Lesson 3C.4.1

3C.4.1 Direct impact of spheres Quiz: Pearson Edexcel Further Maths, Unit 28

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3C.4.1, Direct impact of spheres: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 28: Direct impact, written with Revision Ninja.

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The 20 questions

  1. What is Newton's experimental law of restitution for direct impact of two spheres, with speeds u1, u2 before and v1, v2 after along the line of centres?

    • v1 + v2 = e (u1 + u2)
    • v1 v2 = e u1 u2
    • v2 - v1 = e (u2 - u1)
    • v2 - v1 = -e (u2 - u1)

  2. What is the range of the coefficient of restitution e?

    • -1 <= e <= 1
    • 0 <= e <= 1
    • e >= 1
    • 0 <= e <= 2

  3. What happens to two spheres after a direct impact with coefficient of restitution e = 0?

    • Come to rest
    • Swap velocities
    • Move together
    • Rebound apart

  4. What happens to total kinetic energy during a direct impact where the coefficient of restitution e = 1?

    • It is conserved
    • It doubles
    • It is lost
    • It halves

  5. Which equation expresses conservation of momentum for two spheres in direct impact?

    • m1 u1 + m2 u2 = m1 v1 + m2 v2
    • m1 v1 + m2 v2 = 0
    • m1 u1 = m2 u2
    • m1 v1 - m2 v2 = m1 u1 - m2 u2

  6. Along which line do velocity changes occur during a direct impact of two smooth spheres?

    • Common tangent
    • Perpendicular line
    • Line of motion
    • Line of centres

  7. At what value of the coefficient of restitution e is kinetic energy loss in a direct impact greatest?

    • 2
    • 1
    • 0
    • 0.5

  8. Spheres of masses 2 kg and 3 kg have velocities 4 m/s and -1 m/s before impact, with e = 0.5. What is the velocity of the 3 kg sphere after impact?

    • 1.5 m/s
    • -0.5 m/s
    • 2 m/s
    • -1 m/s

  9. In the same setting (2 kg at 4 m/s, 3 kg at -1 m/s, e = 0.5), what is the velocity of the 2 kg sphere after impact?

    • -0.5 m/s
    • -2 m/s
    • 2 m/s
    • 0.5 m/s

  10. In the same setting, how much kinetic energy is lost in the impact?

    • 6.25 J
    • 11.25 J
    • 8.75 J
    • 17.5 J

  11. In the same setting, what is the total momentum before and after impact?

    • 11 N s
    • 5 N s
    • 8 N s
    • -3 N s

  12. Sphere A (1 kg, 3 m/s) hits stationary Sphere B (1 kg) with e = 1. What is A's final velocity?

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

  13. Two spheres of masses 2 kg and 1 kg, moving at 6 m/s and at rest, coalesce on impact. What is their common velocity?

    • 2 m/s
    • 3 m/s
    • 4 m/s
    • 6 m/s

  14. A sphere of mass 4 kg moves at 3 m/s and hits a stationary sphere of mass 2 kg with e = 0.6. What is the velocity of the 2 kg sphere after impact?

    • 3.2 m/s
    • 2.4 m/s
    • 4.8 m/s
    • 1.8 m/s

  15. Two spheres approach each other with speeds 5 m/s and 1 m/s in opposite directions. The coefficient of restitution is 0.25. What is the speed of separation?

    • 3 m/s
    • 1.5 m/s
    • 0.25 m/s
    • 6 m/s

  16. Spheres of masses 2 kg and 3 kg have velocities 4 m/s and -1 m/s. For what value of e does the 2 kg sphere come to rest after impact?

    • 1/3
    • 1/4
    • 1/2
    • 2/3

  17. A sphere (mass m, 5 m/s) hits stationary sphere (mass 2m) with e = 1. What is its new velocity?

    • -5 m/s
    • 0 m/s
    • -5/3 m/s
    • 5/3 m/s

  18. Two equal masses m move directly towards each other: one moves at u and the other is at rest. With e = 0.5, what fraction of the kinetic energy is lost?

    • 37.5%
    • 50%
    • 25%
    • 75%

  19. When coefficient of restitution e < 1, into what is kinetic energy primarily converted during impact?

    • Chemical energy
    • Potential energy
    • Nuclear energy
    • Heat and sound

  20. Sphere A (4kg, 2m/s) hits Sphere B (2kg, -2m/s) with e = 0.5. What is A's final velocity?

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

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