Momentum and impulse: Grade 12 Past Paper Questions

A car of mass 1 600 kg travelling to the right at 80 km·h⁻¹ runs into the back of a stationary bakkie of unknown mass. The two vehicles stick together and move to the right at 6 m·s⁻¹. 4.1 Convert 80 km·h⁻¹ to m·s⁻¹. 4.2 Calculate the change in momentum of the car. 4.3 Write down the magnitude and direction of the change in momentum of the bakkie. 4.4 State the principle of conservation of linear momentum in words. 4.5 Calculate the mass of the bakkie.

Two trolleys, A and B, of masses 1,5 kg and 2 kg respectively, are held in a stationary position on a straight, horizontal, frictionless track, with a compressed spring between them. The trolleys are released and the spring takes t seconds to return to its natural length. The spring then falls to the ground. Trolley A moves to the left, while trolley B moves to the right and then up a frictionless inclined plane, rising to a maximum vertical height of 1,5 m. Ignore the rotational effects of the wheels. 4.1 Write down the principle of conservation of mechanical energy in words. 4.2 Calculate the speed of trolley B at the bottom of the inclined plane. 4.3 For the t seconds that the spring takes to return to its natural length: 4.3.1 Calculate the change in momentum of trolley B. 4.3.2 Write down the change in momentum of trolley A. 4.4 Calculate the speed of trolley A after t seconds.

Two trolleys A and B of mass 3,2 kg and 2,6 kg respectively are held at rest on a straight horizontal, frictionless track, with a compressed spring between them. After the trolleys are released, the spring extends to its natural length and then falls onto the track. Trolley A now moves with a constant velocity of 0,4 m·s⁻¹ to the left, while trolley B moves with a constant unknown velocity to the right. Trolley B reaches the end of the track after 1,3 s. 4.1 State the principle of conservation of linear momentum in words. 4.2 Calculate the distance travelled by trolley B in 1,3 s. The average force exerted by the extended spring on each trolley while they were in contact with the spring was 4,2 N. 4.3 Calculate the time it took the spring to extend to its natural length. 4.4 Trolley B is now replaced by trolley C, which has a larger mass. The same compressed spring is placed between trolleys A and C. The trolleys are then released. The average force exerted by the extended spring on the trolleys remains at 4,2 N for the same period of time as calculated in 4.3. How does the magnitude of the velocity of trolley C compare to the magnitude of the velocity of trolley B after the spring has fallen to the track? Write only GREATER THAN, LESS THAN or EQUAL TO. Explain the answer.

Trolley A of mass 7,2 kg moves to the right at 0,4 m·s⁻¹ in a straight line on a horizontal floor. It collides with a stationary trolley B of mass 5,3 kg. After the collision, the trolleys lock together and move to the right. Ignore any frictional effects. 4.1 State the principle of conservation of linear momentum in words. 4.2 Calculate the magnitude of the: 4.2.1 Velocity of the trolleys immediately after the collision. 4.2.2 Average net force exerted by trolley A on trolley B during the collision, if the collision time is 0,02 s.

Car A of mass 900 kg is stationary at a traffic light when it is hit from behind by Car B, of mass 1100 kg, travelling at 19 m·s⁻¹ to the right. Immediately after the collision, Car A moves to the right at 10 m·s⁻¹. 4.1 State the law of conservation of linear momentum in words. 4.2 Calculate the velocity of car B immediately after the collision. 4.3 "Modern cars are designed to partially crumple on impact. A crumple zone is a specially designed part of a motor vehicle that is designed to deform or collapse during a collision." Explain how crumple zones are used as a safety measure in motor vehicles. 4.4 Determine, by means of a calculation, whether the collision between car A and car B is elastic or inelastic. 4.5 A traffic officer arrives at the accident scene and makes the following observation: "In a head-on collision involving two cars of different masses, the risk of passenger injury in the heavier car is lower than in the lighter car." Use physics principles to explain the observation made by the traffic officer.

A bullet of mass 6 g is shot horizontally into a 194 g wooden block, which is at rest on a horizontal surface. The bullet hits the block with a velocity of 200 m·s⁻¹ and remains stuck in the block. Ignore the effects of friction. 4.1 State the principle of conservation of momentum in words. 4.2 Calculate the speed of the block-bullet system immediately after the bullet struck the block. Immediately after the impact, the block-bullet system enters a rough section PQ, which is 5 m long, before coming to rest. 4.3 Calculate the acceleration of the block-bullet system. 4.4 A box, of mass 60 kg, slides down a rough incline which makes an angle of 25° with the horizontal. The box experiences a constant frictional force of 180 N. 4.4.1 Draw a free-body diagram showing all the forces acting on the box. 4.4.2 Write down the name of the force which does zero work on the box.

