Coefficient of Restitution

Newton's law of restitution introduces the coefficient of restitution e, which measures the "bounciness" of a collision. This is a central concept in AQA Further Mechanics 1.

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1 Newton's Law of Restitution

For a direct (head-on) collision between two particles:

e = speed of separation / speed of approach

where 0 <= e <= 1.

• e = 1: perfectly elastic (no KE lost)
• e = 0: perfectly inelastic (particles coalesce)
• 0 < e < 1: partially elastic

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2 Precise Formulation

If particle A has velocity u_1 before and v_1 after, and particle B has velocity u_2 before and v_2 after (all measured in the same positive direction):

Speed of approach = u_1 - u_2 (assuming A approaches B, so u_1 > u_2)

Speed of separation = v_2 - v_1 (B moves faster than A after collision)

e = (v_2 - v_1) / (u_1 - u_2)

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3 Worked Example 1 -- Ball Hitting a Wall

A ball hits a wall at 10 m s^(-1). The coefficient of restitution is 0.7. Find the rebound speed.

Solution: