· web viewwhen they collide, the two vehicles become tightly locked together. (i) calculate the...

07 Momentum

330 minutes

330 marks

Q1. (a) The amount of damage caused when a car collides with a wall depends on the amount of energy transferred.

If the speed of a car doubles, the amount of energy transferred in a collision increasesfour times.

Explain, as fully as you can, why this is so.

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(b) The diagram shows a car and a lorry about to collide.

When they collide, the two vehicles become tightly locked together.

(i) Calculate the speed of the vehicles immediately after the collision.

(Show your working. There is no need to change to standard units.)

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Answer ....................................... km/h(6)

(ii) The collision between the car and the lorry is inelastic.

Explain, in terms of energy, what this means.

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(Total 10 marks)

Q2. (a) When an object is moving it is said to have momentum.Define momentum.

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(b) The diagram below shows one way of measuring the velocity of a bullet.

A bullet is fired into a block of wood suspended by a long thread.The bullet stops in the wooden block.The impact of the bullet makes the block swing.The velocity of the wooden block can be calculated from the distance it swings.

In one such experiment the block of wood and bullet had a velocity of 2 m/simmediately after impact. The mass of the bullet was 20 g and the mass of the wooden block 3.980 kg.

(i) Calculate the combined mass of the block of wood and bullet.

........................................................................... Mass ....................................(1)

(ii) Calculate the momentum of the block of wood and bullet immediately after impact.

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…...................................................................... Momentum ............................(3)

(iii) State the momentum of the bullet immediately before impact.

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(iv) Calculate the velocity of the bullet before impact.

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……................................................................. Velocity ........................... m/s(3)

(v) Calculate the kinetic energy of the block of wood and bullet immediately after impact.

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…….............................................................. Kinetic energy ......................... J(3)

(vi) The kinetic energy of the bullet before the impact was 1600 joules. This is much greater than the kinetic energy of the bullet and block just after the impact.What has happened to the rest of the energy?

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(Total 13 marks)

Q3. The drawing below shows two railway trucks A and B, moving in the same direction. TruckA, of mass 1500 kg, is initially moving at a speed of 8 m/s. Truck B, of mass 2000 kg, is initially

moving at a speed of 1 m/s.

Truck A catches up and collides with truck B. The two trucks become coupled together as shown in the diagram.

(a) Calculate:

(i) the initial momentum of truck A.

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......................................................... momentum ................................... kg m/s

(ii) the initial momentum of truck B.

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......................................................... momentum ................................... kg m/s

(iii) the total momentum of the trucks before the collision.

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................................................. total momentum ................................... kg m/s(6)

(b) Calculate the speed of the coupled trucks after the collision.

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(c) (i) How is the total kinetic energy of the trucks changed as a result of the collision?A calculated answer is not needed for full marks.

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(ii) State an energy transfer which accounts for part of the change in the total kinetic energy of the trucks during the collision.

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(iii) What would have been the effect on the change of total kinetic energy of the trucks if the collision had been more elastic?

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(Total 14 marks)

Q4. (a) How can the momentum of an object be calculated?

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(b) In a collision momentum is always conserved. What does this mean?

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(c) Two trolleys are placed on a frictionless runway as shown in the diagram below. Trolley A has a protruding pin, and trolley B is fitted with a piece of soft cork so that the trolleys will stick together after colliding.

Trolley A has a mass of 2 kg, and trolley B has a mass of 1 kg. Trolley B is stationary. Trolley A strikes trolley B at a speed of 6 m/s. Both trolleys then move to the right together.

(i) Calculate the speed at which trolleys A and B jointly move after the collision.

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(ii) Calculate the change in kinetic energy which occurs during the collision.

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(Total 12 marks)

Q5. The diagram below shows two balls on the bowling green. Ball A is moving with a velocity of 4 m/s, and is about to collide with ball B which is stationary. Both balls have a mass of1.5 kg.

After the collision both balls move to the right but the velocity of A is now 1 m/s.

(a) (i) Calculate the momentum of ball A just before the collision.

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Answer ...................... kg m/s(1)

(ii) What is the total momentum of balls A and B after the collision?

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Answer ....................... kg m/s(1)

(iii) Calculate the momentum of ball A just after the collision.

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Answer ....................... kg m/s(1)

(iv) Calculate the momentum of ball B just after the collision.

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Answer ....................... kg m/s(1)

(v) Calculate the velocity of ball B just after the collision.

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Answer ............................ m/s(1)

(b) Calculate the loss of kinetic energy in the collision.

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Answer ............................... J(3)

(Total 8 marks)

Q6. (a) The diagram shows a car being driven at 14 rn/s. The driver has forgotten to clear a thick layer of snow from the roof.

Which of the following has the smallest momentum? Draw a circle around your answer.

the car the driver the snow

Give a reason for your answer.

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(b) Seeing an obstacle in the road, the driver applies the car brakes. The car slows down in a straight line.

(i) Does the momentum of the car increase, decrease or stay the same?

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(ii) As the car slows down the snow starts to slide. In which direction will the snow start to slide, backwards, forwards or sideways?

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Give a reason for your choice of direction.

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(c) Draw a circle around the unit which can be used to measure momentum.

Nm J/s Ns(1)

(Total 7 marks)

Q7. (a) The picture shows two ice hockey players skating towards the puck. The players, travelling in opposite directions, collide, fall over and stop.

(i) Use the following equation and the data given in the box to calculate the momentum of player number 3 before the collision. Show clearly how you work out your answer and give the unit.

momentum = mass × velocity

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Momentum of player 3 = .......................................(3)

(ii) What is the momentum of player 4 just before the collision?

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(iii) The collision between the two players is not elastic. What is meant by an elasticcollision?

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(b) The pictures show what happened when someone tried to jump from a stationary rowing boat to a jetty.

Use the idea of momentum to explain why this happened.

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(c) The diagram shows one type of padded body protector which may be worn by a horse rider.

If the rider falls off the horse, the body protector reduces the chance of the rider being injured. Use the idea of momentum to explain why.

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(Total 10 marks)

Q8. The picture shows luggage which has been loaded onto a conveyor belt.

Each piece of luggage has a different mass.

Mass of A = 22 kg mass of B = l2 kg mass of C = 15 kg

(a) (i) What is the momentum of the luggage before the conveyor belt starts to move?

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(ii) When the conveyor belt is switched on the luggage moves with a constant speed. Which piece of luggage A, B or C has the most momentum?

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(iii) At one point the conveyor belt turns left. The luggage on the belt continues to move at a constant speed.

Does the momentum of the luggage change as it turns left with the conveyor belt?

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(b) Draw a circle around the unit which can be used to measure momentum.

J/s kg m/s Nm(1)

(Total 7 marks)

Q9. (a) What is the principle of conservation of momentum?

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(b) The diagram shows a simplified aircraft jet engine.

Adapted from GCSE Physics by Tom Duncan. John Murray (Publishers) Ltd.

(i) What is the function of the turbine?

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(ii) Explain how the engine produces a forward thrust.

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(c) During flight, air enters the engine at 175 m/s and leaves at 475 m/s. A forward thrust of 105 kN is produced.

Use the following equation to calculate the mass of air passing through the engine every second. (Ignore the mass of the burned fuel.)

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Mass of air = ............................................... kg(2)

(Total 9 marks)

Q10. (a) When two objects collide, and no other forces act, then conservation of momentumapplies.

(i) What does the term conservation of momentum mean?

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(ii) Apart from collisions and similar events, give another type of event in whichconservation of momentum applies.

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(iii) Write, in words, the equation which you need to use to calculate momentum.

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(iv) The diagram shows a straight and horizontal runway and two trolleys, X and Y, which can move on the runway.

X has a mass of 0.2 kg and its velocity is 1.2 m/s to the right. Y has a mass of 0.1 kg and is stationary. When X collides with Y they stick together.

Calculate the velocity of the trolleys after the collision.

Show clearly how you work out your answer and give the unit and direction.

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Velocity of the trolleys = ......................................................................(5)

(v) What assumption did you make in order to calculate your answer to part (a)(iv)?

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(b) Just before it hits a target, a bullet has a momentum of 5 kg m/s. It takes 0.00125 s for the target to stop the bullet.

Calculate the force, in newtons, needed to do this.

Write, in words, the equation that you will need to use and show clearly how you work out your answer.

Force = ................................................ newtons(3)

(Total 13 marks)

Q11. (a) The diagram shows a hammer which is just about to drive a nail into a block of wood.

The mass of the hammer is 0.75 kg and its velocity, just before it hits the nail, is 15.0 m/s downward. After hitting the nail, the hammer remains in contact with it for 0.1 s. After this time both the hammer and the nail have stopped moving.

(i) Write down the equation, in words, which you need to use to calculate momentum.

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(ii) What is the momentum of the hammer just before it hits the nail?

Show how you work out your answer and give the units and direction.

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Momentum = ...................................................................(3)

(iii) What is the change in momentum of the hammer during the time it is in contact with the nail?

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(iv) Write down an equation which connects change in momentum, force and time.

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(v) Calculate the force applied by the hammer to the nail.

Show how you work out your answer and give the unit.

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Force = ............................................................................(3)

(b) A magazine article states that:

“Wearing a seat belt can save your life in a car crash.”

Use your understanding of momentum to explain how this is correct.

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(Total 13 marks)

Q12. The roads were very icy. An accident was recorded by a security camera.

Car A was waiting at a road junction. Car B, travelling at 10 m/s, went into the back of car A. This reduced car B’s speed to 4 m/s and caused car A to move forward.

The total mass of car A was 1200 kg and the total mass of car B was 1500 kg.

(i) Write down the equation, in words, which you need to use to calculate momentum.

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(ii) Calculate the change in momentum of car B in this accident.

Show clearly how you work out your final answer and give the unit.

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Change in momentum = .........................................(3)

(iii) Use your knowledge of the conservation of momentum to calculate the speed, in m/s, of car A when it was moved forward in this accident.

Show clearly how you work out your final answer.

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Speed = ............................................................ m/s(3)

(Total 7 marks)

Q13. The diagram shows a small, radio-controlled, flying toy. A fan inside the toy pushes air downwards creating the lift force on the toy.