A ball X, of mass 10 kg, is moving eastwards with a velocity of 2 m·s⁻¹. It collides elastically with another ball, Y, of mass 2 kg which was moving with an unknown velocity vY. Immediately after the collision, ball X comes to rest and ball Y moves eastwards with a kinetic energy of 36 J. Ignore friction. 4.1 Explain the meaning of the term elastic collision. 4.2 Calculate velocity vY. The balls were in contact with each other for 0,1 s during the collision. 4.3 Calculate the magnitude of the force that ball X exerted on ball Y during the collision.

A 70 kg gymnastic dancer jumped in the air and landed her left foot on the floor at 8 m·s⁻¹. She slid and came to a complete stop after 0,6 seconds. 4.1 Define the term impulse in words. 4.2 Calculate the dancer's change in momentum. 4.3 Determine the net force which the floor exerts on the dancer's foot. 4.4 What is the effect on the magnitude of the force which the floor exerts on the dancer's foot if she lands in a shorter period? Choose from: Increases, Decreases or Remains the same. Use relevant laws in physics to explain your answer.

Ball A and ball B move towards each other along a horizontal surface. Ball B has a mass of 0,3 kg and an initial speed of 15 m·s⁻¹. The balls collide. The vector shown represents the change in momentum of ball A: Δp = 2,4 kg·m·s⁻¹. Ignore the effects of friction. 4.1 State the principle of conservation of linear momentum in words. 4.2 What was the initial direction of ball A? Choose from LEFT or RIGHT. 4.3 Calculate the velocity of ball B after the collision.

Trolley A of mass 1,5 kg is at rest on a frictionless horizontal surface. A second trolley B, of mass 2 kg, travelling horizontally at a constant speed v, collides with trolley A. The trolleys stick together and move at a constant velocity to the right, covering a distance of 0,8 m in 2 s. Ignore all frictional and rotational effects. 4.1 State the principle of conservation of linear momentum in words. 4.2 Calculate speed v with which trolley B moves before the collision. 4.3 Is the collision elastic or inelastic? 4.4 During another collision, trolley B exerts a greater force on trolley A and the change in momentum of trolley A is the same as before. How is the time for the collision affected? Choose from INCREASES, DECREASES or REMAINS THE SAME. Write down a relevant equation that supports the answer.

A boy, of mass 60 kg, on ice skates, is stationary on a frictionless surface. He throws an object, of mass 4 kg, at 3 m·s⁻¹ horizontally in the westerly direction, as shown in the diagram below. At the instant the object leaves the boy's hand, the boy starts moving. Ignore the effects of friction. 4.1 In which direction does the boy move? Write down only EAST or WEST. 4.2 Name and state the law which explains the direction in which the boy experiences a force when he throws the object. 4.3 Calculate the speed of the boy immediately after the object leaves his hand. 4.4 How will the answer to QUESTION 4.3 be affected if: 4.4.1 The boy throws the object at a higher velocity in the same direction. Choose from: INCREASES, DECREASES or REMAINS THE SAME. 4.4.2 The boy throws the object of double the mass at the same velocity. Choose from: INCREASES, DECREASES or REMAINS THE SAME. 4.4.3 Explain the answer to QUESTION 4.4.2.

QUESTION 4 Trolley X of mass 1,2 kg travels at 8 m·s⁻¹ east and collides with trolley Y of mass 0,5 kg which is initially at rest. Ignore all frictional effects. The velocity-time graph below shows the velocity of trolley X before, during and after the collision with trolley Y. 4.1 State the principle of conservation of linear momentum. 4.2 Calculate the magnitude of the: 4.2.1 Velocity of trolley Y immediately after the collision. 4.2.2 Average net force that trolley X exerts on trolley Y during the collision. 4.3 Is the collision ELASTIC or INELASTIC? Explain the answer by means of suitable calculations.

QUESTION 4: A bullet with a mass of 300 g is fired horizontally with a velocity of 340 m·s⁻¹ to the right toward a stationary wooden block of mass 10 kg. The bullet embeds itself in the block. The combined bullet-block system then moves together across a rough horizontal surface from point A to point B in three-quarters of a second, as shown in the diagram below. The bullet-block system comes to a standstill when it reaches point B. 4.1 Calculate the momentum of the bullet before the collision. 4.2 Calculate the velocity of the bullet-block system immediately after the collision. 4.3 Calculate the average force exerted by the rough surface on the bullet-block system during the given time interval. 4.4 Sketch a labelled vector diagram (not to scale) to illustrate the relationship among the initial momentum (pᵢ), final momentum (p_f) and change in momentum (Δp) for the bullet.

