P5 Momentum Collision Calculations

P5 Momentum Collision Calculations Question Practice Name: Class: Date: Time: 88 minutes Marks: 88 marks Comments: PHYSICS ONLY Page of 24

(a) How can the momentum of an object be calculated? (2) (b) In a collision momentum is always conserved. What does this mean? (2) (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 ck so that the trolleys will stick together after colliding. Trolley A has a mass of 2 kg, and trolley B has a mass of 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. (4) Calculate the change in kinetic energy which occurs during the collision. (4) (Total 2 marks) Page 2 of 24

2 (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 increases four times. Explain, as fully as you can, why this is so. (3) (b) The diagram shows a car and a lry 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 wking. There is no need to change to standard units.) Answer km/h (6) The collision between the car and the lry is inelastic. Explain, in terms of energy, what this means. () (Total 0 marks) Page 3 of 24

3 (a) When two objects collide, and no other fces act, then conservation of momentum applies. (i) What does the term conservation of momentum mean? (2) Apart from collisions and similar events, give another type of event in which conservation of momentum applies. () (iii) Write, in wds, the equation which you need to use to calculate momentum. () (iv) The diagram shows a straight and hizontal 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.2 m/s to the right. Y has a mass of 0. 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 wk out your answer and give the unit and direction. Velocity of the trolleys = (5) Page 4 of 24

(v) What assumption did you make in der to calculate your answer to part (a)(iv)? () (b) Just befe it hits a target, a bullet has a momentum of 5 kg m/s. It takes 0.0025 s f the target to stop the bullet. 4 (a) Calculate the fce, in newtons, needed to do this. Write, in wds, the equation that you will need to use and show clearly how you wk out your answer. Fce = newtons The diagram shows a hammer which is just about to drive a nail into a block of wood. (3) (Total 3 marks) The mass of the hammer is 0.75 kg and its velocity, just befe it hits the nail, is 5.0 m/s downward. After hitting the nail, the hammer remains in contact with it f 0. s. After this time both the hammer and the nail have stopped moving. (i) Write down the equation, in wds, which you need to use to calculate momentum. () Page 5 of 24

What is the momentum of the hammer just befe it hits the nail? Show how you wk 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, fce and time. () (v) Calculate the fce applied by the hammer to the nail. Show how you wk out your answer and give the unit. Fce = (3) Page 6 of 24

(b) A magazine article states that: 5 (a) Wearing a seat belt can save your life in a car crash. Use your understanding of momentum to explain how this is crect. (4) (Total 3 marks) In any collision, the total momentum of the colliding objects is usually conserved. (i) What is meant by the term momentum is conserved? () In a collision, momentum is not always conserved. Why? () Page 7 of 24

(b) The diagram shows a car and a van, just befe and just after the car collided with the van. (i) Use the infmation in the diagram to calculate the change in the momentum of the car. Show clearly how you wk out your answer and give the unit. Change in momentum = (3) Use the idea of conservation of momentum to calculate the velocity of the van when it is pushed fward by the collision. Show clearly how you wk out your answer. Velocity = m/s fward (2) (Total 7 marks) Page 8 of 24

6 The figure below shows a skateboarder jumping fwards off his skateboard. The skateboard is stationary at the moment the skateboarder jumps. (a) The skateboard moves backwards as the skateboarder jumps fwards. Explain, using the idea of momentum, why the skateboard moves backwards. (3) Page 9 of 24

(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 fwards at a velocity of 0.3 m / s. Velocity of skateboard = m / s (3) (Total 6 marks) 7 Quantities in physics are either scalars vects. (a) Use the crect answers from the box to complete the sentence. acceleration direction distance speed time Velocity is in a given. (2) (b) Complete the table to show which quantities are scalars and which quantities are vects. Put one tick ( ) in each row. The first row has been completed f you. Quantity Scalar Vect Momentum Acceleration Distance Fce Time (3) Page 0 of 24