When the toy is hovering in mid-air, the fan is pushing 1.5 kg of air downwards every10 seconds. Before the toy is switched on, the air is stationary.

(a) Use the equations in the box to calculate the velocity of the air when the toy is hovering.


force =

Show clearly how you work out your answer.

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Velocity = ................................................. m/s(3)

(b) Explain why the toy accelerates upwards when the fan rotates faster.

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(c) The toy is not easy to control so it often falls to the ground.

Explain how the flexible polystyrene base helps to protect the toy from being damaged when it crashes into the ground.

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(Total 8 marks)

Q14. The diagram shows the forces on a small, radio-controlled, flying toy.

(a) (i) The mass of the toy is 0.06 kg.Gravitational field strength = 10 N/kg

Use the equation in the box to calculate the weight of the toy.

weight = mass × gravitational field strength

Show clearly how you work out your answer and give the unit.

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Weight = .................................................(3)

(ii) Complete the following sentence by drawing a ring around the correct line in the box.

When the toy is hovering stationary in mid-air, the lift force is

bigger than

the same as

smaller than

the weight of the toy.

(1)

(b) When the motor inside the toy is switched off, the toy starts to accelerate downwards.

(i) What does the word accelerate mean?

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(ii) What is the direction of the resultant force on the falling toy?

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(iii) Does the momentum of the toy increase, decrease or stay the same?

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(Total 8 marks)

Q15. In an experiment at an accident research laboratory, a car driven by remote control was crashed into the back of an identical stationary car. On impact the two cars joined together and

moved in a straight line.

(a) The graph shows how the velocity of the remote-controlled car changed during the experiment.

(i) How is the velocity of a car different from the speed of a car?

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(ii) Use the graph to calculate the distance travelled by the remote-controlled car before the collision.


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Distance = ............................................... m(2)

(iii) Draw, on the grid below, a graph to show how the velocity of the second car changed during the experiment.

(2)

(iv) The total momentum of the two cars was not conserved.

What does this statement mean?

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(b) The graph line shows how the force from a seat belt on a car driver changes during a collision.

Scientists at the accident research laboratory want to develop a seat belt that produces a constant force throughout a collision.

Use the idea of momentum to explain why this type of seat belt would be better for a car driver.

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(Total 8 marks)

Q16. The picture shows two children, X and Y, skating towards each other at an ice rink.

The children collide with each other, fall over and stop.

(a) Before the collision the children had different amounts of kinetic energy.

(i) What are the two factors that determine the kinetic energy of the children?

1 ........................................................................................................................

2 ........................................................................................................................(2)

(ii) What was the total kinetic energy of the children after they had fallen over and stopped?

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(b) The total momentum of the children before and after the collision is zero.

(i) Use the equation in the box and the data given in the diagram to calculate the momentum of child Y before the collision.



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Momentum = ............................................... kg m/s(2)

(ii) Complete the following sentence using one of the words in the box.

conserved decreased increased

The total momentum of the two children was ..................................................(1)

(Total 6 marks)

Q17. The diagram shows a child on a playground swing.The playground has a rubber safety surface.

(a) The child, with a mass of 35 kg, falls off the swing and hits the ground at a speed of 6 m/s.

(i) Use the equation in the box to calculate the momentum of the child as it hits the ground.



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Momentum = ............................................................(3)

(ii) After hitting the ground, the child slows down and stops in 0.25 s.Use the equation in the box to calculate the force exerted by the ground on the child.

force =


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Force = ............................................................ N(2)

(b) The diagram shows the type of rubber tile used to cover the playground surface.

Explain how the rubber tiles reduce the risk of children being seriously injured when they fall off the playground equipment.

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(c) The ‘critical fall height’ is the height that a child can fall and not be expected to sustain a life-threatening head injury.A new type of tile, made in a range of different thicknesses, was tested in a laboratoryusing test dummies and the ‘critical fall height’ measured. Only one test was completed on each tile.

The results are shown in the graph.

The ‘critical fall height’ for playground equipment varies from 0.5 m to 3.0 m.

Suggest two reasons why more tests are needed before this new type of tile can be usedin a playground.

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(d) Developments in technology allow manufacturers to make rubber tiles from scrap car tyres.

Suggest why this process may benefit the environment.

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(Total 11 marks)

Q18. The diagram shows a child on a playground swing.

(a) The playground surface is covered in rubber safety tiles. The tiles reduce the risk ofserious injury to children who fall off the swing.

The graph gives the maximum height that a child can fall onto rubber safety tiles ofdifferent thicknesses and be unlikely to get a serious head injury.

(i) Describe how the maximum height of fall relates to the thickness of the rubber safety tile.

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(ii) The maximum height of any of the playground rides is 2 metres.

What tile thickness should be used in the playground?

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(b) Use phrases from the box to complete the following sentences.

the force on the work done to stop the time taken to stop

(i) Falling onto a rubber surface compared to a hard surface increases

............................................................ the child.(1)

(ii) Momentum is lost more slowly falling onto a rubber surface than on a hard surface.

This reduces ............................................................ the child.(1)

(Total 5 marks)

Q19. (a) The diagram shows three skiers, X, Y and Z, on a moving chairlift.The mass of each skier is given in the table.

Which one of the skiers, X, Y or Z, has the most momentum?

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Give the reason for your answer.

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(2)

(b) At one point in the journey, the chairlift accelerates to a higher speed.

What happens to the momentum of the three skiers as the chairlift accelerates?

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(Total 3 marks)

Q20. (a) The diagram shows an athlete at the start of a race. The race is along a straight track.

In the first 2 seconds, the athlete accelerates constantly and reaches a speed of 9 m/s.

(i) Use the equation in the box to calculate the acceleration of the athlete.


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Acceleration = ..............................(2)

(ii) Which one of the following is the unit for acceleration?

Draw a ring around your answer.

J/s m/s m/s2 Nm(1)

(iii) Complete the following sentence.

The velocity of the athlete is the .................................................................... of the

athlete in a given direction.(1)

(iv) Complete the graph to show how the velocity of the athlete changes during the first 2 seconds of the race.

(2)

(b) Many running shoes have a cushioning system. This reduces the impact force on the athlete as the heel of the running shoe hits the ground.

The bar chart shows the maximum impact force for three different makes of running shoe used on three different types of surface.

(i) Which one of the three makes of running shoe, A, B or C, has the best cushioning system?

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Explain the reason for your answer.

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(ii) The data needed to draw the bar chart was obtained using a robotic athlete fitted with electronic sensors.

Why is this data likely to be more reliable than data obtained using human athletes?

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(Total 10 marks)

Q21. (a) The diagram shows a car travelling at a speed of 12 m/s along a straight road.

(i) Use the equation in the box to calculate the momentum of the car.


Mass of the car = 900 kg


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Momentum = .............................. kg m/s(2)

(ii) Momentum has direction.

Draw an arrow on the diagram to show the direction of the car’s momentum.(1)

(b) The car stops at a set of traffic lights.

How much momentum does the car have when it is stopped at the traffic lights?

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(Total 5 marks)

Q22.(a) Complete the sentence.

In a closed system, when two objects collide, the total momentum of the two objects

before the collision is ...................................................................................... the total

momentum of the two objects after the collision.(1)

(b) The diagram shows a car before and after the car collides with a stationary van.

The handbrake of the van is not on.

Use the information in the diagram to calculate the velocity, v, in metres per second, with which the van moves forwards after the collision.

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Velocity = ........................................................ m/s(4)

(c) The graph shows the velocity of the car before, during and after the collision.

Use the graph to calculate the distance travelled by the car, in metres, after the collision.

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Distance = ............................................ m(2)

(d) The collision causes the car driver to jerk forward.

Explain why wearing a seat belt reduces the risk of the driver being injured in the collision.

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(Total 10 marks)

Q23. (a) In any collision, the total momentum of the colliding objects is usually conserved.

(i) What is meant by the term ‘momentum is conserved’?

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(ii) In a collision, momentum is not always conserved.

Why?

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(b) The diagram shows a car and a van, just before and just after the car collided with the van.

Before collisionAfter collision

(i) Use the information in the diagram and the equation in the box to calculate thechange in the momentum of the car.



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Change in momentum =..................................................(3)

(ii) Use the idea of conservation of momentum to calculate the velocity of the van when it is pushed forward by the collision.


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Velocity =.................................................. m/s forward(2)

(Total 7 marks)

Q24. (a) The diagram shows three identical go-karts, P, Q and R, travelling at different speeds along the straight part of an outdoor racetrack.

Which go-kart, P, Q or R, has the greatest momentum?

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(b) The total mass of go-kart Q and the driver is 130 kg.

(i) Use the equation in the box to calculate the total momentum of go-kart Q and the driver.



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Momentum = ...........................................(2)

(ii) Which of the following is the unit of momentum?


J/s kg m/s Nm

(1)

(c) To race safely at high speed, a go-kart driver must have fast reaction times and the outdoor racetrack should be dry.

(i) How would being tired affect a driver’s reaction time?

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(ii) How would a wet track affect the braking distance of a go-kart?

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(Total 7 marks)

Q25.The arrows in the diagram represent the horizontal forces acting on a motorbike at one moment in time.

(a) The mass of the motorbike and rider is 275 kg.

Use the equation in the box to calculate the acceleration of the motorbike at this moment in time.

resultant force = mass × acceleration


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Acceleration = ............................................................ m/s2

(3)

(b) A road safety organisation has investigated the causes of motorbike accidents.

The main aim of the investigation was to find out whether there was any evidence that young, inexperienced riders were more likely to be involved in an accident than older, experienced riders.

Data obtained by the organisation from a sample of 1800 police files involving motorbike accidents, is summarised in the table.

Size of motorbikeengine

Percentage of allmotorbikes sold

Total number inthe sample of

1800accident files

up to 125 cc 36 774

126 to 350 cc 7 126

351 to 500 cc 7 162

over 500 cc 50 738

Most of the motorbikes with engines up to 125 cc were ridden by young people.The motorbikes with engines over 500 cc were ridden by older, more experienced riders.

(i) In terms of the main aim of the investigation, is this data valid?

Draw a ring around your answer. NO YES

Explain the reason for your answer.