1.4 The vector diagram below shows the initial momentum (p₁), the final momentum (p₂) and the change in momentum (Δp) for a car that moved on a straight horizontal road. Which ONE of the following sketch graphs correctly shows the momentum of the car for the time the car moved on the road? (four sketch graphs of momentum versus time, labelled A to D). 1.5 A stone of mass m is dropped from a height h above the ground. Ignore the effects of air friction. Which ONE of the following combinations in the table below correctly represents the kinetic energy and the total mechanical energy of the stone at the instant the stone has fallen through a distance of ¼h? A. Kinetic energy ¾mgh, total mechanical energy ¼mgh. B. Kinetic energy ¼mgh, total mechanical energy ¾mgh. C. Kinetic energy ¾mgh, total mechanical energy mgh. D. Kinetic energy ¼mgh, total mechanical energy mgh.

1.3 A ball moving horizontally has constant momentum p and kinetic energy K. The ball collides with a wall and bounces back horizontally. Immediately after the collision, the ball has momentum ½p. The mass of the ball remains constant. Which ONE of the following is the kinetic energy of the ball immediately after the collision? A. ¼K. B. ½K. C. 2K. D. 4K. 1.4 A force F acts on a box as the box moves from rest down a rough incline at a constant acceleration. The force is parallel to the incline, as shown in the diagram below. Choose the option that correctly completes the following statement. The work done by the gravitational force is … the work done by the frictional force and the work done by F. A. Equal to the sum of. B. Less than the sum of. C. Greater than the sum of. D. Equal to the difference between.

1.1 An astronaut with a mass of 70 kg is on a planet where his weight is 550 N. The gravitational acceleration on the planet is ... m·s⁻². A. 7,86. B. 0,13. C. 38 500. 1.2 A ball of mass m travelling to the right at velocity v strikes a wall and rebounds to the left at velocity 0,25v. The change in momentum of the ball is ... A. 0,75mv left. B. 1,25mv left. C. 0,75mv right. D. 1,25mv right. 1.3 A girl throws a ball upwards. Which ONE of the following combinations give the directions of the ball's velocity, acceleration, and the net force that the ball experiences as it travels upwards just after leaving the girl's hand?

1.3 Two blocks, P and Q, of masses m₁ and m₂ respectively, are held at rest on a frictionless horizontal floor with a compressed spring between them. When the blocks are released and the spring drops to the floor, block Q moves to the right with velocity v. Which ONE of the following represents the momentum of block P after the blocks are released? A. m₁v to the right. B. m₂v to the right. C. m₁v to the left. D. m₂v to the left. 1.4 The magnitude of the gravitational force that spheres X and Y exert on each other is F. The mass of sphere X is now doubled while the mass of sphere Y and the distance between the centres of the spheres remain the same. Which ONE of the following combinations is correct for the magnitude of the forces that the spheres now exert on each other? A. Force that X exerts on Y is F; force that Y exerts on X is F. B. Force that X exerts on Y is F; force that Y exerts on X is 2F. C. Force that X exerts on Y is 2F; force that Y exerts on X is F. D. Force that X exerts on Y is 2F; force that Y exerts on X is 2F.

1.1 Which ONE of the following physical quantities is the rate of change of momentum? A. Impulse. B. Acceleration. C. Power. D. Force. 1.2 An object is dropped from the top of a tall building. After time t, the object's momentum is p. What will the momentum of the object be after time 2t? Ignore the effect of air friction. B. p. C. 2p. D. 3p. 1.3 A boy pushes a heavy box across a rough floor with a constant force of 250 N. The box experiences a constant frictional force of 50 N while it is moving. The magnitude of the force exerted by the box on the boy is ... A. 50 N. B. 200 N. C. 250 N. D. 300 N.

1.1 The physical quantity which is a quantitative measure of the resistance of an object to any change in its state of rest or motion is called ... A. Weight. B. Acceleration. C. Mass. D. Friction. 1.2 The magnitude of the gravitational acceleration on Earth is g. What will the value of the gravitational acceleration be on planet X, which has the same mass as Earth, but half the radius? A. ¼g. B. ½g. C. 2g. D. 4g. 1.3 Which one of the following best describes an inelastic collision? A. Both momentum and kinetic energy are conserved. B. Total kinetic energy is not conserved but total linear momentum is conserved. C. Neither kinetic energy nor momentum are conserved. D. Kinetic energy is conserved but total linear momentum is not conserved.

