Page 1 of 21 4.6 Mechanics and Materials - Momentum 1 – Questions Q1. A bullet of mass 10 g is fired with a velocity of 100 m s –1 from a stationary rifle of mass 4.0kg. Consider the rifle and bullet to be an isolated system. What are the recoil velocity of the rifle and the total momentum of the rifle and bullet just after firing? Recoil velocity / m s –1 Total momentum / kg m s –1 A 0.25 0 B 0.25 1.0 C 0.40 0 D 0.40 1.0 (Total 1 mark) Q2. A cricket ball of mass 0.16 kg travelling at a speed of 35 ms –1 is hit by a bat and, as a result of the impact, leaves the bat in the opposite direction at 30 ms –1 . If the duration of the impact is 52 ms, what is the magnitude of the average force on the ball? A 0.015 N B 0.20 N C 15 N D 200 N (Total 1 mark) Q3. A body X moving with a velocity v makes an elastic collision with a stationary body Y of equal mass on a smooth horizontal surface. Which line, A to D, in the table gives the velocities of the two bodies after the collision? velocity of X velocity of Y
Transcript
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4.6 Mechanics and Materials - Momentum 1 – Questions
Q1. A bullet of mass 10 g is fired with a velocity of 100 m s–1 from a stationary rifle of mass 4.0 kg. Consider the rifle and bullet to be an isolated system.
What are the recoil velocity of the rifle and the total momentum of the rifle and bullet just after firing?
Recoil velocity / m s–1
Total momentum / kg m s–1
A 0.25 0
B 0.25 1.0
C 0.40 0
D 0.40 1.0 (Total 1 mark)
Q2. A cricket ball of mass 0.16 kg travelling at a speed of 35 ms–1 is hit by a bat and, as a result of the impact, leaves the bat in the opposite direction at 30 ms–1. If the duration of the impact is 52 ms, what is the magnitude of the average force on the ball?
A 0.015 N
B 0.20 N
C 15 N
D 200 N (Total 1 mark)
Q3. A body X moving with a velocity v makes an elastic collision with a stationary body Y of equal mass on a smooth horizontal surface.
Which line, A to D, in the table gives the velocities of the two bodies after the collision?
velocity of X velocity of Y
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A
B
C v 0
D 0 v
(Total 1 mark)
Q4. A ball of mass 2.0 kg, initially at rest, is acted on by a force F which varies with time t as shown by the graph.
What is the velocity of the ball after 8.0 s?
A 20 ms–1
B 40 ms–1
C 80 ms–1
D 160 ms–1
(Total 1 mark)
Q5. The graph shows how the force acting on a body changes with time.
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The body has a mass of 0.25 kg and is initially at rest. What is the speed of the body after 40 s assuming no other forces are acting?
A 200 ms–1
B 400 ms–1
C 800 ms–1
D 1600 ms–1
(Total 1 mark)
Q6. Two ice skaters, initially at rest and in contact, push apart from each other. Which line, A to D, in the table states correctly the change in the total momentum and the total kinetic energy of the two skaters?
total momentum total kinetic energy
A unchanged increases
B unchanged unchanged
C increases increases
D increases unchanged
(Total 1 mark)
Q7. A stationary unstable nucleus of mass M emits an α particle of mass m with kinetic energy E
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What is the speed of recoil of the daughter nucleus?
A
B
C
D (Total 1 mark)
Q8. A ball is released so that it falls vertically. The graph shows how the resultant force acting on the ball changes with time.
Which one of the following is represented by the area under the graph?
A distance travelled
B gain in kinetic energy
C acceleration
D impulse (Total 1 mark)
Q9.
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When hitting golf balls long distances, golfers follow through with the swing. Doing this increases the time for which the club head is in contact with the ball.
The figure below is a stroboscopic photograph of a golf swing. The images were taken at equal time intervals.
(a) Sketch, on the axes below, how the speed of the club head varies with time over the whole swing.