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...............................................................................................................(2)

(ii) The organisation concluded that:

“Young, inexperienced riders are more likely to be involved in a motorbike accident than older, experienced riders”.

Explain how the data supports this conclusion.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(c) Of particular concern to motorbike riders is the design of steel crash barriers. Riders falling off and sliding at high speed into a steel support post are often seriously injured.

One way to reduce the risk of serious injury is to cover the post in a thick layer of high impact polyurethane foam.

(i) Use the ideas of momentum to explain how the layer of foam reduces the risk of serious injury to a motorbike rider sliding at high speed into the support post.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(3)

(ii) Crash barrier tests use dummies that collide at 17 m/s with the barrier. Each test costs about £12 000. New safety devices for crash barriers are tested many times to make sure that they will improve safety.

Do you think that the cost of developing the new safety devices is justified?

Draw a ring around your answer. NO YES


...............................................................................................................

...............................................................................................................(1)

(Total 11 marks)

Q26. Motorway accidents have many causes.

(a) Which one of the following is most likely to increase the chance of a car being in an accident?

Tick ( ) the box next to your answer.

The car has just had new tyres fitted.

The driver has been drinking alcohol.

A road surface in dry conditions


........................................................................................................................

........................................................................................................................(2)

(b) The diagram shows three designs of motorway crash barriers.

Steel sheets Steel ‘ropes’ Solid concrete

Before a new design of barrier is used, it must be tested.A car of mass 1500 kg is driven at 30 m/s to hit the barrier at an angle of 20 degrees.This barrier must slow the car down and must not break.

Explain why the mass of the car, the speed of the car and the angle at which the car hits the barrier must be the same in every test.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(c) A group of scientists has suggested that new designs of crash barriers should be first tested using computer simulations.

Which two statements give sensible reasons for testing new barrier designs using a computer simulation?

Put a tick ( ) in the box next to each of your answers.

The design of the barrier can be changed easily.

Data for different conditions can be obtained quickly.

Simulations are more realistic than using cars and barriers.

(1)(Total 5 marks)

Q27. (a) (i) The diagram shows three vehicles travelling along a straight road at 14 m/s.

Which vehicle has the greatest momentum?

............................................................


...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(ii) Use the equation in the box to calculate the momentum of the motorbike when it travels at 14 m/s.



...............................................................................................................

...............................................................................................................

Momentum = ............................................................kg m/s(2)

(b) The motorbike follows the lorry for a short time, and then accelerates to overtake both the lorry and van.

(i) Complete the following sentence by drawing a ring around the correct line in the box.

When the motorbike starts to overtake, the kinetic energy

decreases.

of the motorbike stays the same.

increases.

(1)

(ii) Give a reason for your answer to part (b)(i).

...............................................................................................................

...............................................................................................................(1)

(iii) The graph shows the velocity of the motorbike up to the time when it starts to accelerate. The motorbike accelerates constantly, going from a speed of 14 m/s to a speed of 20 m/s in a time of 2 seconds. The motorbike then stays at 20 m/s.

Complete the graph to show the motion of the motorbike over the next 4 seconds.

(3)(Total 9 marks)

Q28. (a) Complete the following sentence.

The momentum of a moving object has a magnitude, in kg m/s,

and a .................................................. .(1)

(b) A car being driven at 9.0 m/s collides with the back of a stationary lorry.The car slows down and stops in 0.20 seconds. The total mass of the car and driver is 1200 kg.

Use the equations in the box to calculate the average force exerted by the lorry on the car during the collision.


........................................................................................................................

........................................................................................................................

Force = .................................................. N(2)

(c) Within 0.04 s of the car hitting the back of the lorry, the car driver's airbag inflates.The airbag deflates when it is hit by the driver’s head.

Use the idea of momentum to explain why the airbag reduces the risk of the drive sustaining a serious head injury.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(3)

(Total 6 marks)

Q29. (a) A van has a mass of 3200 kg. The diagram shows the van just before and just after it collides with the back of a car.

After collision

Before collision

Just before the collision, the van was moving at 5 m/s and the car was stationary.

(i) Use the equation in the box to calculate the momentum of the van just before the collision.



...............................................................................................................

...............................................................................................................

Momentum = .............................. kg m/s(2)

(ii) The collision makes the van and car join together.

What is the total momentum of the van and the car just after the collision?

Momentum = .............................. kg m/s(1)

(iii) Complete the following sentence by drawing a ring around the correct line in the box.

more than

The momentum of the car before the collision is the same as

the

less than

momentum of the car after the collision.(1)

(b) A seat belt is one of the safety features of a car.

In a collision, wearing a seat belt reduces the risk of injury.

Use words or phrases from the box to complete the following sentences.

decreases stays the same increases

In a collision, the seat belt stretches. The time it takes for the person held by the seat belt to lose momentum compared to a person not wearing a seat belt,

.................................................................................................... .

The force on the person’s body ............................................................................. and so reduces the risk of injury.

(2)(Total 6 marks)

Q30.(a) The picture shows two teenagers riding identical skateboards.The skateboards are moving at the same speed and the teenagers have the same mass.

Why do the teenagers not have the same momentum?

........................................................................................................................

........................................................................................................................(1)

(b) One of the skateboards slows down and stops. The teenager then jumps off the skateboard, causing it to recoil and move in the opposite direction.

The momentum of the teenager and skateboard is conserved.

(i) What is meant by ‘momentum being conserved’?

...............................................................................................................

...............................................................................................................(1)

(ii) The teenager, of mass 55 kg, jumps off the skateboard at 0.4 m/s causing the skateboard to recoil at 10 m/s.

Use the equation in the box to calculate the mass of the skateboard.


...............................................................................................................

...............................................................................................................

...............................................................................................................

Mass = ............................................................ kg(3)

(c) Once the skateboard starts to recoil, it soon slows down and its kinetic energy decreases.

Explain why.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(Total 7 marks)

Q31. The picture shows three skateboarders, A, B and C.

Skateboarder A is not moving.Skateboarder B is moving towards the ramp at a constant speed.Skateboarder C is moving on the ramp at a constant speed.

(a) The skateboarders have different amounts of kinetic energy.

Which two factors affect the kinetic energy of the skateboarders?

Put a tick ( ) in the box next to your answer.

direction and mass

mass and speed

speed and direction

(1)

(b) The skateboarders also have different amounts of momentum.

(i) Which one of the skateboarders has the smallest amount of momentum?


A B C


...............................................................................................................

...............................................................................................................(2)

(ii) Skateboarder B has a mass of 55 kg.

Use the equation in the box to calculate the momentum of skateboarder B when moving at 4 m/s.



...............................................................................................................

...............................................................................................................

Momentum = .................................................. kg m/s(2)

(Total 5 marks)

Q32. The picture shows players in a cricket match.

(a) A fast bowler bowls the ball at 35 m/s. The ball has a mass of 0.16 kg.

Use the equation in the box to calculate the kinetic energy of the cricket ball as it leaves the bowler’s hand.

kinetic energy = × mass × speed2


........................................................................................................................

........................................................................................................................

........................................................................................................................

Kinetic energy = ............................................................ J(2)

(b) When the ball reaches the batsman it is travelling at 30 m/s. The batsman strikes the ball which moves off at 30 m/s in the opposite direction.

(i) Use the equation in the box to calculate the change in momentum of the ball.



...............................................................................................................

...............................................................................................................

Change in momentum = ........................................................... kg m/s(2)

(ii) The ball is in contact with the bat for 0.001 s.

Use the equation in the box to calculate the force exerted by the bat on the ball.


...............................................................................................................

...............................................................................................................

Force = ............................................................ N(1)

(c) A fielder, as he catches a cricket ball, pulls his hands backwards.

Explain why this action reduces the force on his hands.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(Total 7 marks)

Q33. (a) A car is being driven along a straight road. The diagrams, A, B and C, show the horizontal forces acting on the moving car at three different points along the road.

Describe the motion of the car at each of the points, A, B and C.

(3)

(b) The diagram below shows the stopping distance for a family car, in good condition, driven at 22 m/s on a dry road. The stopping distance has two parts.

(i) Complete the diagram below by adding an appropriate label to the second part of the stopping distance.

.............................................................

.............................................................(1)

(ii) State one factor that changes both the first part and the second part of the stopping distance.

...............................................................................................................(1)

(c) The front crumple zone of a car is tested at a road traffic laboratory. This is done by using a remote control device to drive the car into a strong barrier. Electronic sensors are attached to the dummy inside the car.

(i) At the point of collision, the car exerts a force of 5000 N on the barrier.

State the size and direction of the force exerted by the barrier on the car.

...............................................................................................................

...............................................................................................................(1)

(ii) Suggest why the dummy is fitted with electronic sensors.

...............................................................................................................

...............................................................................................................(1)

(iii) The graph shows how the velocity of the car changes during the test.

Use the graph to calculate the acceleration of the car just before the collision with the barrier.

Show clearly how you work out your answer, including how you use the graph, and give the unit.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................

Acceleration = ............................................................(3)

(Total 10 marks)

Q34. (a) The diagrams, A, B and C, show the horizontal forces acting on a moving car.

Draw a line to link each diagram to the description of the car’s motion at the moment when the forces act.

Draw only three lines.

stationary

A

constant speed

B

slowing down

C

accelerating forwards

(3)

(b) The front crumple zone of a car is tested at a road traffic laboratory. This is done by using a remote control device to drive the car into a strong barrier. Electronic sensors are attached to a dummy inside the car.

(i) Draw an arrow in Box 1 to show the direction of the force that the car exerts on the

barrier.(1)

(ii) Draw an arrow in Box 2 to show the direction of the force that the barrier exerts on the car.

(1)

(iii) Complete the following by drawing a ring around the correct line in the box.

The car exerts a force of 5000 N on the barrier. The barrier does not move. The force

more than

exerted by the barrier on the car will be equal to 5000 N.

less than

(1)

(iv) Which one of the following gives the most likely reason for attaching electronic sensors to the dummy?


To measure the speed of the car just before the impact.

To measure the forces exerted on the dummy during the impact.

To measure the distance the car travels during the impact.

(1)(Total 7 marks)

Q35. (a) The diagrams, A, B and C, show the horizontal forces acting on a moving car.

