# Exampro GCSE Physics. P2 Momentum and Energy Calculations Self Study Higher tier. Name: Class: Author: Date: Time: 110. Marks: 110.

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1 Exampro GCSE Physics P2 Momentum and Energy Calculations Self Study Higher tier Name: Class: Author: Date: Time: 0 Marks: 0 Comments: Page of 33

2 Q. The figure below shows a skateboarder jumping forwards off his skateboard. The skateboard is stationary at the moment the skateboarder jumps. (a) The skateboard moves backwards as the skateboarder jumps forwards. Explain, using the idea of momentum, why the skateboard moves backwards (3) Page 2 of 33

3 (b) The mass of the skateboard is.8 kg and the mass of the skateboarder is 42 kg. Calculate the velocity at which the skateboard moves backwards if the skateboarder jumps forwards at a velocity of 0.3 m / s. Use the correct equation from the Physics Equations Sheet Velocity of skateboard =... m / s (3) (Total 6 marks) Q2. (a) In any collision, the total momentum of the colliding objects is usually conserved. (i) What is meant by the term momentum is conserved? () (ii) In a collision, momentum is not always conserved. Why? () Page 3 of 33

4 (b) The diagram shows a car and a van, just before and just after the car collided with the van. (i) Use the information in the diagram and the equation in the box to calculate the change in the momentum of the car. momentum = mass x velocity Show clearly how you work out your answer and give the unit. 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. Show clearly how you work out your answer. Velocity =... m/s forward (2) (Total 7 marks) Page 4 of 33

5 Q3. (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 5.0 m/s downward. After hitting the nail, the hammer remains in contact with it for 0. 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. () (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. Momentum =... (3) (iii) What is the change in momentum of the hammer during the time it is in contact with the nail? () (iv) Write down an equation which connects change in momentum, force and time. () Page 5 of 33

6 (v) Calculate the force applied by the hammer to the nail. Show how you work out your answer and give the unit. 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 (4) (Total 3 marks) Q4. (a) In any collision, the total momentum of the colliding objects is usually conserved. (i) What is meant by the term momentum is conserved? () (ii) In a collision, momentum is not always conserved. Why? () Page 6 of 33

7 (b) The diagram shows a car and a van, just before and just after the car collided with the van. Before collision After collision (i) Use the information in the diagram and the equation in the box to calculate the change in the momentum of the car. momentum = mass velocity Show clearly how you work out your answer and give the unit. 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. Show clearly how you work out your answer. Velocity =... m/s forward (2) (Total 7 marks) Page 7 of 33

8 Q5. 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 0 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 200 kg and the total mass of car B was 500 kg. (i) Write down the equation, in words, which you need to use to calculate momentum. () (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. 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. Speed =... m/s (3) (Total 7 marks) Page 8 of 33

9 Q6. 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. momentum = mass velocity Show clearly how you work out your answer and give the unit. 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 = Show clearly how you work out your answer. Force =... N (2) Page 9 of 33

10 (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. (3) Page 0 of 33

11 (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 laboratory using 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 used in a playground (2) (d) Developments in technology allow manufacturers to make rubber tiles from scrap car tyres. Suggest why this process may benefit the environment. () (Total marks) Page of 33

12 Q7. 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.5 kg of air downwards every 0 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. momentum = mass velocity force = Show clearly how you work out your answer Velocity =... m/s (3) (b) Explain why the toy accelerates upwards when the fan rotates faster (2) Page 2 of 33

13 (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 (3) (Total 8 marks) ## The table shows the braking distances for a car at different speeds and kinetic energy. The braking distance is how far the car travels once the brakes have been applied. Braking distance in m Speed of car in m/s Kinetic energy of car in kj Page 3 of 33

14 (a) A student suggests, the braking distance is directly proportional to the kinetic energy. (i) Draw a line graph to test this suggestion. (3) (ii) Does the graph show that the student s suggestion was correct or incorrect? Give a reason for your answer () (iii) Use your graph and the following equation to predict a braking distance for a speed of 35 metres per second (m/s). The mass of the car is 800 kilograms (kg). Show clearly how you obtain your answer. kinetic energy = ½ mv Braking distance =... m (2) (iv) State one factor, apart from speed, which would increase the car s braking distance.... () Page 4 of 33