(2)
(b) Explain in terms of the impulse acting on the ball the advantage to the golfer of following through with the swing.
(c) The club head is in contact with the ball for a time of 180 μs. The mass of the club head is 0.17 kg and that of the ball is 0.045 kg. At the moment of contact the ball is
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at rest and the club head is moving with a speed of 35 ms–1. The ball moves off with an initial speed of 58 ms–1.
(i) Calculate the average force acting on the ball while the club head is in contact with it.
average force on ball ____________________ N (2)
(ii) Deduce the average force acting on the club head due to its collision with the ball.
average force on club head ____________________ N (1)
(iii) Explain why it is not possible to transfer all the kinetic energy of the club head to the ball.
Q10. A ball of mass m travelling at velocity v collides normally with a smooth wall, as shown in the diagram, and rebounds elastically.
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Which line, A to D, in the table, gives the correct expressions for the magnitude of the change of momentum, and the change of kinetic energy, of the ball?
magnitude of change of momentum change of kinetic energy
A 2mv 0
B 2mv mv2
C 0 0
D 0 mv2
(Total 1 mark)
Q11. A railway truck of mass 8000 kg travels along a level track at a velocity of 2.5 ms–1 and collides with a stationary truck of mass 12000 kg. The two trucks move together at the same velocity after the collision.
What is the change in momentum of the 8000 kg truck due to the impact?
A 8000 N s
B 12000 N s
C 20000 N s
D 25000 N s (Total 1 mark)
Q12.
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The nucleus of a radioactive isotope X is at rest and decays by emitting an α particle so that a new nuclide Y is formed. Which one of the following statements about the decay is correct?
A The momentum of Y is equal and opposite to the momentum of the α particle.
B The momentum of Y is equal to the momentum of X.
C The kinetic energy of Y is equal to the kinetic energy of the α particle.
D The total kinetic energy is the same before and after the decay. (Total 1 mark)
Q13. The graph shows how the resultant force, F, acting on a body varies with time, t.
What is the change in momentum of the body over the 5 s period?
A 2N s
B 8N s
C 10N s
D 12N s (Total 1 mark)
Q14. A gas molecule of mass m moving at velocity u collides at right angles with the side of a container and rebounds elastically. Which one of the following statements concerning the motion of the molecule is incorrect?
A The magnitude of the change in momentum of the molecule is zero.
B The magnitude of the change in momentum of the molecule is 2mu.
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C The force exerted by the molecule on the side of the container is equal to the force exerted by the container on the molecule.
D The change in kinetic energy of the molecule is zero. (Total 1 mark)
Q15. Which one of the following is a possible unit of impulse?
A Ns–1
B kg ms–1
C kg ms–2
D sN–1
(Total 1 mark)
Q16. Water of density 1000 kg m–3 flows out of a garden hose of cross-sectional area 7.2 × 10–4 m2 at a rate of 2.0 × 10–4 m3 per second. How much momentum is carried by the water leaving the hose per second?
A 5.6 ×10–5 N s
B 5.6 × 10–2 N s
C 0.20 N s
D 0.72 N s (Total 1 mark)
Q17. The graph shows how the force acting on a rocket varies with time.
Which one of the following is represented by the area under the graph?
A distance travelled
B gain in kinetic energy
C change in velocity
D change in momentum
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(Total 1 mark)
Q18. A golf club strikes a stationary golf ball of mass 4.8 × 10–2 kg and the ball leaves the club with a speed of 95 m s–1. If the average force exerted on the ball is 7800 N, how long are the ball and club in contact?
A 5.8 × 10–4 s
B 1.2 × 10–2 s
C 0.51 s
D 0.58 s (Total 1 mark)
Q19. (a) Explain what is meant by a thermal neutron.
(b) A student sets up the arrangement, shown in the diagram below, to demonstrate the principle of moderation in a nuclear reactor.