Draw a line to link each diagram to the description of the car’s motion at the moment when the forces act.

Draw only three lines.

stationary

A

constant speed

B

slowing down

C

accelerating forwards

(3)

(b) The front crumple zone of a car is tested at a road traffic laboratory. This is done by using a remote control device to drive the car into a strong barrier. Electronic sensors are attached to a dummy inside the car.

(i) Draw an arrow in Box 1 to show the direction of the force that the car exerts on the barrier.

(1)

(ii) Draw an arrow in Box 2 to show the direction of the force that the barrier exerts on the car.

(1)

(iii) Complete the following by drawing a ring around the correct line in the box.

The car exerts a force of 5000 N on the barrier. The barrier does not move. The force

more than

exerted by the barrier on the car will be equal to 5000 N.

less than

(1)

(iv) Which one of the following gives the most likely reason for attaching electronic sensors to the dummy?


To measure the speed of the car just before the impact.

To measure the forces exerted on the dummy during the impact.

To measure the distance the car travels during the impact.

(1)(Total 7 marks)

##

(a) ideas that greater speed means more kinetic energygains 1 mark

but any evidence of the formula ½ mv2

but making the case that kinetic energy depends on the speed squaredgains 3 marks

or that 22 = 43

(b) (i) any evidence of concept of momentum or mass × speed(or velocity) in words or figures e.g. 9.5 × 20 or 0.5 × 40

gains 1 mark

but correct values for momentum of lorry and cari.e. 190 and 20 [ignore units]gains 2 marks

but initial momentum correctly calculated170 or 190 – 20gains 3 marks

THENevidence when calculating final speed of idea that momentum is conserveduse of combined mass

each gain 1 mark

but17 [or 0.1 × figure for initial momentum](NB direction not required)

gains 3 marks6

(ii) kinetic energy is lostfor 1 mark

[credit (some kinetic) energy transferred as heat/sound][NB Accept only answers in terms of energy as required by the question]

1[10]

M2. (a) product of mass and velocity1

(b) (i) 4kg or 4000g1

(ii) M = 8kgm/s or Nsfor 3 marks

else M = 8for 2 marks

else M – mv or 4 × 2for 1 mark

3

(iii) 8 kgm/s (watch e.c.f.)1

(iv) v = 400for 3 marks

else v = 8/0.02for 2 marks

else M – mv, v – M/m or 8 = 0.02vfor 1 mark

3

(v) ke = 8for 3 marks

else ke = 1/2 (4 × 22)for 2 marks

else ke = 1/2 (mv2)for 1 mark

3

(vi) transferred to heat and soundor does work against wood/pushing wood aside/deforming bullet

1[13]

M3. (a) Throughout the question the equation M = mv is credited once only. This is the first time it appears. The mark scheme below assumesit will appear in (i).

(i) M = mv m × v sufficient not m × s, mass × speed= 1500 × 8= 12 000(see marking of calculations)

3

(ii) M = mvM = 2000 × 1 = 2000(see marking of calculations)

2

(iii) must be sum of (i) and (ii) 14 000for 1 mark

1

(b) total mass = 3500momentum = 14 000 (conserved)M = mv or v = 14 000/3500v = 4m/s5

(c) (i) it reducesfor 1 mark

1

(ii) ke to sound/heatfor 1 mark

1

(iii) change smallerfor 1 mark

1[14]

M4. (a) mass and velocity/speed multipliedfor 1 mark each

2

(b) total momentum before and after collision are the samefor 1 mark each

2

(c) (i) MAUA + MBUB = (MA + MB)v2 × 6 = (2 + 1)vv = 4m/s

for 1 mark each4

(ii) 1/2 mv2 (before) – 1/2 mv2 (after) 1/2 2.36 – 1/2 3.16 = 12J

for 1 mark each4

[12]

M5. (a) (i) 6for 1 mark

1

(ii) 6for 1 mark

1

(iii) 1.5for 1 mark

1

(iv) 4.5

for 1 mark1

(v) 3for 1 mark

1

(b) initial ke = 12J;

final ke = 0.75J + 6.75J;

energy loss = 4.5Jfor 1 mark each

(If wrong; any correct ke value gains 1 mark; maximum of 2path through calculation clear and correct gains 1 mark)(ignore either ball – max 1 mark)

3[8]

M6. (a) the snow1

smallest massdo not accept it is not movingaccept weight for massaccept it’s the lightest

1

(b) (i) decrease1

velocity reducingaccept speed for velocityaccept it is stoppingdo not accept the brakes are onaccept car is decelerating

1

(ii) forwards1

direction of momentum does not change or the car stops and snow does notdependent on forwards givenaccept answers given in terms of Newton’s second or first law of motionaccept momentum of snowdo not accept the snow still has momentum

1

(c) Ns1

[7]

M7. (a) (i) direction indicatedaccept to right or + or – or arrow drawn on diagram

1

3001

kg m/s or Ns1

(ii) 300 (kg m/s)1

(iii) there is no change in the total KEor total KE is constant

1

(b) momentum of person towards jetty = momentum of boat away from jettyor total momentum is constant so as person goes one way boat goes the other

1 mark is for the idea of momentum conservation1 is for direction

2

(c) time of collision increasesdo not accept momentum is conserved

1

so a smaller force is exerteddo not accept designed to absorb energy or momentum

1

to produce the same change of momentum or impulse forcedo not accept cushions fall

1[10]

M8. (a) (i) zeroaccept nothing

1

speed is zeroaccept not moving

1

(ii) A1

largest mass or weightaccept heaviest luggagedo not accept largest luggage

1

(iii) momentum does changeaccept yes

1

direction is changingaccept velocity is changingdo not accept answers in terms ofspeed changing

1

(iv) kg m/s1

[7]

M9. (a) Total momentum (of a system of bodies) remains constantaccept momentum before (a collision) = momentum after (a collision)

1

Provided no external force acts1

(b) (i) rotate the compressor1

(ii) • fuel is mixed with the air and ignited

• causing an increase in the pressure or temperature or speed of the gasesaccept air out faster than air in accept gases have momentum or

• force backwards

• exhaust gases have momentum(backwards) or force (backwards)

if the answer is in terms of force then this third point must be scored before the fourth can be credited

• engine or aircraft has (equal) momentum forwards or force forwards4

(c) m = 350answer 0.35 one mark onlyallow one mark if 105 000 or 475-175 or 300 have been used

2[9]

M10. (a) (i) eitherthe momentum in a particular direction after (the collision) is the same as themomentum in that direction before (the collision)

accept ‘momentum before equals momentum after’ for 1 mark

or total momentum after (the collision) equals the total momentum before(the collision) (2)

accept ‘momentum before equals momentum after’ for 1 mark2

(ii) explosion(s)or (action of a) rocket (motor(s))or (action of a) jet (engine)or firing a gun

accept any other activity in which things move apart as a result of the release of internal energy eg throwing a ball

1

(iii) momentum = mass velocity or any correctly transposed versionaccept momentum = mass speedaccept p = mvdo not accept momentum = msor M = mv

1

(iv) 0.8if answer 0.8 not given, any two for (1) each:momentum of X = 0.2 1.2= momentum of X and Y after impact= 0.3 v or = (0.1 + 0.2) v

3

m/s1

to the right

1

(v) any one from:

conservation of momentum (applies)

no external forcesdo not accept just ‘no (other) forces act’

friction is negligible / insignificant

no friction

no air resistance1

(b) force = (change in) momentum ÷ timeor any correctly transposed version

1

4000 or 4 kilonewtonsdependent on correct or no equationforce = 5 ÷ 0.00125 gains 1 mark

2[13]

M11. (a) (i) momentum = mass × velocityaccept … × speed or any transposed version

1

(ii) 11.2 to 11.30.75 × 15 for 1 mark

2

kg m/s down(wards) or Ns down(ward)n.b. both unit and direction required for this mark

1

(iii) 11.2 to 11.3accept same numerical answer as part (a)(ii)accept answer without any unit or with the same unit as in part (a)(ii), even if incorrect, but any other unit cancels the mark

1

(iv) force =

accept transposed version

1

(v) 112 to 113 or numerical value from (a)(ii) × 1011.25 ÷ 0.1 or (a)(ii) ÷ 0.1 for 1 mark

2

newton(s)or Naccept Newton(s)do not credit ‘Ns’ or n

1

(b) (the user will experience a) large change in momentumdo not credit just ‘… momentum changes’

1

(but) seat belt increases the time for this to occur orseat belt stops you hitting something which would stop you quickly

do not credit just ‘… stops you hitting the windscreen etc.’1

(so) the force on the user is less(*)1

(so) less chance of (serious / fatal) injury(*)(*) depends on previous response re momentum or continued movement

1[13]

M12. (i) momentum (change in) = mass × velocity (change in)accept ... speed

1

(ii) 90001500 × 6 for 1 mark but not from incorrect equation

2

kilogram metre(s) per second or kg m/s1

(iii) either 7.5 (m/s)

or change in momentum of car B change in momentum of car A (1)9000 = 1200 × v (1)

or v = 9000 ÷ 1200 (1)

or error carried forward from part (ii)

examples5 (m/s) if 6000 offered in (ii) (3)12.5(m/s) if 15000 offered in (ii)(3)

3[7]

M13. (a) 4 (m/s)1 mark for correct transformation of either equation1 mark for correct substitution with or without transformation1 mark for correct use of 0.6Nmax score of 2 if answer is incorrect

3

(b) greater change in momentum

or greater mass of air (each second)

or increase in velocity of airaccept speed for velocity

force upwards increasedlift force is increaseddo not accept upthrust

1

or force up greater than force downaccept weight for force down

1

(c) • increase the time to stop1

• decrease rate of change in momentum or same momentum changeaccept reduced deceleration/ acceleration

1

• reducing the force on the toydo not accept answers in terms of the impact/ force being absorbeddo not accept answers in terms of energy transferdo not credit impact is reduced

1[8]

M14. (a) (i) 0.6allow 1 mark for correct substitution

2

newtonsaccept Ndo not accept naccept Newtons

1

(ii) the same as1

(b) (i) changed velocityaccept increased/ decreased for changeaccept speed for velocityaccept change directionaccept getting faster/ sloweraccept start/ stop movingaccept correct equation in terms of change in speed or change in velocity

