Impact and energy loss — compare kinetic energy before and after impact: In a real (non-perfectly elastic) collision between bodies, how does the kinetic energy of the system immediately after impact compare to that immediately before impact?

Introduction / Context:
Collision problems in engineering mechanics distinguish between conservation laws for momentum and energy. Linear momentum of an isolated system is conserved during impact, but kinetic energy is generally not conserved unless the impact is perfectly elastic.

Given Data / Assumptions:

• Consider typical real impacts with coefficient of restitution e between 0 and 1.
• No external impulses during the short impact interval.
• Internal deformations and heat/sound generation may occur.

Concept / Approach:

During a real collision, part of the system’s kinetic energy transforms into internal energy (deformation, heat, sound). Therefore, the kinetic energy after impact is less than that before impact, except in the ideal e = 1 case (perfectly elastic), where kinetic energy is conserved, and the perfectly plastic case (e = 0), where losses are maximal.

Step-by-Step Solution:

Verification / Alternative check:

Test limiting cases: e = 1 → no loss (rare ideal). e = 0 → bodies coalesce, maximum loss of kinetic energy. Most real contacts have 0 < e < 1, so KE decreases.

Why Other Options Are Wrong:

(a) is only true for perfectly elastic impacts; (b) contradicts physical dissipation; (d) overgeneralizes; (e) is unnecessary since the qualitative comparison holds regardless of masses.

Common Pitfalls:

Confusing momentum conservation (always for isolated systems) with kinetic energy conservation (only for e = 1).

Final Answer:

before impact is more than after impact