(c) The diagram shows two supermarket trolleys moving in the same direction. Trolley A is full of shopping, has a total mass of 8 kg and is moving at a velocity of 2 m / s with a kinetic energy of 6 J. Trolley B is empty, has a mass of 4 kg and is moving at a velocity of 0.5 m / s with a kinetic energy of 0.5 J. (i) Calculate the momentum of both trolley A and trolley B. Give the unit. Momentum of trolley A = Momentum of trolley B = Unit (4) The trolleys in the diagram collide and join together. They move off together. Calculate the velocity with which they move off together. Velocity = m / s (3) Page of 24

(iii) In a different situation, the trolleys in the digram move at the same speeds as befe but now move towards each other. Calculate the total momentum and the total kinetic energy of the two trolleys befe they collide. Total momentum = Total kinetic energy = J (2) (Total 4 marks) 8 (a) A car driver sees the traffic in front is not moving and brakes to stop his car. The stopping distance of a car is the thinking distance plus the braking distance. (i) What is meant by the braking distance? () The braking distance of a car depends on the speed of the car and the braking fce. State one other fact that affects braking distance. () (iii) How does the braking fce needed to stop a car in a particular distance depend on the speed of the car? () Page 2 of 24

(b) Figure shows the distance time graph f the car in the 0 seconds befe the driver applied the brakes. Use Figure to calculate the maximum speed the car was travelling at. Show clearly how you wk out your answer. Maximum speed = m / s (2) Page 3 of 24

(c) The car did not stop in time. It collided with the stationary car in front, joining the two cars together. Figure 2 shows both cars, just befe and just after the collision. (i) The momentum of the two cars was conserved. What is meant by the statement momentum is conserved? () Calculate the velocity of the two joined cars immediately after the collision. Velocity = m / s (3) Page 4 of 24

(d) Since 965, all cars manufactured f use in the UK must have seat belts. It is safer f a car driver to be wearing a seat belt, compared with not wearing a seat belt, if the car is involved in a collision. Explain why. (4) (Total 3 marks) Page 5 of 24

Mark schemes (a) mass and velocity/speed multiplied f mark each 2 (b) total momentum befe and after collision are the same f mark each 2 (c) (i) M A U A + M B U B = (M A + M B )v 2 6 = (2 + )v v = 4 m/s f mark each /2 mv 2 (befe) /2 mv 2 (after) /2 2.36 /2 3.6 = 2 J f mark each 4 4 [2] 2 (a) ideas that greater speed means me kinetic energy gains mark but any evidence of the fmula ½ mv 2 but making the case that kinetic energy depends on the speed squared gains 3 marks that 2 2 = 4 3 (b) (i) any evidence of concept of momentum mass speed ( velocity) in wds figures e.g. 9.5 20 0.5 40 gains mark but crect values f momentum of lry and car i.e. 90 and 20 [igne units] gains 2 marks but initial momentum crectly calculated 70 90 20 gains 3 marks Page 6 of 24

THEN evidence when calculating final speed of idea that momentum is conserved use of combined mass each gain mark but 7 [ 0. figure f initial momentum] (NB direction not required) gains 3 marks 6 kinetic energy is lost f mark [credit (some kinetic) energy transferred as heat/sound] [NB Accept only answers in terms of energy as required by the question] [0] 3 (a) (i) either the momentum in a particular direction after (the collision) is the same as the momentum in that direction befe (the collision) accept momentum befe equals momentum after f mark (iii) total momentum after (the collision) equals the total momentum befe (the collision) (2) accept momentum befe equals momentum after f mark explosion(s) (action of a) rocket (mot(s)) (action of a) jet (engine) 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 momentum = mass velocity any crectly transposed version accept momentum = mass speed accept p = mv do not accept momentum = ms M = mv 2 Page 7 of 24

(iv) 0.8 if answer 0.8 not given, any two f () each: momentum of X = 0.2.2 = momentum of X and Y after impact = 0.3 v = (0. + 0.2) v 3 m/s to the right (v) any one from: conservation of momentum (applies) no external fces do not accept just no (other) fces act friction is negligible / insignificant no friction (b) no air resistance fce = (change in) momentum time any crectly transposed version 4000 4 kilonewtons dependent on crect no equation fce = 5 0.0025 gains mark 2 [3] Page 8 of 24

