6.03i Restitution and collisions Quiz: OCR Further Maths, Unit 3

The 20 questions

1. What is the possible range of values for the coefficient of restitution, e?

   • e > 1
   • -1 <= e <= 1
   • 0 <= e <= 1
   • e < 0

2. What value of the coefficient of restitution describes a perfectly elastic collision?

   • e > 1
   • e = 0
   • e = 1
   • e = 0.5

3. What value of the coefficient of restitution corresponds to a completely inelastic collision?

   • e = -1
   • e = 1
   • e > 1
   • e = 0

4. What happens to total kinetic energy during a perfectly elastic collision between two smooth spheres?

   • It is conserved
   • It decreases maximally
   • It increases
   • It becomes zero

5. What happens to two colliding bodies in a completely inelastic collision where e = 0?

   • They explode apart
   • They rebound perfectly
   • They stop completely
   • They coalesce

6. What can be said about kinetic energy loss in a completely inelastic collision?

   • Minimum loss
   • Zero loss
   • Infinite loss
   • Maximum loss

7. For a smooth sphere hitting a fixed plane perpendicularly at u, what is its rebound speed v?

   • v = e / u
   • v = u + e
   • v = u / e
   • v = eu

8. What is Newton's experimental law formula relating separation speed to approach speed for direct impact?

   • Approach = e * separation
   • Separation = approach / e
   • Separation = approach + e
   • Separation = e * approach

9. A sphere hits a smooth wall perpendicularly at 10 ms^-1 with e = 0.6. What is its rebound speed?

   • 16 ms^-1
   • 4 ms^-1
   • 60 ms^-1
   • 6 ms^-1

10. Two spheres separate at 4 ms^-1 after a direct collision with e = 0.8. What was their approach speed?

    • 5 ms^-1
    • 4.8 ms^-1
    • 3.2 ms^-1
    • 0.2 ms^-1

11. A ball approaches a wall at 8 ms^-1 and rebounds at 2 ms^-1. What is the value of e?

    • 0.5
    • 0.25
    • 4.0
    • 0.75

12. During an oblique impact with a smooth wall, what happens to the velocity component parallel to the wall?

    • Becomes zero
    • Multiplied by e
    • Reverses direction
    • Remains unchanged

13. During an oblique impact with a smooth wall, what happens to the velocity component perpendicular to the wall?

    • Remains unchanged
    • Becomes zero
    • Scaled by -e
    • Scaled by e

14. A sphere with velocity 3i + 4j ms^-1 hits a wall along i with e = 0.5. Rebound velocity?

    • -1.5i + 4j ms^-1
    • 1.5i + 2j ms^-1
    • -3i - 2j ms^-1
    • 3i - 2j ms^-1

15. Why does the velocity component parallel to a smooth fixed plane remain constant during impact?

    • Conservation of energy
    • Zero parallel impulse
    • Zero mass
    • Zero perpendicular force

16. A sphere hits a plane perpendicularly with e = 0.5. What fraction of kinetic energy remains after impact?

    • 0.125
    • 0.75
    • 0.5
    • 0.25

17. A sphere hits a plane at angle alpha to the normal and rebounds at angle beta. What is tan(beta)?

    • tan(alpha)
    • e * tan(alpha)
    • 1 / (e * tan(alpha))
    • tan(alpha) / e

18. Sphere A with velocity (4, 2) collides directly with stationary sphere B along i. Sphere A's j-component afterwards?

    • 4
    • 2
    • 1
    • 0

19. A sphere of mass m hits a fixed wall perpendicularly at speed u with restitution e. What is KE loss?

    • m u^2 (1 - e)
    • 0.5m u^2 e^2
    • 0.5m u^2 (1 - e^2)
    • 0.5m u^2 (1 - e)

20. Why are superelastic collisions where e > 1 excluded from this A-level maths syllabus?

    • Mass is lost
    • Impulse is zero
    • Kinetic energy increases
    • Velocity becomes infinite

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