1.1 Which ONE of the following is NOT TRUE about the frictional force? A. Is proportional to the applied force. B. Is proportional to the normal force. C. Is independent of the area of contact. D. Is independent of the velocity of motion. 1.2 A ball is thrown vertically upwards. Which ONE of the following combinations of physical quantities of the ball have non-zero values at its highest point? Ignore the effects of air friction. A. Kinetic energy and time. B. Acceleration and weight. C. Displacement and momentum. D. Potential energy and velocity. 1.3 Which ONE of the following is equal to the rate of change of momentum? A. FΔt. B. Δp. C. ma. D. p.

A ball with an unknown mass, m, is thrown horizontally due east towards a wall, and it strikes the wall at a velocity of 36 km·h⁻¹ and rebounds back off the wall at an unknown velocity. Diagrams show the initial momentum (4 kg·m·s⁻¹) and the change in momentum (5,2 kg·m·s⁻¹) of the ball. 5.1 Describe linear momentum. 5.2 Calculate the: 5.2.1 Mass of the ball. 5.2.2 Velocity at which the ball leaves the wall after contact. The letters A to D in the table below represent four organic compounds from different homologous series. Use the table to answer the questions that follow. 6.1 Define homologous series. 6.2 Write down the letter(s) that represent(s) each of the following: 6.2.1 Compound produced during a condensation reaction. 6.2.2 Functional isomer of propanal.

1.4 A ball is thrown vertically upwards into the air. Ignore the effects of air friction. The net force acting on the ball when the ball is at its highest point is ... A. Zero. B. Equal to the weight of the ball. C. Less than the weight of the ball. D. Greater than the weight of the ball. 1.5 Which ONE of the following statements is always true for inelastic collisions in an isolated system? A. Both momentum and kinetic energy are conserved. B. Both momentum and kinetic energy are not conserved. C. Momentum is conserved, but kinetic energy is not conserved. D. Kinetic energy is conserved, but momentum is not conserved. 1.6 An object moving horizontally at a constant velocity suddenly encounters a rough horizontal surface. The object continues to move over this rough surface. Which ONE of the following statements is correct? The net work done on the object during the motion over the rough surface is ... A. Zero. B. Positive. C. Negative. D. Constant. 1.7 The hooter of a car emits sound of constant frequency as the car moves away from a stationary listener. Which ONE of the following properties of the sound heard by the listener will NOT change? A. Speed. B. Frequency.

1.3 The graph below shows how the momentum (p) of an object changes with time (t). During which ONE of the following time intervals, measured in seconds, is the magnitude of the net force acting on the object the greatest? A. 0 to 1. B. 1 to 2. C. 2 to 3. D. 3 to 4. 1.4 A ball is dropped from a height above a floor. The ball makes an elastic collision with the floor at time t₀ and bounces vertically upwards. Ignore air resistance. Which ONE of the following graphs shows how the total mechanical energy of the ball changes with time? (four sketch graphs of total mechanical energy versus time, labelled A to D).

4.3 On the same set of axes, sketch the velocity-time graphs of the motion of ball A and ball B until they reach the ground. Label the graphs A and B respectively. Clearly indicate the following on your graph: the initial velocities of both balls; the times at which the balls reach the ground as t₁ for ball A and t₂ for ball B. 4.4 Ball A bounces and reaches a certain height above the window. The collision of the ball and the ground is elastic. Sketch the position-time graph for ball A from the moment it was dropped until it reaches the top of the window after the ball bounced from the ground. Take the ground as zero reference. Clearly indicate the initial and final height of the ball on your graph. A 4 kg metal object slides to the right at a constant speed of 7 m·s⁻¹ and it collides with a 5 kg metal object moving towards it at the same speed. They collide at point X. The collision lasts 0,03 seconds after which they stick together and move in the same direction. Ignore the effects of friction. 5.1 State Newton's Second Law in terms of momentum in words. 5.2 Calculate the: 5.2.1 Velocity of the combined system after the collision. 5.2.2 Average net force that the 4 kg object exerts on the 5 kg object. 5.3 What would happen to the magnitude of the impulse if softer objects were used and the net force remains the same? Write only INCREASES, DECREASES or REMAINS THE SAME. Explain the answer.

1.4 Two trolleys A and B, of masses m₁ and m₂ respectively, are held at rest on a frictionless surface with a compressed spring between them. When the trolleys are released, the spring expands and drops. If the velocity of trolley A is now +v, what is the velocity of trolley B? 1.5 A motor lifts a load vertically upwards at a constant speed. Which ONE of the following combinations of the work done by the motor and the power dissipated by the motor is correct?