1

(ii) down(wards)accept towards the groundaccept ↓do not accept south

1

(iii) increase

velocity is increasingcan only credit second mark if answer is increase

or it is acceleratingaccept speed for velocityaccept is moving faster

1

accept an answer in terms of resultant force downwardsmention of weight/ mass increasing negates second mark

1[8]

M15. (a) (i) velocity includes direction

accept velocity is a vector1

(ii) 64allow 1 mark for obtaining values of 16 and 4 from the graphor marking correct area or correct attempt to calculate an area

2

(iii) any two from:

• velocity zero from 0 to 4 seconds

• increasing in 0.2 s (or very rapidly) to 8 m/s

• decreasing to zero over the next 8 seconds 2

(iv) momentum before does not equal momentum afterignore reference to energy

or total momentum changes

or an external force was applied1

(b) to reduce the momentum of the driver1

a smaller (constant) force would be neededdo not accept reduces the impact / impulse on the driver

1[8]

M16. (a) (i) massdo not accept weight

1

speedaccept velocityanswers can be in either order

1

(ii) zeroaccept nothing

1

(b) (i) 100allow 1 mark for correct substitution of data

2

(ii) conserved1

[6]

M17. (a) (i) 210allow 1 mark for correct substitution i.e. 35 × 6

2

kg m/s or Nsdo not accept n for Naccept 210 000g m/s for 3 marks

1

(ii) 840if answer given is not 840 accept their (a)(i) in kg m/s ÷ 0.25 correctly calculated for both marksallow 1 mark for correct substitution i.e. 210 ÷ 0.25 or their (a)(i) ÷0.25

2

(b) increases the time to stopaccept increases impact timedo not accept any references to slowing down time

1

decreases rate of change in momentumaccept reduces acceleration/decelerationreduces momentum is insufficient

1

reduces the force (on the child)1

(c) any two from:

• insufficient range of tests/thicknesses for required cfhaccept need data for thicknesses above 80 mm/ cfh 2.7 mnot enough tests is insufficient

• (seems to be) some anomalous data

• (repeats) needed to improve reliability (of data)accept data/ results are unreliabledo not accept maybe systematic/random errordo not accept reference to precision

• need to test greater range/variety of dummiesaccept children for dummies

accept specific factor such as weight/height/size2

(d) Tyres do not need to be dumped/burned/ less land-fill/ saves on rawmaterials

accept less wastedo not accept recycling on its own

1[11]

M18. (a) (i) the thicker the tile, the greater the(fall) heightaccept the higher (the fall) the thicker the tileaccept there is a positive correlationdo not accept they are proportional

1

(ii) 60 (mm)accept any number or range between 60 and 85 inclusiveif units are given must match range

1

(minimum thickness) needed to reduce risk of injuryreason must match thickness choicedo not accept to keep child safeaccept an answer in terms of – the thicker the tile, the less chance there is of a serious injury if the answer given is greater than 60accept answers in terms of use of graph e.g. the graph shows that for a 2m fall a thickness of 60 mm is neededminimum level answer’ the graph shows that’s what’s needed’ accept only if 60 is the answer

1

(b) (i) the time taken (to stop)1

(ii) (the) force (on)1

[5]

M19. (a) Yaccept the one in the middleaccept 90

1

has the biggest massreason does not score if X or Z is chosenaccept weight for massaccept weighs the mostaccept they are the heaviestaccept has a larger massdo not accept weighs 90kg’s on its ownbiggest/larger on its own is not sufficient

1

(b) increases1

[3]

M20. (a) (i) 4.5allow 1 mark for correct substitution i.e. 9 ÷ 2

2

(ii) m/s2

accept answer given in (a)(i) if not contradicted here1

(iii) speed1

(iv) straight line from the origin passing through (2s, 9m/s)allow 1 mark for straight line from the origin passing through to t = 2 secondsallow 1 mark for an attempt to draw a straight line from the origin passing through (2,9)allow 1 mark for a minimum of 3 points plotted with no line provided if joined up would give correct answer. Points mustinclude(0,0) and (2,9)

2

(b) (i) Bif A or C given scores 0 marks in total

1

smallest (impact) force1

on all/ every/ any surfacesthese marks are awarded for comparative answers

1

(ii) (conditions) can be repeated

or

difficult to measure forces with human athletesaccept answers in terms of variations in human athletes e.g.athletes may have different weights area / size of feet may be different difficult to measure forces athletes run at different speedsaccept any answer that states or implies that with humans the conditions needed to repeat tests may not be constante.g.athletes unable to maintain constant speed during tests (or during repeat tests)do not accept the robots are more accurateremoves human error is insufficientfair test is insufficient

1[10]

M21. (a) (i) 10800allow 1 mark for correct substitution i.e. 900 × 12

2

(ii) arrow pointing towards the leftallow anywhere on the diagram or at bottom of the page

1

(b) zeroaccept 0 / none / nothing

1

velocity is zeroaccept speed for velocityaccept stopped / not movingaccept a calculation i.e. 900 × 0 = 0

1[5]

M22.(a) equal to

or

the same as1

(b) momentum of car before collision = 1200 × 10 = 12 0001

momentum after collision = 12 0001

or

momentum is conserved equating

ie 12 000 = 1200 × 2 + 3200v1

3 (m/s)correct answer with or without working gains 4 marks

1

(c) correct area used from the graph1

1.5 (m)correct answer with or without working gains 2 marks

1

(d) the time taken for the driver to stop (moving forward) increases1

which decreases the rate of change in momentumaccept reduces deceleration

1

so the force on the driver is reduced1

[10]

M23. (a) (i) momentum before = momentum afteror(total) momentum stays the same

accept no momentum is lostaccept no momentum is gained

1

(ii) an external force acts (on the colliding objects)accept colliding objects are not isolated

1

(b) (i) 9600allow 1 mark for correct calculation of momentum before or afterie 12000 or 2400

orcorrect substitution using change in velocity = 8 m/sie 1200 × 8

2

kg m/sthis may be given in words rather than symbols

orNs

1

(ii) 3 or their (b)(i) ÷ 3200 correctly calculatedallow 1 mark for stating momentum before = momentum afterorclear attempt to use conservation of momentum

2[7]

M24. (a) Rreason cannot score if R is not chosen

1

has the greatest speed / velocityaccept it is going at 28 m/sanswer should be comparative

1

(b) (i) 3250allow 1 mark for correct substitution of 130 and 25ie 130 × 25accept 2600 or 3640 for 1 mark

2

(ii) kg m/saccept answer given in (b)(i) if no answer given here

1

(c) (i) increase itaccept make it sloweraccept slow it downaccept make it longeraccept (reactions) would be slowerdo not accept if the answer clearly refers to distancecomparative answers expected

1

(ii) increase it

accept make it longerdo not accept if the answer clearly refers to timecomparative answers expected

1[7]

M25. (a) 4.22 marks for correct substitution and transformation, ie 1155/275allow 1 mark for correct resultant force with a subsequent incorrect method, ie 1155allow 1 mark for an incorrect resultant force with a subsequent correct method,eg answers of 7.27 or 10.34 gain 1 mark

3

(b) (i) YESmarks are for the explanation

any two from:

• data (from police files) can be trusted

• data answers the question askedallow a conclusion can be made from the data

• large sample used

NO

any two from:

• the sample is not representative

• the sample size is too small

• accident files do not indicate age / experience of ridersan answer YES and NO can score 1 mark from each set of mark points

2

(ii) more accidents with motorbikes up to 125 ccaccept for 2 marks an answer in terms of number of under 125 cc to accidents ratio compared correctly with number of over 500 cc to accidents ratio

1

even though there are fewer of these bikes than bikes over 500 cc1

(c) (i) increases the time taken to stopaccept increases collision time

1

decreases rate of change in momentumaccept reduces acceleration / deceleration

accept reduces momentum is insufficient

1

reduces the force (on the rider)1

(ii) YES

any sensible reason, eg:the mark is for the reason

• cannot put a price on life / injuryaccept may save lives

• fewer (serious) injuriesaccept reduces risk of injury

• reduces cost of health care / compensation

NO

any sensible suggestion, eg:

• money better spent on …needs to be specific

• total number of riders involved is small1

[11]

M26. (a) The driver has been drinking alcohol.reason only scores if this box is ticked

1

driver's reaction time increasesaccept slower reactionsaccept slower reaction time

orthinking distance / stopping distance increases

do not accept braking distance increasesordriver less alert

accept driver may fall asleep / be tired1

(b) they are all variables that could affect outcome / resultsaccept specific effect of changing one of the variablesaccept to make the test validignore reliable

1

so data / barriers can be comparedaccept to see which is / works best / safestdo not accept fair test on its own

1

(c) ticks in both the top and middle boxes1

[5]

M27. (a) (i) lorryreason only scores if lorry chosen

1

greatest massaccept weight for massaccept heaviestaccept correct calculations for all 3 vehiclesthe biggest is insufficient

1

(ii) 2450allow 1 mark for correct substitutionie 175 × 14

2

(b) (i) increasesaccept any clear indication of the correct answer

1

(ii) speed increasesaccept velocity for speedaccept gets fasterdo not accept it accelerates on its ownmoves more is insufficient

1

(iii) straight line going to 6, 20allow 1 mark for a curve going to 6,20or a straight line diagonally upwards but missing 6,20

2

horizontal line from 6,20 to 8,20allow a horizontal line from where their diagonal meets 20m/s to 8,20

1[9]

M28. (a) direction1

(b) 54 000allow 1 mark for calculating and identifying momentum as 10 800orallow 1 mark for correct substitution into second equation

ie 2

(c) increases the time taken (for head) to stopaccept increases impact timedo not accept reference to slowing down time unless qualified

1

decreases rate of change in momentumaccept reduces acceleration / decelerationaccept increases the time taken to reduce momentum to zero is worth 2 marksreduces momentum is insufficient

1

reduces the force (on the head)1

[6]

M29. (a) (i) 16 000allow 1 mark for correct substitution ie 3200 × 5

2

(ii) 16 000 or their (a)(i)

1

(iii) less than1

(b) increases1

decreasescorrect order only

1[6]

