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 e = 0?

    • They bounce back at the same speed they arrived
    • They pass through each other
    • They move together with a common velocity along the line of centres
    • They are perfectly elastic and keep all their kinetic energy

  4. What happens to the kinetic energy in a direct impact with e = 1?

    • It is conserved, and the relative speed of separation equals the speed of approach
    • Both spheres come to rest
    • Momentum is lost during the impact
    • The total kinetic energy doubles

  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. For two spheres in direct impact, where are the velocities?

    • Perpendicular to the line of centres
    • At 45 degrees to the line of centres
    • The velocities are zero
    • Along the line joining the centres of the spheres

  7. When is the kinetic energy lost in a direct impact largest?

    • It is zero when e = 0
    • When e = 1, and it is zero when e = 0
    • When e = 0, and it falls to zero when e = 1
    • It is the same for all values of e

  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. Two equal spheres of mass 1 kg each: sphere A moves at 3 m/s and sphere B is at rest. The impact has e = 1. What happens?

    • Both move off together at 1.5 m/s
    • Both bounce back at 3 m/s
    • A stops and B moves off at 3 m/s
    • A moves on at 3 m/s and B stays at rest

  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 of mass m moving at 5 m/s hits a sphere of mass 2m at rest, with e = 1. What is the velocity of the first sphere after impact?

    • 5/3 m/s forward
    • -10/3 m/s
    • -5/3 m/s, so it rebounds at 5/3 m/s
    • 0 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. Why does a restitution coefficient e less than 1 mean that kinetic energy is lost in an impact?

    • The spheres stop exerting forces on each other
    • Momentum is destroyed during the impact
    • The spheres gain energy from the surface
    • Some kinetic energy is converted into heat, sound and permanent deformation

  20. A sphere of mass 4 kg moves at 2 m/s and hits a sphere of mass 2 kg moving at -2 m/s, with e = 0.5. What is the velocity of the 4 kg sphere after impact?

    • 2 m/s
    • -1 m/s
    • 1 m/s
    • 0 m/s, so it comes to rest

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