1.3 The velocity versus time sketch graph below is for the motion of a ball that is projected vertically upwards from the top of a building. The ball reached its greatest height above the ground at a certain time. Which point on the graph corresponds to this greatest height? A. P. B. Q. C. R. D. S. 1.4 Two hard objects collide inelastically in an isolated system. Which ONE of the following statements is correct for this collision? A. Both total momentum and total kinetic energy are conserved. B. Neither total momentum nor total kinetic energy is conserved. C. Total momentum is not conserved, but total kinetic energy is conserved. D. Total momentum is conserved, but total kinetic energy is not conserved. 1.5 Engine P has a greater maximum power output than engine Q. Which ONE of the following statements is correct when P and Q each operate at their maximum power output? A. Q does more work than P in the same amount of time. B. P and Q do the same amount of work in the same amount of time. C. P and Q do the same amount of work, but Q does it in a shorter time than P. D. P and Q do the same amount of work, but P does it in a shorter time than Q.

1.4 A person of mass M is moving to the left on a skateboard of mass m. The initial velocity of the person and the skateboard is v. The person then jumps off the skateboard and is stationary while the skateboard continues to move to the left. Which of the following expressions can be used to correctly calculate the speed of the skateboard after the person jumps off? A. (M+m)v/m. B. (Mv+mv)/m. C. mv/(M+m). D. (M−m)v/m. 1.5 An apple falls from a tree. Which of the following statements about the falling apple is TRUE? Ignore all effects of air friction. A. Total momentum is conserved. B. Total kinetic energy is conserved. C. The total mechanical energy is conserved. D. The gravitational potential energy is conserved. 1.6 An ambulance moves towards a stationary listener at a constant speed while emitting soundwaves with a wavelength of 0,72 m. The wavelength of a soundwave observed by the listener becomes ... A. Larger than 0,72 m. B. Smaller than 0,72 m. C. Equal to 0,72 m. D. Larger and then zero.

The box now passes point A on the incline at a speed of 4 m·s⁻¹ before passing point B, which is 15 m lower down the incline. 4.4.3 Calculate the kinetic energy of the box as it passes point A. 4.4.4 Calculate the magnitude of the resultant force acting on the box between point A and B. 4.4.5 State the work-energy theorem in words. 4.4.6 Use the work-energy theorem to calculate the speed of the box as it passes point B. A 200 W motor, operating at a certain efficiency, pulls a crate of mass 90 kg up a slope at a constant speed, taking 30 s to raise the crate from point X to Y of the slope. 5.1 Define the term power. 5.2 Calculate the: 5.2.1 Energy supplied by the motor to the crate in 30 s. 5.2.2 Gain in gravitational potential energy of the crate between X and Y. 5.2.3 Magnitude of the frictional force acting on the crate between X and Y.

1.4 A trolley with a mass m has momentum p. The kinetic energy of the trolley will be: A. pm. B. p/m. C. pm/2. D. p²/(2m). 1.5 An object is moved from rest in a straight line across a flat surface by a changing horizontal force. The changing force is plotted against the position of the object to produce the graph below. The work done on the object by the applied force from x = 0 m to x = 8 m is: A. 40 J. B. 80 J. C. 108 J. D. 125 J. 1.6 The reason why the observed pitch of the sound wave of an ambulance decreases as the ambulance moves away from a stationary observer is because the: A. amplitude of the sound wave increases. B. amplitude of the sound wave decreases. C. wavelength of the sound wave increases. D. wavelength of the sound wave decreases.

1.3 A 2 kg ball is moving horizontally at 2 m·s⁻¹ when it strikes a wall and rebounds at the same speed in the opposite direction. Which ONE of the following represents the magnitude of the change in momentum of the ball? A. 0 kg·m·s⁻¹. B. 4 kg·m·s⁻¹. C. 8 kg·m·s⁻¹. D. 16 kg·m·s⁻¹. 1.4 What is the IUPAC name of the ester shown below? A. Ethyl propanoate. B. Methyl propanoate. C. Methyl propanone. D. Butan-2-one. 1.5 Consider two organic compounds of the alkane group that have the same molecular formula but different boiling points. What is the cause of the difference in their boiling points? A. Absence of hydrogen bonding. B. Branching. C. Chain length. D. Functional group. 1.6 When but-1-ene reacts with hydrogen bromide (HBr), two structural isomers are produced. Which ONE correctly describes the IUPAC name of the major product and the type of reaction occurring? A. 1-bromobutane, substitution. B. 2-bromobutane, addition. C. 1-bromobutane, addition. D. 2-bromobutane, substitution.