q

12. SBP 2012 Paper 1 Question 5Diagram 12(a) shows an empty bottle rolling when a train started to move forward. Diagram 12(b) shows the same empty bottle rolling in the opposite direction when the train stopped suddenly.

Diagram 12(a) Diagram 12(b)This situation is due to

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A Inertia B Impulse C Acceleration D Impulsive force

13. SBP 2012 Paper 1 Question 6Which of the following will produce the highest common velocity, v after collision? The trolleys are identical and of the same initial velocity.

Before collision After collisionA

B

C

D

14. SBP 2013 Paper 1 Question 6

Diagram 14 shows a man jumping out of a boat onto a jetty. he noticed that the boat moves backwards as he jumped.

Diagram 14Which of the following physics concepts is the best to explain the situation in Diagram 14?

A Inertia C Principle of conservation of energyB Impulsive force D Principle of conservation of momentum

15. SBP 2014 Paper 1 Question 4

Diagram 15 shows the fireman holding the hose needs the support of another fireman so that he does not fall backward, when water rushes out of hose with a very high speed and volume.

Diagram 15Which principle explains the situation above?

A Pascal principle C Principle of conservation of energyB Bernoulli principle D Principle of conservation of momentum

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16. SPM 2008 Paper 1 Question 6Diagram 16 shows two identical balls, P and Q, moving towards each other with a velocity of v and 2v respectively.The collision between the two balls is an elastic collision.

Diagram 16Which statement is correct about the elastic collision?A The momentum of ball P before the collision is equal to the momentum of ball Q before the

collisionB The total momentum before the collision is equal to the total momentum after the collisionC The kinetic energy of ball P before collision is equal to the kinetic energy of ball Q before the

collisionD The total kinetic energy before the collision is not equal to the total kinetic energy after the

collision.

17. SPM 2009 Paper 1 Question 5Diagram 17 shows the position of a plate before and after the table cloth is snatched away.

Diagram 17The plate remains stationary due to

A Inertia B impulse C momentum D linear motion

18. SPM 2009 Paper 1 Question 11A body stays stationary, or continues to move with a uniform velocity, unless there is an external force that changes its state of motion.Which law is explained by the above statement?A Newton’s first law of motionB Newton’s second law of motionC Newton’s third law of motion

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19. SPM 2010 Paper 1 Question 4Diagram 19 shows two identical wooden blocks, R and S, placed on trolleys P and Q respectively.

Diagram 19What happens to the wooden blocks R and S when trolley P collides with the stationary trolley Q?

R SA Pushed to the right Pushed to the rightB Pushed to the right Pushed to the leftC Pushed to the left Pushed to the leftD Pushed to the left Pushed to the right

20. SPM 2010 Paper 1 Question 10In which situation can the principle of conservation of momentum be applied?

A C

B D

21. SPM 2011 Paper 1 Question 5Diagram 21 shows three identical coins, P, Q and R, at rest on a horizontal plane.

Diagram 21What will happen when P collides with Q?

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P Q RA Moves Stationary StationaryB Stationary Stationary MovesC Moves Moves StationaryD Moves Stationary Moves

22. SPM 2012 Paper 1 Question 5Which phenomenon shows the effect of inertia?

A C

B D

23. SPM 2012 Paper 1 Question 7

Diagram 23 shows two trolleys before and after collision.

Diagram 23What is the velocity of both trolleys after collision?

A 0.60 m s-1 B 0.83 m s-1 C 1.20 m s-1 D 2.00 m s-1

24. SPM 2014 Paper 1 Question 4Diagram 24 shows a cat chasing a rat.

Diagram 24The inertia of the cat is bigger than the rat becauseA the size of the cat is bigger than the rateB the mass of the cat is bigger than the ratC the length of the cat it more than ratD the height of the cat is more than the rat

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