Coefficient of restitution for perfectly elastic impact: For perfectly elastic bodies undergoing a direct impact, what is the value of the coefficient of restitution (dimensionless)?

Introduction / Context:
The coefficient of restitution e quantifies the ratio of relative speeds after and before impact along the line of impact. It is key to collision problems in mechanics, from bouncing balls to vehicle crash idealizations.

Given Data / Assumptions:

• Ideal, perfectly elastic collision.
• Line of impact is well defined; no energy loss.

Concept / Approach:
By definition, for perfectly elastic impact there is no loss of kinetic energy associated with the normal component of relative velocity. Therefore, the separation speed equals the approach speed along the line of impact, giving e = 1.

Step-by-Step Solution:

Verification / Alternative check:
In energy terms, ideal elasticity conserves kinetic energy (along the normal), consistent with e = 1. Real materials have 0 < e < 1.

Why Other Options Are Wrong:

• 0 or 0.5: imply partially or fully inelastic collisions.
• “Between 0 and 1”: applies to real, non-ideal materials, not perfectly elastic ones.
• > 1: physically unrealistic for passive impacts (would add energy).

Common Pitfalls:
Confusing tangential effects or rotation with the normal restitution definition.

Final Answer:
1.0