Impact mechanics — kinetic energy loss In a direct (head-on) impact between two bodies, the loss of kinetic energy _____ on the value of the coefficient of restitution (e).

Introduction / Context:
The coefficient of restitution e measures how “bouncy” a collision is. It directly influences post-impact relative speed and therefore the change in kinetic energy. Understanding this dependence is crucial in collision analysis in mechanics and vehicle safety.

Given Data / Assumptions:

• Straight-line, head-on impact.
• Coefficient of restitution e in the range 0 ≤ e ≤ 1.
• No external impulses during the short impact interval.

Concept / Approach:
For two masses m1 and m2 with initial relative speed u_rel and final relative speed v_rel, restitution states: v_rel = e * u_rel (opposite direction). Total kinetic energy change depends on both masses and e. Perfectly elastic (e = 1) collisions conserve kinetic energy; perfectly inelastic (e = 0) collisions maximize kinetic energy loss for the given masses and initial speeds.

Step-by-Step Solution:

Verification / Alternative check:
Special cases: e = 1 → ΔK = 0 (no loss). e = 0 → bodies stick together (maximum loss). Intermediate values yield intermediate losses, confirming dependence on e.

Why Other Options Are Wrong:

• Does not depend / always zero: Contradicted by the limiting cases above.
• Independent of masses or relative speed: ΔK also depends on masses and initial relative speed; e is one of several parameters.

Common Pitfalls:
Assuming momentum conservation implies energy conservation. Momentum is always conserved for isolated impacts; kinetic energy is not unless e = 1.

Final Answer:
depends