A golf ball of mass 50 g is initially hanging vertically and just touching a hockey ball of mass 150 g. The golf ball is pulled up to the side and released. It has a speed of 1.3 m s−1 when it collides head-on with the hockey ball. After the collision the balls move in opposite directions with equal speeds of 0.65 m s−1.
(i) Calculate the height above its initial position from which the golf ball is released. Assume that there is no air resistance.
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height ____________________ m (2)
(ii) Show that momentum is conserved in the collision and that the collision is perfectly elastic.
(4)
(iii) Calculate the percentage of the kinetic energy of the golf ball transferred to the hockey ball during the collision.
percentage transferred ____________________ % (2)
(iv) Explain how this demonstration relates to the moderation process in a reactor and state one way in which the collisions in a reactor differ from the collision in the demonstration.
Q20. What is represented by the area under a force–displacement graph?
A rate of change of kinetic energy
B change in momentum
C work done
D acceleration (Total 1 mark)
Q21. Trolley T1, of mass 2.0 kg, collides on a horizontal surface with trolley T2, which is also of mass 2.0 kg. The collision is elastic. Before the collision T1 was moving at 4.0 m s–1 and T2 was at rest.
Which one of the following statements is correct?
Immediately after the collision
A T1 is at rest and T2 moves at 4.0 m s–1.
B T1 will rebound from T2 at 4.0 m s–1.
C T1 and T2 will both move at 2.8 m s–1.
D T1 and T2 will both move at 1.4 m s–1. (Total 1 mark)
Q22. Which one of the following has the same unit as the rate of change of momentum?
A work
B energy
C acceleration
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D weight (Total 1 mark)
Q23. The Rosetta space mission placed a robotic probe on Comet 67P in 2014.
(a) The total mass of the Rosetta spacecraft was 3050 kg. This included the robotic probe of mass 108 kg and 1720 kg of propellant. The propellant was used for changing velocity while travelling in deep space where the gravitational field strength is negligible.
Calculate the change in gravitational potential energy of the Rosetta spacecraft from launch until it was in deep space. Give your answer to an appropriate number of significant figures.
Mass of the Earth = 6.0 × 1024 kg Radius of the Earth = 6400 km
change in gravitational potential energy ____________________ J (4)
(b) As it approached the comet, the speed of the Rosetta spacecraft was reduced to match that of the comet. This was done in stages using four ‘thrusters’. These were fired simultaneously in the same direction.
(c) Each thruster provided a constant thrust of 11 N.
Calculate the deceleration of the Rosetta spacecraft produced by the four thrusters when its mass was 1400 kg.
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decleration ____________________ m s–2
(1)
(d) Calculate the maximum change in speed that could be produced using the 1720 kg of propellants.
Assume that the speed of the exhaust gases produced by the propellant was 1200 m s–1
maximum change in speed ____________________ m s–1
(3)
(e) When the robotic probe landed, it had to be anchored to the comet due to the low gravitational force. Comet 67P has a mass of about 1.1 × 1013 kg. A possible landing site was about 2.0 km from the centre of mass.
(i) Calculate the gravitational force acting on the robotic probe when at a distance of 2.0 km from the centre of mass of the comet.
gravitational force ____________________ N (3)
(ii) Calculate the escape velocity for an object 2.0 km from the centre of mass of the comet.
escape velocity ____________________ m s–1
(3)
(iii) A scientist suggests using a drill to make a vertical hole in a rock on the surface of the comet. The anchoring would be removed from the robotic probe before the drill was used. The drill would exert a force of 25 N for 4.8 s.
Explain, with the aid of a calculation, whether this process would cause the robotic probe to escape from the comet.
(b) When a stationary unstable nucleus emits an α particle with velocity v the resulting nucleus recoils with velocity V, as shown in the diagram.
The mass of the α particle is m and the mass of the recoiling nucleus is N.
(i) Show how the principle of conservation of momentum may be used to derive an expression for V in terms of N, m and v.