4 (a) (i) momentum = mass velocity.2 to.3 accept speed any transposed version 0.75 5 f mark kg m/s down(wards) Ns down(ward) (iii).2 to.3 n.b. both unit and direction required f this mark accept same numerical answer as part (a) accept answer without any unit with the same unit as in part (a), even if increct, but any other unit cancels the mark 2 (iv) fce = accept transposed version (v) 2 to 3 numerical value from (a) 0.25 0. (a) 0. f mark 2 newton(s) N accept Newton(s) do not credit Ns n (b) (the user will experience a) large change in momentum do not credit just momentum changes (but) seat belt increases the time f this to occur seat belt stops you hitting something which would stop you quickly do not credit just stops you hitting the windscreen etc. (so) the fce on the user is less(*) (so) less chance of (serious / fatal) injury(*) (*) depends on previous response re momentum continued movement [3] Page 9 of 24

5 (a) (i) momentum befe = momentum after accept no momentum is lost accept no momentum is gained (total) momentum stays the same an external fce acts (on the colliding objects) accept colliding objects are not isolated (b) (i) 9600 kg m/s Ns allow mark f crect calculation of momentum befe after ie 2000 2400 crect substitution using change in velocity = 8 m/s ie 200 8 this may be given in wds rather than symbols do not accept ns 2 3 their (b)(i) 3200 crectly calculated allow mark f stating momentum befe = momentum after clear attempt to use conservation of momentum 2 [7] Page 20 of 24

6 (a) momentum befe (jumping) = momentum after (jumping) accept momentum (of the skateboard and skateboarder) is conserved befe (jumping) momentum of skateboard and skateboarder is zero accept befe (jumping) momentum of skateboard is zero accept befe (jumping) total momentum is zero after (jumping) skateboarder has momentum (fwards) so skateboard must have (equal) momentum (backwards) answers only in terms of equal and opposite fces are insufficient (b) 7 accept 7 f 3 marks allow 2 marks f momentum of skateboarder equals 2.6 0 = 42 0.3 + (.8 v) allow mark f stating use of conservation of momentum 3 [6] 7 (a) speed must be in crect der direction (b) Quantity Scalar Vect Momentum Acceleration Distance Fce Time any three crect sces 2 marks any two crect sces mark only one crect sces zero 3 Page 2 of 24

(c) (i) 6 and 2 6 2 sces 2 marks allow mark f crect substitution, ie 8 2 4 0.5 kg m / s N s.5 (m / s) their p A + p B = 2 v crectly calculated allow 2 marks f crect substitution, ie 8 = 2 v their p A + p B = 2 v 8 their p A + p B sces mark if no other mark awarded 3 3 (iii) 4 (kg m / s) their p A - p B 6.5 (J) [4] 8 (a) (i) distance travelled under the braking fce accept distance travelled between applying the brakes and stopping (iii) any one from: icy / wet roads accept weather (conditions) (wn) tyres road surface accept gradient of road mass (of car and passengers) accept number of passengers (efficiency / condition of the) brakes. friction / traction is insufficient greater the speed the greater the braking fce (required) must mention both speed and fce Page 22 of 24

(b) 22.5 allow mark f showing crect use of the graph with misread figures f showing e.g. 90 4 an answer 7 gains mark any answer such as 7.4 7.5 sces 0 2 (c) (i) momentum befe = momentum after (total) momentum stays the same accept no momentum is lost accept no momentum is gained igne statements referring to energy 5 allow 2 marks f crectly obtaining momentum befe as 2 000 allow 2 marks f 500 8 = 2400 v allow mark f a relevant statement re conservation of momentum allow mark f momentum befe = 500 8 3 Page 23 of 24

(d) the seat belt stretches driver takes a longer (impact) time to slow down and stop (than a driver hitting a hard surface / windscreen / steering wheel) f the (same) change of momentum accept so smaller deceleration / negative acceleration a smaller fce is exerted (so driver less likely to have serious injury than driver without seat belt) the seat belt stretches () do not accept impact f fce driver travels a greater distance while slowing down and stopping (than a driver hitting a hard surface / windscreen / steering wheel) () f (same) amount of wk done () accept f (same) change of KE a smaller fce is exerted (so driver less likely to have serious injury than driver without seat belt) () do not accept impact f fce [3] Page 24 of 24