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97/3334–6FE Reference Handbook 10.4 · Dynamics · Impact
1. Constant Acceleration2. Newton’s Second Law3. Work–Energy Principle4. No-Time Acceleration Equation5. Position–Time Equation6. Impulse–Momentum Principle7. Translational Kinetic Energy8. Normal (Centripetal) Acceleration9. Level-Ground Projectile Range10. Power11. Angular Form of Newton’s Second Law12. Relative Velocity13. Coefficient of Restitution14. Elastic Spring Energy15. Rigid-Body Rotation: Tangential and Normal Accel.16. Mass Moment of Inertia17. Conservation of Mechanical Energy18. Angular Impulse–Momentum19. Rolling Without Slip20. Polar / Path Normal–Tangential Acceleration21. Instantaneous Center of Zero Velocity22. Work of a Variable Force

Handbook formula

Coefficient of Restitution

e is the ratio of relative speed after impact to before, along the line of impact. e=1 elastic, e=0 plastic. Combined with conservation of momentum along the line of impact (no external impulse) to find the two unknown velocities.

Coefficient of restitution
(m/s)
Velocity along the impact line

Step-by-step solved example

m1=m2, u1=4 m/s, u2=0, e=1. Final velocities?

ABR
Line-of-impact velocities before/after; e is the normal-component ratio.

  1. 1. Momentum

    m(4)+0 = m v1'+m v2' → v1'+v2'=4.

  2. 2. e

    e=1 → v2'−v1'=4. Solve: v1'=0, v2'=4 m/s (they exchange).

Answer: v1'=0, v2'=4 m/s

10 practice questions

0/10 correct

1.e=0 means

2.e=1 means

3.Along the impact line with no external impulse

4.e is defined with

5.If both masses equal and e=0, common v' =

6.e cannot exceed 1 in ordinary collisions because

7.Oblique impact: tangential

8.Ball dropped on a floor with e, rebound speed is

9.Rebound height / drop height equals

10.Units of e are