15 (b) The diagram shows a car before and during a crash test. The car hits the wall at 4 metres per second (m/s) and takes 0.25 seconds (s) to stop. (i) Write down the equation which links acceleration, change in velocity and time taken.... () (ii) Calculate the deceleration of the car.... Deceleration =... m/s 2 () (iii) In an accident the crumple zone at the front of a car collapses progressively. This increases the time it takes the car to stop. In a front end collision the injury to the car passengers should be reduced. Explain why. The answer has been started for you. By increasing the time it takes for the car to stop, the (2) (Total marks) Page 5 of 33

16 Q9. The diagram below shows an experiment where a pendulum swings backwards and forwards. A pendulum is a small heavy weight suspended by a light string. (a) (i) In which position, A, B or C, does the pendulum have least potential energy? Explain your answer. () (ii) In which position, A, B or C, does the pendulum have greatest kinetic energy? Explain your answer. () (iii) After a few minutes the size of the swings becomes smaller. Explain why this happens. () (b) If the experiment were repeated on the Moon the pendulum would swing more slowly. Suggest a reason for this. (2) (Total 5 marks) Page 6 of 33

17 Q0. A racing driver is driving his car along a straight and level road as shown in the diagram below. (a) The driver pushes the accelerator pedal as far down as possible. The car does not accelerate above a certain maximum speed. Explain the reasons for this in terms of the forces acting on the car. (4) (b) The racing car has a mass of 250 kg. When the brake pedal is pushed down a constant braking force of N is exerted on the car. (i) Calculate the acceleration of the car. (ii) Calculate the kinetic energy of the car when it is travelling at a speed of 48 m/s. Page 7 of 33

18 (iii) When the brakes are applied with a constant force of N the car travels a distance of 44 m before it stops. Calculate the work done in stopping the car. (2) (Total 6 marks) Q. The diagram shows a high jumper. In order to jump over the bar, the high jumper must raise his mass by.25 m. The high jumper has a mass of 65 kg. The gravitational field strength is 0 N/kg. Page 8 of 33

19 (a) The high jumper just clears the bar. Use the following equations to calculate the gain in his gravitational potential energy. weight = mass gravitational field strength (newton, N) (kilogram, kg) (newton/kilogram, N/kg) change in gravitational potential energy = weight change in vertical height (joule, J) (Newton, N) (metre, m) Gain in gravitational potential energy... J (4 (b) Use the following equation to calculate the minimum speed the high jumper must reach for take-off in order to jump over the bar. kinetic energy = mass [speed] 2 (joule, J) (kilogram, kg) [(metre/second) 2, (m/s) 2 Speed... m/s (3) (Total 7 marks) Page 9 of 33

20 Q2. SPEED KILLS - was the heading of an advertising campaign. The scientific reason for this is that energy is transferred from the vehicle to the person it knocks down. (a) The bus and the van are travelling at the same speed. The bus is more likely to cause more harm to a person who is knocked down than the van would. Explain why (2) (b) A car and its passengers have a mass of 200 kg. It is travelling at 2 m/s. (i) Calculate the increase in kinetic energy when the car increases its speed to 8 m/s. Show clearly how you work out your answer and give the unit Increase in kinetic energy =... (5) Page 20 of 33

21 (ii) Explain why the increase in kinetic energy is much greater than the increase in speed () (Total 8 marks) Q3. The diagram shows a motorbike of mass 300 kg being ridden along a straight road. The rider sees a traffic queue ahead. He applies the brakes and reduces the speed of the motorbike from 8 m/s to 3 m/s. (a) Use the equation in the box to calculate the kinetic energy lost by the motorbike. kinetic energy = mass speed 2 Show clearly how you work out your answer. Kinetic energy lost =... J (2) Page 2 of 33

22 (b) (i) How much work is done on the motorbike by the braking force? () (ii) What happens to the kinetic energy lost by the motorbike? () (Total 4 marks) Page 22 of 33