M30. (a) (moving in) different / opposite directionsaccept one has positive momentum the other negative momentumaccept they have different velocities

1

(b) (i) momentum before = momentum afteror(total) momentum stays the sameaccept no momentum is lostaccept no momentum is gained

1

(ii) 2.2allow 1 mark for calculation of teenagers’ momentum as22 (kgm/s) andallow 1 mark for correct statement, eg momentumbefore = momentum afterorallow 2 marks for a numerical expression of above, eg55 × 0.4 = m × 10or 0 = (55 × 0.4) + (m × (-10))

3

(c) any two from:

• work is done

• (against) frictionany reference to increasing friction negates this marking point

• (transforming) (kinetic) energy into heat2

[7]

M31. (a) mass and speed1

(b) (i) Areason cannot score if B or C chosen

1

velocity = 0 (m/s)accept speed for velocityaccept not movingaccept lowest velocity / speed

1

(ii) 220allow 1 mark for correct substitution,ie 55 × 4 provided no subsequent step shown

2[5]

M32. (a) 98allow 1 mark for correct substitutionie ½ × 0.16 × 35 × 35 provided no subsequent step shownan answer of 98 000 scores 0

2

(b) (i) 9.6allow 1 mark for (change in velocity =) 60ignore negative sign

2

(ii) 9600ignore negative sign

ortheir (b)(i) ÷ 0.001 correctly calculated, unless (b) (i) equals 0

1

(c) increases the time1

to reduce/change momentum (to zero)only scores if 1st mark scoreddecreases rate of change of momentum scores both marks provided there are no contradictionsaccept decreased acceleration/decelerationequations on their own are insufficient

1[7]

M33. (a) A constant speed / velocityaccept steady pacedo not accept terminal velocitydo not accept stationary

1

B accelerationaccept speeding up

1

C decelerationaccept slowing downaccept accelerating backwardsaccept accelerating in reversedo not accept decelerating backwards

1

(b) (i) the distance the car travels under the braking forceaccept braking distance

1

(ii) speed/velocity/momentum1

(c) (i) 5000 (N) to the leftboth requiredaccept 5000(N) with the direction indicated by an arrow drawn pointing to the leftaccept 5000(N) in the opposite direction to the force of the car (on the barrier)accept 5000(N) towards the car

1

(ii) to measure/detect forces exerted (on dummy / driver during the collision)1

(iii) 4allow 1 mark for showing a triangle drawn on the straight part of the graphor correct use of two pairs of coordinates

2

m/s2

do not accept mps2

1[10]

M34.(a) 3 lines drawnall correctallow 1 mark for each correct lineif two or more lines are drawn from any diagram then all these lines are incorrect

3

(b) (i) horizontal arrow to the rightjudge by eyeaccept an arrow drawn outside the box if it is labelled correctly

1

(ii) horizontal arrow to the leftjudge by eyeaccept an arrow drawn outside the box if it is labelled correctly

1

(iii) equal to1

(iv) to measure the forces exerted on the dummy during the impact1

[7]

M35.(a) 3 lines drawnall correctallow 1 mark for each correct lineif two or more lines are drawn from any diagram then all these lines are incorrect

3

(b) (i) horizontal arrow to the rightjudge by eyeaccept an arrow drawn outside the box if it is labelled correctly

1

(ii) horizontal arrow to the leftjudge by eyeaccept an arrow drawn outside the box if it is labelled correctly

1

(iii) equal to1

(iv) to measure the forces exerted on the dummy during the impact1

[7]

E1. In (a) few candidates used the formula ½mv2 to answer this question.

In (b)(i) many candidates realised the need to use the idea of momentum in this question (though some tried to answer using the formula or kinetic energy); fewer correctly calculated the separate moments of the moving vehicles and fewer still combined these correctly (a common error being to add them rather than subtract them). Most of the candidates who obtained a numerical answer for the total initial momentum were able to calculate a final combined speed consistent with their earlier figure.

In (ii) the idea of a loss of kinetic energy in an inelastic collision (and/or the transfer of kinetic energy e.g. as heat and sound) was seldom stated.

E2. This was not an easy topic but the majority of candidates gained marks in many sections of the question.

(a) This was intended as an easy introduction to the question. Very many candidates who clearly knew momentum was mass x velocity failed to say so in response to this Question and so failed to gain the mark.

(b) In (i)few candidates failed to gain the mark. In (ii)the vast majority correctly calculated the momentum, and then in part (iii)repeated their answer to gain that mark. It was in part (iv)that the weaker candidates began to run into trouble mainly by using a mass of 4 kg and working back to a velocity of 2 m/s. A number of candidates turned the Question on its head at this point; they took the 1600 joules given in part (vi)and used a kinetic energy calculation to find the velocity. They were awarded all three marks. In (v)many candidates quoted the kinetic energy equation and went on to calculate the kinetic energy successfully. Part (vi)presented little trouble to the candidates with energy losses as heat and sound being common.

E3. Part (a) was generally very well answered with very many candidates gaining full marks. When working was shown some candidates used momentum as mass times speed rather than times velocity.

Part (b) proved to be more difficult. The more able candidates gave 14 000/3500 = 4m/s to very quickly gain the five marks. Most other candidates made some creditable start to the problem to gain part marks.

In (c)(i) most candidates correctly answered that the kinetic energy would be reduced. In (ii) many candidates gave a correct energy transfer, the common answer being kinetic energy to sound. However a surprising number of candidates did not refer to an energy transfer, only mentioning the outcome of the transfer. Answers like “sound was given off” were not uncommon. In part (iii) a number of candidates did not answer the question which was concerned with the

change of kinetic energy, instead they referred to the total kinetic energy after the collision being greater. Such answers were not credited with the mark.

E4. In part (a) the vast majority of candidates successfully gained both marks for multiplying mass by velocity. Although there were many correct answers to part (b) some candidates lost marks for referring to the momentum of ‘an object’ being the same before and after a collision. A very few answered in terms of the energy before and after the collision and so failed to gain marks. In part (c) very many candidates scored all the marks with correct calculations. There were few part correct answers, those who did not score marks generally lost all the marks through lack of knowledge of the principle of conservation of momentum. A few getting part (i) wrong nevertheless went on to gain full marks in part (ii) by correctly using the incorrect data generated in part (i).

E5. The calculations on momentum were well answered by many candidates, a fair number of whom went on to complete the kinetic energy calculations in part (b).

E6. Most candidates were very familiar with the concept of momentum and answered this question well. However in part (a) a number of candidates assumed the snow was stationary. There were many good answers to part (b), but few correct choices of unit in part (c).

E7. In part (a)(i) many candidates calculated the correct value and gave the correct unit, although very few realised that momentum is a vector quantity and gave the direction. In part (a)(iii) the definition of an elastic collision was not well known, many candidates answering in terms of momentum conservation only. The remaining parts of this question were not well answered, showing a lack of understanding of momentum conservation in part (b) and the effect of momentum change in part (c). Many candidates tried to use moments to explain why the boat tipped rather than moved or answered in terms of force without mentioning momentum. Again, in part (c) very little reference was made to momentum, although some realised the padding was, in effect, a crumple zone and knew that increased impact time would lead to a reduced force. Parts (b) and (c) illustrated the inability of many candidates to apply their knowledge to unfamiliar situations.

E8. In part (a)(i) the majority of candidates understood that an object that is not moving has zero momentum. Most candidates also realised in part (a)(ii) that the luggage with the largest mass has the most momentum. However, in part (a)(iii) few candidates appreciated that momentum changed when the direction changed. The unit of momentum was generally known.

E9. This question proved to be one of the most demanding on this paper. Many candidates confused momentum with energy in part (a) and few remembered that no external forces should act. In part (b) most had only a sketchy idea of the physics involved and only scored a mark for mentioning the fuel combustion. The most common misconception was that the exhaust gases push against the atmosphere to achieve propulsion. The calculation in part (c) was also poorly attempted. The majority scored a mark for finding the change in velocity but were not able to go on to calculate the mass correctly.

E10. In part (a)(i) most candidates were able to give a partial version of the required equation but few mentioned that this is the total momentum or gave the direction. Many candidates ignored the instructions; for example, in part (ii) they chose examples of collisions and similar events, in part (iii) they gave symbol equations instead of the word equations they were asked for and in part (iv) threw away a mark by failing to state that the trolleys would move to the right after the collision. The examiners did not consider that ‘no forces act’ was a sufficient response in part (v). The response ‘no external forces act’ is quite correct. However it was hardly ever seen. The answer ‘4000 newtons’ was fairly common. However it was often seen as a consequence of some completely false equation such as force = mass + time and consequently received no marks. The examiners are not pleased to note that some candidates are so confused that they think that 0.00625 N or 6.25 N might be the force of a bullet.

E11. (a) (i) Most candidates were able to give a correct version of the required equation.

(ii) Most candidates gave the correct numerical answer in this part. However, only a minority were able to give the correct unit for momentum and most chose to ignore the instruction to give the direction. Consequently many candidates lost the third mark.

(iii) Some candidates showed that they did not appear to understand what was going on, or had not given themselves time to read the whole question and think about it. Rather than repeat their numerical answer to part (a)(ii) they chose to modify it,

usually by a factor of two or of ten.

(iv) The equation required in this part was usually stated correctly, although just ‘momentum’ was sometimes erroneously given for ‘change in momentum’.

(v) The calculation for this part was usually correct with the correct unit.

(b) This part revealed that an important application of this equation is not generally related to it. There were some excellent answers which were confident and well expressed. However, many candidates seemed to have a poor understanding of the concept of change of momentum and could not relate it to the time and force they had just referred to. Some claimed that in a crash the momentum of the vehicle is transferred to the passengers, and that your seat belt prevents you from moving, but no one claimed that wearing a seat belt was a bad idea.

E12. Parts (i) and (ii) were usually correctly answered with most candidates giving the correct unit. In part (iii) those who appeared confident that the change in momentum of car A would be equal to the change in momentum of car B were able to proceed to the calculation of car A'’ speed after the impact. Others, who often seemed to have little understanding of this area of the Specification, did not get any marks for this part.

