Collision Theory – Coefficient of Restitution for Inelastic Impacts For inelastic bodies undergoing impact, what is the typical range of the coefficient of restitution e?

Introduction / Context: The coefficient of restitution e quantifies how “bouncy” a collision is by comparing relative speeds after and before impact. Understanding its range distinguishes elastic, inelastic, and perfectly inelastic collisions in dynamics problems.

Given Data / Assumptions:

• Two bodies collide along the line of impact.
• No external impulse acts during the very short impact interval.
• e is defined along the common normal at impact.

Concept / Approach: By definition, e = (relative speed of separation) / (relative speed of approach). Its value categorizes collisions: e = 1 (perfectly elastic), 0 < e < 1 (inelastic), e = 0 (perfectly inelastic, bodies stick together). Values e > 1 indicate impact with added energy (e.g., active systems) and are not typical for passive mechanical impacts.

Step-by-Step Solution: Identify inelastic collision: some kinetic energy lost. Use definition: inelastic ⇒ 0 < e < 1. Perfectly inelastic special case: e = 0. Hence for inelastic bodies in general, e lies between 0 and 1.

Verification / Alternative check: Examine energy loss: elastic collisions conserve kinetic energy; inelastic collisions do not. Since speed of separation is reduced relative to approach, the ratio e must be less than 1 but nonnegative.

Why Other Options Are Wrong: zero only: corresponds to perfectly inelastic, not all inelastic. one only: elastic, not inelastic. more than one / less than zero: not applicable to passive mechanical collisions modeled without active energy input.

Common Pitfalls: Confusing “inelastic” with “perfectly inelastic”. Misapplying e across tangential directions instead of the line of impact.

Final Answer: between zero and one