23 M. (a) momentum before (jumping) = momentum after (jumping) accept momentum (of the skateboard and skateboarder) is conserved before (jumping) momentum of skateboard and skateboarder is zero accept before (jumping) momentum of skateboard is zero accept before (jumping) total momentum is zero after (jumping) skateboarder has momentum (forwards) so skateboard must have (equal) momentum (backwards) answers only in terms of equal and opposite forces are insufficient (b) 7 accept 7 for 3 marks allow 2 marks for momentum of skateboarder equals 2.6 or 0 = (.8 v) or allow mark for stating use of conservation of momentum 3 [6] M2. (a) (i) momentum before = momentum after accept no momentum is lost accept no momentum is gained or (total) momentum stays the same (ii) an external force acts (on the colliding objects) accept colliding objects are not isolated (b) (i) 9600 allow mark for correct calculation of momentum before or after ie 2000 or 2400 or correct substitution using change in velocity = 8 m/s ie kg m/s or Ns this may be given in words rather than symbols do not accept ns Page 23 of 33

24 (ii) 3 or their (b)(i) 3200 correctly calculated allow mark for stating momentum before = momentum after or clear attempt to use conservation of momentum 2 [7] M3. (a) (i) momentum = mass velocity accept speed or any transposed version (ii).2 to for mark kg m/s down(wards) or Ns down(ward) n.b. both unit and direction required for this mark (iii).2 to.3 accept 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 2 (iv) force = accept transposed version (v) 2 to 3 or numerical value from (a)(ii) or (a)(ii) 0. for mark newton(s) or N accept Newton(s) do not credit Ns or n 2 Page 24 of 33

25 (b) (the user will experience a) large change in momentum do not credit just momentum changes (but) seat belt increases the time for this to occur or seat belt stops you hitting something which would stop you quickly do not credit just stops you hitting the windscreen etc. (so) the force on the user is less(*) (so) less chance of (serious / fatal) injury(*) (*) depends on previous response re momentum or continued movement [3] M4. (a) (i) momentum before = momentum after or (total) momentum stays the same accept no momentum is lost accept no momentum is gained (ii) an external force acts (on the colliding objects) accept colliding objects are not isolated (b) (i) 9600 allow mark for correct calculation of momentum before or after ie 2000 or 2400 or correct substitution using change in velocity = 8 m/s ie kg m/s this may be given in words rather than symbols or Ns (ii) 3 or their (b)(i) 3200 correctly calculated allow mark for stating momentum before = momentum after or clear attempt to use conservation of momentum 2 [7] Page 25 of 33

26 M5. (i) momentum (change in) = mass velocity (change in) accept... speed (ii) for mark but not from incorrect equation kilogram metre(s) per second or kg m/s 2 (iii) either 7.5 (m/s) or change in momentum of car B change in momentum of car A () 9000 = 200 v () or v = () or error carried forward from part (ii) examples 5 (m/s) if 6000 offered in (ii) (3) 2.5(m/s) if 5000 offered in (ii) (3) 3 [7] M6. (a) (i) 20 allow mark for correct substitution i.e kg m/s or Ns do not accept n for N accept g m/s for 3 marks 2 (ii) 840 if answer given is not 840 accept their (a)(i) in kg m/s 0.25 correctly calculated for both marks allow mark for correct substitution i.e or their (a)(i) (b) increases the time to stop accept increases impact time do not accept any references to slowing down time decreases rate of change in momentum accept reduces acceleration/deceleration reduces momentum is insufficient reduces the force (on the child) Page 26 of 33

27 (c) any two from: insufficient range of tests/thicknesses for required cfh accept need data for thicknesses above 80 mm/ cfh 2.7 m not enough tests is insufficient (seems to be) some anomalous data (repeats) needed to improve reliability (of data) accept data/ results are unreliable do not accept maybe systematic/random error do not accept reference to precision need to test greater range/variety of dummies accept children for dummies accept specific factor such as weight/height/size 2 (d) Tyres do not need to be dumped/burned/ less land-fill/ saves on raw materials accept less waste do not accept recycling on its own [] M7. (a) 4 (m/s) mark for correct transformation of either equation mark for correct substitution with or without transformation mark for correct use of 0.6N max score of 2 if answer is incorrect 3 Page 27 of 33