E13. (a) This calculation was not often correct. Many candidates were unable to use the correct pieces of data appropriately. There was widespread confusion between mass and force, and even time and velocity were interchanged in many equations. However, some candidates did complete the calculation well.

(b) Many candidates recognised that there was more air pushed down per unit time or that the air was moving faster. Some candidates confused the air moving faster with the toy moving faster. Although many candidates scored one mark, few candidates were able to link the increased air movement to the subsequent acceleration in order to score both marks.

(c) This was poorly done with most candidates not considering momentum but trying to use their knowledge of polystyrene to answer the question. Many responses centred on the air content of the polystyrene or the air resistance slowing it down on its descent.

E14. (a) (i) Most candidates were able to use the data and equation provided to produce a numerical value for the weight of the toy but there were few responses which stated

the correct unit.

(ii) Most of the candidates were aware that the forces involved would need to be balanced to enable the toy to hover.

(b) (i) Most candidates were able to explain the term ‘acceleration’ however, there were many references to ‘move’, ‘increase’ etc without any elaboration.

(ii) This was question was generally answered correctly however, there were a number of incorrect references to ‘south’.

(iii) Half of the candidates understood that the momentum would increase but few could give a valid reason why.

E15. (a) (i) Most candidates stated that velocity is speed in a given direction. Few candidates stated that velocity is either speed in a straight line or velocity = speed × time.

(ii) A good proportion of candidates obtained 64 metres but many candidates correctly obtained 16 and 4 from the graph and then divided the two numbers. Some candidates did a longer calculation and obtained the complete area under the graph.

(iii) This question was well done with the majority of candidates scoring both marks. However some candidates either misread the question and redrew graph 1 or were at least one small square out in their accuracy.

(iv) Many candidates were able to score a mark however the majority simply quoted the law of conservation of momentum.

(b) Many candidates did not score any marks here and wrote about whiplash and trying to avoid serious injuries. Some realised that if the force was to be constant over the same time period then it must be smaller. Some candidates were familiar with the equation linking force and rate of change of momentum but were unable to link this with any logical explanation.

E16. (a) (i) Most candidates were able to identify velocity or speed but weight was often given as an incorrect alternative to mass.

(ii) A pleasing number of correct answers given. However a significant number of candidates tried to complete a calculation that involved total mass and a velocity value.

(b) (i) The substitution of values and the subsequent calculation was handled well by the

majority of candidates who scored maximum credit.

(ii) Only a minority of candidates understood that the momentum was conserved.

E17. (a) (i) The calculation was well done with most candidates obtaining 210. However, only half of those obtaining this correct answer were also able to give the correct unit.

(ii) Most candidates who scored 2 or 3 marks for part (a)(i) obtained the correct answer. Those who did not tended to multiply 210 by 0.25 instead of dividing. A number of candidates subtracted 6 or 35 from 210 before dividing by 0.25 thereby losing both marks.

(b) This was either done very well or very poorly. It was not always clear that the rubber tile increased the time to stop and some candidates went straight to the second marking point i.e. increases the time for the change in momentum. Occasionally when a poor answer was written the candidate managed to salvage a mark by finishing with ‘the force is reduced’. A lot of candidates mentioned ‘air gaps’ and ‘bouncing/cushion effect,’ gaining no credit.

(c) The answers were very variable. Many were very vague and referred to accuracy rather than reliability or human error rather than anomalies. The range of thicknesses being insufficient was seldom referred to.

(d) This was generally done well; a few candidates just mentioned recycling without explanation and gained no credit. The most popular answers concerned either burning or use of land-fills, a few candidates mentioned deforestation of rubber trees but these were not penalised!

E18. (a) (i) Most candidates were able to describe the relationship between the maximum height from which a child could fall without serious head injury and the appropriate thickness of rubber safety tiles in a playground.

(ii) The identification from the graph of the correct thickness for a fall of 2m was well done with the second marking point being scored most often by an answer that referred to use of the graph.

(b) (i) Few candidates scored this mark. The vast majority of candidates chose the answer ‘the work done to stop’.

(ii) Just over half of the candidates knew that ‘the force on’ the child would reduced.

E19. (a) Most candidates that correctly chose the skier with the greatest mass as the person with greatest momentum also supplied the appropriate reason for their choice. However a significant minority of candidates chose X or Z and gained no marks.

(b) The majority of candidates were aware that acceleration would produce an increase in the momentum of the three skiers. However there was a large number of candidates that clearly had not read the question correctly and gave answers in terms of an increase in speed.

E20. Foundation Tier

(a) (i) This was well answered with most candidates gaining both marks.

(ii) It is surprising that only just over 50 % of the candidates knew the unit of acceleration.

(iii) For a standard piece of recall it was surprising that only 50 % of candidates scored a mark.

(iv) Less than 50 % of candidates drew the correct line and gained 2 marks. Many candidates did not take into account the final velocity of 9 m/s. Others did not relate the idea of constant acceleration to a straight line.

(b) (i) Candidates that chose the correct shoe of the three on test often gave a suitable reason for their choice to achieve 2 marks, but then failed to appreciate that this shoe was the best on all of the listed types of surface.However nearly 50% of candidates were unable to interpret the bar chart correctly and chose either A or C.

(ii) Most correct answers were in terms of human variability but many candidates mentioned the robot’s consistency. A significant number of candidates did not recognize the importance of the word ‘reliable’ and answered in terms of sensor accuracy.

Higher Tier

(a) (i) Most candidates obtained the correct answer although a few candidates multiplied 9 × 2 instead of dividing.

(ii) The majority of candidates knew that the unit of acceleration was m/s2.

(iii) The majority of candidates gave the correct answer.

(iv) Most candidates produced a straight line with a ruler from the origin to (2,9). Those who did not obtain full marks were generally not accurate enough. A number of candidates did not link the idea of constant acceleration with the need to draw a straight line.

(b) (i) Many candidates correctly chose B but then failed to compare this shoe with both A and C or mention that it was the best shoe on all three surfaces. However a significant number of candidates did score all three marks.

(ii) The majority of candidates obtained the mark, usually giving answers in terms of variations in human athletes eg weight / size of foot may be different and they run at different speeds. A common fault was to be too vague and say that the robots are more accurate or they remove human error; a few answered with the standard response ‘it’s a fair test’ without qualifying the statement.

E21. (a) (i) The majority of candidates correctly substituted the data into the equation and calculated a correct answer.

(ii) This was generally answered well. Unfortunately, a number of candidates chose to draw several arrows rather than the requested single arrow.

(b) This part of the question was answered well but there were some instances where candidates had given the momentum as 900 then explained the reason by substituting numerical values for the mass and velocity and presented the equation ‘900 × 0 = 900’.

E23. (a) (i) There was much confusion throughout this question between momentum and energy. Clearly a large number of candidates consider them to be the same. Less than half of the candidates gave a correct answer. Those that did often scored the mark with a simple statement such as ‘momentum before = momentum after’.

(ii) Very few candidates answered this correctly. Incorrect answers often talked about elastic and inelastic collisions in terms of energy conservation. There were also a lot of references to crumple zones, walls, immovable objects etc. Those candidates gaining credit often simply stated an ‘external force acts’.

(b) (i) Many candidates scored 1 mark for calculating the momentum of the car either before or after. However, many candidates failed to develop the idea and subtract the two numbers. Units proved troublesome; far too often it was given as kg/m/s or kgm/s2, occasionally answers were given as N.

(ii) The better, well prepared candidates scored both marks. However, the incorrect answer 10 - 2 = 8 m/s was very common. Too few candidates seemed able to write down ‘momentum before =; momentum after’ and hence obtain the answer.

E24. (a) This question was answered well with a majority of the candidates achieving both marks. However, there were some responses which indicated that candidates had interpreted ‘m/s’ as being momentum per second. Some candidates thought that R had the most momentum because it was in front.

(b) (i) Most candidates were able to multiply the mass by the velocity correctly. However, a significant minority of candidates substituted the numbers correctly but seemed not to have a calculator to enable them to give the correct answer.

(ii) The majority of candidates responded correctly with errors being equally split between the two wrong answers provided. A few candidates had unfortunately tried to split the correctly paired unit circling only either kg or m/s.

(c) (i) This question was answered well with most candidates responding in terms of an increase in reaction time although some incorrect responses were clearly directed towards distance, rather than time.

(ii) This question was poorly answered mainly due to candidates not answering the question set ie, what happens to braking distances in wet conditions.

Candidates wrote excellent responses in terms of aquaplaning, skidding, lack of traction, wet brakes, the need to brake earlier, the need for less braking force, the increased possibility of accidents, the need to drive slower, etc. However, these responses failed to address the question.

E25. (a) Many candidates obtained the correct answer having correctly calculated the resultant force as 1155 N. Correct calculation of the force 1155 N then multiplying by the mass of 275 kg was a common error gaining just one mark. The use of an incorrect force with the correct method, gained many candidates one compensatory mark.

(b) (i) Many candidates failed to understand that the question was referring to the validity of the data with many answers given in the form of a conclusion rather than answering the question about valid data. Those candidates who realised the question was about the data, answered mainly in terms of the reliability of police files (YES) or on the lack of information about ages (NO). Many candidates quoted the number of files in the source, but as they failed to express whether this was a large or a small sample, failed to score a mark for this. There was also evidence of much rewriting of answers, mostly to little or no advantage.

(ii) Just over half of candidates gained one mark for describing how the smaller motorbikes had more accidents and a small minority of candidates went on to note how there were fewer smaller bikes than larger bikes, or calculated ratios.

(c) (i) Very few candidates gained full marks on this question, in spite of it being a well examined aspect of the course. A change in context does disguise what is needed to all but the highest scoring candidates, in spite of the stem referring to momentum.

Over half of candidates scored zero. The quality of the explanation was often poor. There are still a large number of answers referring to cushioning the impact rather than reducing the force. The‘decreases rate of change of momentum’ is the most frequently missed mark. A number of candidates confused their response with references to kinetic energy and stopping distances.

(ii) Most candidates gave the answer that the new safety barriers would save lives, or reduce injuries, which gained the mark. Those who thought that 17m/s was too slow to crash or cause serious injury had confused the unit with mph.‘Money could be better spent’ was rarely a complete answer and so did not score a mark very often.

