Impact mechanics – definition check In a perfectly or partially elastic collision, the coefficient of restitution is defined as the ratio of the relative speed of separation after impact to the relative speed of approach before impact. Evaluate the statement.

Introduction / Context:
The coefficient of restitution, usually denoted by e, quantifies how “bouncy” a collision is. It compares how fast bodies separate after impact with how fast they were approaching before impact. This parameter is central to solving impact problems in engineering mechanics and physics.

Given Data / Assumptions:

• Two bodies collide with finite relative velocity along the line of impact.
• Coefficient of restitution e is a material/interaction property for the particular impact condition.
• Analysis is along the common normal at the point of contact (line of impact).

Concept / Approach:
By definition, e = (relative speed of separation along line of impact) / (relative speed of approach along line of impact). For perfectly elastic impact, e = 1; for perfectly plastic impact, e = 0; for real impacts, 0 < e < 1. This definition holds for both direct (collinear) and oblique impacts when components are resolved along the line of impact.

Step-by-Step Solution:

Verification / Alternative check:
For a head-on elastic collision of equal masses, velocities exchange and e = 1. For a perfectly plastic collision, bodies stick and separation speed is zero, giving e = 0. Both special cases align with the stated ratio definition.

Why Other Options Are Wrong:

• False: contradicts the formal definition used universally.
• True only for head-on collisions / equal masses: incorrect; the definition holds generally when resolved along the impact line.

Common Pitfalls:
Confusing total speed with the component along the line of impact. Tangential components may remain unchanged for smooth impacts and must not be included in e.

Final Answer:
True