28 (b) greater change in momentum or greater mass of air (each second) or increase in velocity of air accept speed for velocity force upwards increased lift force is increased do not accept upthrust or force up greater than force down accept weight for force down (c) increase the time to stop decrease rate of change in momentum or same momentum change accept reduced deceleration/ acceleration reducing the force on the toy do not accept answers in terms of the impact/ force being absorbed do not accept answers in terms of energy transfer do not credit impact is reduced [8] M8. (a) (i) linear scales used do not credit if less than half paper used points plotted correctly all of paper used (straight) line of best fit drawn allow a tolerance of half square (ii) correct and straight line through origin all needed e.c.f. if their (a)(i) is straight but not through the origin - incorrect because line does not go through origin credit a calculation that shows proportionality Page 28 of 33

29 (iii) (iv) 62 ± 0.5 (m) credit mark for KE = or 490kJ credit mark for correct use of graph clearly shown any one from: wet or icy or worn or smooth road accept slippery slope brakes worn accept faulty brakes car heavily loaded worn tyres downhill slope do not accept anything to do with thinking distance e.g. driver tired or drunk 2 (b) (i) acceleration = accept correct transformation accept accept m/s = 2 do not accept acceleration = (ii) 56 accept 56 (iii) deceleration is reduced accept deceleration is slower accept acceleration force on car and or passengers is reduced accept an answer in terms of change in momentum for full credit [] M9. (a) (i) B unless unqualified for mark Page 29 of 33

30 (ii) B unless unqualified for mark (iii) energy lost, doing work against air resistance/friction for mark (b) intensity of gravity less (not zero) for mark energies/restoring forces less for mark 2 [5] M0. (a) there is a (maximum) forward force drag/friction/resistance (opposes motion) (not pressure) increases with speed till forward and backward forces equal so no net force/acceleration any 4 for mark each 4 (b) (i) F = ma = 250a a = 8 m/s 2 for mark each 4 (ii) ke = /2 mv 2 ke = / ke = J for mark each 4 (iii) W = Fd W = W = J for mark each 4 [6] Page 30 of 33

31 M. (a) W = 65 0 (allow a maximum of 3 marks if candidate uses g = 9.8N / Kg (as ecf)) gains mark but W = 650 (N) (allow use of p.e.= m g h) gains 2 marks but PE change = or gains 3 marks but PE change = 82.5 (J) (allow 83J or 82J) gains 4 marks 4 (b) k.e. = p.e. gains mark but (speed)² = / 65 or 82.5 = ½ 65 (speed)² ecf gains 2 marks but speed = 5 (m/s) (allow ) (if answer = 25mls check working: 82.5 = ½ m v gains mark for KE = PE) (but if 82.5 = ½m v² = ½ 65 v 2 or v 2 = gains 2 marks) 25, with no working shown gains 0 marks gains 3 marks 3 [7] M2. (a) the greater the mass / weight then the greater the kinetic energy accept the greater the momentum accept greater mass / weight therefore greater force = 2 Page 3 of 33

32 (b) (i) Note: this calculation requires candidates to show clearly how they work out their answer k.e. mv 2 accept evidence of equation (J) at 2 m/s accept ½ or 86.4 KJ (J) at 8 m/s accept ½ or 94.4KJ increase in k.e. = NB 0800 = 0 marks N.B. if no working at all then max 3 for a correct numerical answer joules or J accept 08 kilojoules or kj (ii) explanation that ke v 2 [8] M3. (a) answers of 350/ 33750/ gain mark allow mark for correct substitution using both 8 and 3 (b) (i) or their (a) accept statement same as the KE (lost) ignore any units 2 (ii) transformed into heat/ thermal energy sound on its own is insufficient accept transferred/ lost/ for transformed do not accept any other form of energy included as a list [4] Page 32 of 33

33 Page 33 of 33

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