E26. (a) This question was generally answered well with virtually all candidates recognising that drinking alcohol would increase the chance of an accident occurring. However, a number of candidates failed to achieve the second mark due to identifying that there would be an alteration of the driver’s reactions, but not whether the alteration would be positive or negative. Another common error was to state that the ‘driver’s reaction time decreases’.

(b) Virtually all candidates understood the idea that a fair test was required to choose the best barrier to slow a car and not break. However few were able to explain how a change of the three different variables would affect the outcome and prevent a valid set of results being produced, that would provide evidence to which crash barrier was the best of the three under trial.

(c) Just over four fifths of candidates chose the correct answer.

E27. (a) (i) Most candidates were aware that the lorry would have the greatest momentum by reason of its greater mass. Vague responses, such as‘the lorry is bigger’, did not gain a mark. Some candidates took advantage of the relevant equation printed on the same page and calculated the momentum of the three vehicles. Incorrect responses generally involved the motorbike and indicated that the candidates were confusing momentum with the ability of the motorbike to accelerate faster than the other two.

(ii) This part question was generally answered well by those candidates with access to calculators. Candidates should be encouraged to check their calculations carefully as there were a number of instances of errors occurring in the transfer of the numbers from the question stem to the lines provided, to show their method of calculating the momentum of the motorbike.

(b) (i)&(ii)Just over nine tenths of candidates correctly answered that the kinetic energy would increase but they had less success in giving an appropriate reason. Most of the

incorrect responses were in terms of the motorbike accelerating which had been stated in the part question stem. There were also many vague responses involving changes of force, power, friction, engine efficiency, etc.

(iii) Just over three quarters of candidates gained all three marks. Those that did not often drew a diagonal line from (4, 14) up to 20 m/s on the y-axis but the lines did not hit (6, 20) and were not subsequently continued horizontally to 8 s on the x-axis.

E28. (a) It was surprising that only a quarter of the candidates correctly answered ‘direction’ with ‘velocity in m/s’ a very common response. A small minority of candidates did not attempt this part question. It may be that many of these candidates did not look at the page carefully enough to realise there was a question at the top.

(b) Generally this question was well answered by the majority of students, with just over two-thirds scoring full marks. However, a large minority of students couldn’t substitute values from the text into a given equation correctly, often confusing time and speed. Some candidates didn.t recognise that the standard unit for mass is the kg and needlessly changed mass from kg into g, losing marks.

(c) Many candidates concentrated on the details of operation of airbags rather than the explanation of how they reduce risk of injury. There was little mention of ‘momentum’ from many candidates, and over two-fifths scored zero. Some candidates answered in terms of conservation of momentum, indicating that they had learned some physics but were not aware when to apply it. Of those that did give creditworthy answers there was often confusion over ‘reducing momentum’ and ‘reducing the rate of change of momentum’.

E29. (a) (i) This part question was answered very well with a large majority of candidates scoring both marks. However for those candidates failing to score the marks the main problem seemed to be lack of a calculator, or incorrect use of a calculator, evidenced by the use of lengthy iterative processes or missing zeros in their final answer.

(ii) Only a small minority of candidates were aware that the momentum of the vehicles were conserved in the collision, the most incorrect common response being that the momentum had decreased to zero.

(iii) Most candidates failed to appreciate that a stationary car has less momentum than a moving car.

(b) Just over half of the candidates scored both marks.

E30. (a) About two thirds of students scored this mark, showing that they had learnt that momentum has direction. A significant number of students ignored the information given in the question and stated that the two teenagers had different speeds or different mass.

(b) (i) Over two fifths of students scored this mark, giving a clear statement explaining momentum conservation, e.g. ‘momentum before = momentum after’ with many giving atextbook answer including the proviso that no external forces act. Some students suggested that the momentum was used up or ran out, or gave poor answers aboutforces and energy. Some students attempted to apply the rule to the particular case of the skateboard, explaining about the teenager and the boy having equal and/or opposite momenta. Unfortunately they generally did not go on to say that the (total) momentum had not changed.

(ii) Over two fifths of the students showed an excellent understanding of momentum conservation and presented clear working leading to a correct three mark answer. Another two fifths of students gained no marks at all. Their working showed little grasp of the mathematical aspects of momentum. There were many different wrong answers, the most common being 10/0.4 = 25, with no mass values involved at all. Of the remaining students, most gained a single mark for calculating the teenager’s momentum. Very few students obtained the second compensation mark by either stating the conservation of momentum or giving a numerical expression of this.

(c) Many students showed misconceptions about ‘force’ and ‘energy’, e.g. stating that without a force pushing it the board no longer has any energy, that it needs a force to keep it moving, or that friction is stronger than the kinetic energy. Very few connected friction with the work done against it. Too many wrong answers were comparing this question with question (b) and mentioning an increasing frictional force. As a result about two thirds of students did not score on this question. On the other hand, a few students showed clear understanding of the key terms and gained both marks for saying that kinetic energy is transferred as heat because of the friction force. About a third of students gained a single mark, usually for correctly referring to a friction force or, less often, for stating that kinetic energy is transferred by heating.

E31. (a) It was disappointing that only just over half of students could identify mass and speed as the factors that affect kinetic energy.

(b) (i) This was well answered by nearly all students. Most students recognised that because A was stationary or not moving that there would be no momentum.

(ii) This was correctly answered by nearly all students, with most correctly writing down the numerical values of mass and velocity before completing the multiplication.

E32. (a) A large majority of students (85%) scored full marks demonstrating an ability to use the given equation correctly. About 3% of students were able to substitute the values correctly into the equation but then made mistakes with the arithmetic. Approximately 12% of students were unable to correctly substitute values; often using v instead of v2

(b) (i) While most students were able to calculate a momentum using the given equation only about 23% of students recognised that they needed to find the difference between the initial and final momenta. Very few correctly calculated the change in velocity to be 60m/s to gain the compensation mark. Most of the 75% of students who scored zero on this part question only calculated the final momentum, albeit correctly, but unfortunately this was not creditworthy in the context of this question. Some students who did recognise that a change in momentum needed to be calculated confused signs and ended up with a change in momentum of zero thus demonstrating a lack of understanding of the concept.

(ii) Of the 23% of students that answered part (b)(i) correctly only a small number then made errors in this question. The vast majority of students managed to substitute their answer to (b)(i) into the equation for force and calculate the answer correctly, gaining an ‘error carried forward’ mark. Approximately half of the students who failed to score here did so because their answers to part (b)(i) were zero, making it impossible to gain this mark. There were a few students who at this stage realised that their answer of zero earlier must be incorrect so they deleted the calculation that resulted in a force of zero and came up with the correct figures, but failed to amend (b)(i) to match. Just over 83% of students scored this mark.

(c) Just over half of the students gained some credit on this question but only 28% scored both marks. Of these about half gained the marks by correctly stating that ‘the rate of change of momentum had decreased’. Other students were less concise but did tie-up increased time to the change in momentum. Of the students who did not score fully on this part question many offered confused statements, that the change in momentum was smaller, not realising that it is the same change in momentum to bring the ball to a stop or offered vague statements about the time taken slowing down.

E33. (a) Nearly 60% of students scored all three marks. However, “standing still” or “stationary” was a common wrong answer to A, even though the students were told the car was moving. Often, in B and C, students calculated the resultant force and did not describe the motion, just the direction; forwards for B or backwards for C.

(b) (i) Most students correctly gave the distance travelled while braking. Some students correctly wrote about the distance travelled after braking, or distance travelled in the braking time. A common wrong answer was to involve total distance travelled before

the car stops, since this would include the reaction time. Many students lost the mark by putting a list of “braking and stopping distance”.

(ii) Only 25% of students scored this mark. Students often wrote about factors affecting stopping and braking distance; ‘bad weather conditions’ was a very common wrong answer. Also tiredness, being drunk, condition of road and state of vehicle were often given.

(c) (i) This mark was for giving both 5000 N and a clear direction. A lack of a simple arrow drawn in the correct direction kept many students from gaining this mark. Some students simply wrote ‘a very large force’ rather than quantifying it. A common incorrect answer was “5000 N on the car”. One of the most common responses was “5000 N towards the car”, which gained credit. Some students failed to include 5000 N in their answer, just stating that the resultant force was equal and opposite.

(ii) This question is about a dummy being used to measure/record the effects of impact/force. Many students wrote around this answer. “To see the force” was a common incorrect answer. Many students answered in terms of how much damage the dummy received, not mentioning measurement of the forces causing the damage and many students wrote about “impact”, instead of “force”, and did not gain credit for their answer.

(iii) A great number of students knew how to find the gradient of a velocity-time graph in order to calculate the acceleration, However, they failed to use only the straight line part of the graph - between 2 and 4 seconds. As a result, 10/4 was a common answer, giving 2.5 instead of 4. Often, the unit was the only credit-worthy part of an answer, although there were a number of mps, mph, km/s, etc. An answer of 40 was also quite common, multiplying 10 by 4. About half the students gave the correct unit; although m/s was a common incorrect answer. Some students drew a triangle correctly, but failed to use it, gaining one mark only. Some students correctly found 2 and 8, or 1 and 4, but then didn’t know how to calculate the acceleration; obtaining 16 or 0.25.

E34. (a) Just over 67% of students scored all three marks. A further 25% scored two marks. The most common error was to identify car A as being stationary, this was despite the word ‘moving’ being in bold in the stem of the question.

(b) (i) Nearly 90% of students scored this mark.

(ii) Just over 90% of students scored this mark.

(iii) This was not so well answered, with only 43% of students realising that the forces would be equal.

(iv) The majority of students (92%) realised the reason for attaching the sensors to the dummy.

E35. (a) Just over 67% of students scored all three marks. A further 25% scored two marks. The most common error was to identify car A as being stationary, this was despite the word ‘moving’ being in bold in the stem of the question.

(b) (i) Nearly 90% of students scored this mark.

(ii) Just over 90% of students scored this mark.

(iii) This was not so well answered, with only 43% of students realising that the forces would be equal.

(iv) The majority of students (92%) realised the reason for attaching the sensors to the dummy.

· web viewwhen they collide, the two vehicles become tightly locked together. (i) calculate the...

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