MB1-MB2 Conservation of momentum and restitution Quiz: AQA Further Maths, Unit 3

The 20 questions

1. What principle applies to a collision when no external impulse acts on the system?

   • The force on each particle is zero
   • The speed of each particle is conserved
   • Total momentum is conserved
   • Kinetic energy is always conserved

2. What is the coefficient of restitution e in a direct collision?

   • e = (speed of separation)/(speed of approach)
   • e = mv/mu
   • e = (speed of approach)/(speed of separation)
   • e = 1 - (speed of separation)

3. What range of values can the coefficient of restitution take?

   • -1 <= e <= 1
   • Any real number
   • 0 <= e <= 1
   • e >= 1 always

4. What does e = 1 mean for a collision?

   • The collision is perfectly elastic
   • There is no collision
   • The particles stick together
   • The collision is perfectly inelastic

5. What does e = 0 mean for a collision?

   • The particles move together after the collision
   • Momentum is not conserved
   • The collision is perfectly elastic
   • The particles bounce back with equal speed

6. For a particle hitting a smooth fixed surface, how is e defined?

   • Speed after impact divided by speed before impact, perpendicular to the surface
   • e = 1 minus the speed ratio
   • Speed before impact divided by speed after impact
   • The ratio of the masses

7. When velocities are given as 2D vectors, how is conservation of momentum applied?

   • It applies to each component separately
   • Only to the magnitude of the velocity
   • Only to the speed
   • Only to the angle of the velocity

8. A mass 2 kg moving at 3 m/s hits a mass 1 kg at rest, with e = 1. What is the velocity of the 1 kg mass after the collision?

   • 2 m/s
   • 1 m/s
   • 4 m/s
   • 3 m/s

9. A mass 2 kg moving at 3 m/s hits a mass 1 kg at rest and they coalesce. What is their common velocity?

   • 3 m/s
   • 1 m/s
   • 6 m/s
   • 2 m/s

10. A ball hits a smooth wall at 10 m/s perpendicular to it and rebounds at 6 m/s. What is e?

    • 0.6
    • 0.4
    • 1.6
    • 1.67

11. A mass 3 kg moves right at 4 m/s and a mass 1 kg moves left at 2 m/s. They coalesce. What is their common velocity?

    • 4 m/s to the right
    • 1.5 m/s to the right
    • 2.5 m/s to the right
    • 3 m/s to the right

12. A bullet of mass 0.01 kg leaves a rifle of mass 4 kg at 400 m/s. What is the recoil speed of the rifle?

    • 4 m/s
    • 1 m/s
    • 0.1 m/s
    • 10 m/s

13. A particle moving at 8 m/s hits a smooth fixed wall and rebounds at 2 m/s. What is e?

    • 0.25
    • 0.75
    • 0.5
    • 4

14. A mass 1 kg moving at 3 m/s hits an identical mass at rest in a perfectly elastic direct collision. What is the velocity of the first mass afterwards?

    • 1.5 m/s
    • 0
    • -3 m/s
    • 3 m/s

15. A mass 2 kg moves at 5 m/s and hits a 3 kg mass at rest with e = 0.5. What is the velocity of the 3 kg mass after the collision?

    • 3 m/s
    • 0.5 m/s
    • 5 m/s
    • 2.5 m/s

16. In a direct collision of two particles with e = 1, which quantity is conserved in addition to momentum?

    • Impulse
    • Mass of each particle
    • Kinetic energy
    • Speed of each particle

17. A mass 1 kg moving at 4 m/s hits a mass 2 kg at rest with e = 1/2. What is the velocity of the 1 kg mass afterwards?

    • 2 m/s
    • -1 m/s
    • 0 m/s
    • 1 m/s

18. Particles of masses 1 kg and 2 kg have velocities (2, 0) and (0, 3) m/s. They coalesce. What is their common velocity?

    • (4/3, 3) m/s
    • (2/3, 2) m/s
    • (2, 6) m/s
    • (1, 1.5) m/s

19. A mass 2 kg moves at 6 m/s and hits a mass 3 kg at rest with e = 1/3. What is the velocity of the 3 kg mass afterwards?

    • 2 m/s
    • 4 m/s
    • 1.2 m/s
    • 3.2 m/s

20. A ball hits a smooth fixed horizontal surface with normal speed 4 m/s and e = 0.5. What is its rebound normal speed?

    • 4 m/s
    • 2 m/s
    • 0.5 m/s
    • 8 m/s

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