Impact mechanics – kinetic energy loss in a perfectly elastic collision\nIn a perfectly elastic impact, the loss of kinetic energy is:

Introduction / Context:
‘‘Elastic’’ and ‘‘inelastic’’ classify collisions based on kinetic energy behavior. In ideal elastic impacts, kinetic energy is conserved; in inelastic impacts, some kinetic energy transforms into other forms.

Given Data / Assumptions:

• Coefficient of restitution e = 1 for a perfectly elastic impact.
• System is isolated along the line of impact; no external impulses.
• No deformation losses, heat, or sound energy losses in the idealization.

Concept / Approach:
For e = 1, both linear momentum (along the line of impact) and kinetic energy are conserved. Thus the total kinetic energy before equals that after impact.

Step-by-Step Solution:

Verification / Alternative check:
Classic 1D two-body formulas for elastic collision show KE_before − KE_after = 0; numerical examples with equal masses show a perfect velocity swap and identical total KE.

Why Other Options Are Wrong:

• Saying some energy is always lost contradicts the ideal definition of ‘‘perfectly elastic’’.
• ‘‘Depends only on masses’’ is incorrect; for e = 1, KE is conserved irrespective of specific masses.
• ‘‘Cannot be determined’’ is false; it is determined by the definition of elastic impact.

Common Pitfalls:
Confusing real collisions (often slightly inelastic) with the idealized, perfectly elastic case used in theory.

Final Answer:
Agree – zero loss of kinetic energy