(2)
(ii) Assume that all of the energy released in the emission process is transferred as kinetic energy to the α particle and the recoiling nucleus. The total energy released is E. Use your result from part (b)(i) to show that the kinetic energy of the α particle is given by
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(4)
(c) (i) The isotope of radon decays by emitting an α particle.
State the nucleon number of the recoiling nucleus.
nucleon number = ____________________ (1)
(ii) The total energy released when a nucleus of decays is 1.02 × 10−12 J.
Calculate the magnitude of the momentum of the α particle. State an appropriate unit for your answer.
Mass of a nucleon = 1.66 × 10−27 kg
momentum = _______________ unit __________ (4)
(d) Explain why the expressions in parts (b)(i) and (b)(ii) could not be applied when an unstable nucleus decays by emitting a β− particle.
Q25. The graph shows how the resultant force applied to an object of mass 2.0 kg, initially at rest, varies with time.
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What is the speed of the object after 1.0 s?
A 2.5 m s−1
B 5.0 m s−1
C 7.5 m s−1
D 10 m s−1
(Total 1 mark)
Q26. In a test a 500 kg car travelling at 10 m s–1 hits a wall. The front 0.30 m of the car crumples as the car is brought to rest.
What is the average force on the car during the impact?
A 830 N
B 7500 N
C 8300 N
D 83 000 N (Total 1 mark)
Q27. Which line, A to D, in the table correctly shows what is conserved in an elastic collision?
Mass Momentum Kinetic energy Total energy
A conserved not conserved conserved conserved B not conserved conserved conserved not conserved C conserved conserved not conserved conserved D conserved conserved conserved conserved
(Total 1 mark)
Q28. An object is accelerated from rest by a constant force F for a time t. Which graphs represent the variation of time with the change in the kinetic energy and the change in momentum of the object?
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Kinetic energy Momentum
A
B
C
D
A
B
C
D (Total 1 mark)
Q29. A body falls freely, with negligible air resistance. What quantity of the body is its rate of change of momentum?
A mass
B power
C kinetic energy
D weight (Total 1 mark)
Q30. A firework rocket is fired vertically into the air and explodes at its highest point. What are
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the changes to the total kinetic energy of the rocket and the total momentum of the rocket as a result of the explosion?
total kinetic energy
of rocket
total momentum of rocket
A unchanged unchanged
B unchanged increased
C increased unchanged
D increased increased
(Total 1 mark)
Q31. A car of mass 580 kg collides with the rear of a stationary van of mass 1200 kg.
Following the collision, the van moves with a velocity of 6.20 m s–1 and the car recoils in the opposite direction with a velocity of 1.60 m s–1.
What is the initial speed of the car?
A 5.43 m s–1
B 11.2 m s–1
C 12.8 m s–1
D 14.4 m s–1
(Total 1 mark)
Q32. A ball of mass 0.20 kg is thrown and moves in a curved path, as shown below. At Q it is travelling horizontally.
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Assume air resistance is negligible.
What is the momentum of the ball at Q?
A zero
B 2.0 N s
C 3.5 N s
D 4.0 N s (Total 1 mark)
Q33. The graph shows how the force F applied to an object varies with time t.
What is the momentum gained by the object from t = 0 to t = 10 s?
A 18 kg m s–1
B 32 kg m s–1
C 40 kg m s–1
D 58 kg m s–1
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(Total 1 mark)
Q34. Two unpowered toy cars, P and Q, are released from rest from X and travel down the track to Y. Car P has twice the mass of car Q. There is negligible friction.
What quantity is the same for car P and car Q?
A The gravitational potential energy at X.
B The accelerating force at X.
C The velocity when they arrive at Y.
D The momentum when they arrive at Y. (Total 1 mark)
Q35. Two bodies of different masses undergo an elastic collision in the absence of any external force.
Which row gives the effect on the total kinetic energy of the masses and the magnitudes of the forces exerted on the masses during the collision?
