Impact and energy loss in mechanics\n\nWhich one of the following statements about the kinetic energy of a body during an impact (collision) is generally correct?

Introduction / Context:
When two bodies collide, some of the system's mechanical energy can be dissipated as sound, heat, and deformation. This question tests your understanding of how kinetic energy typically changes across an impact in engineering mechanics and physics.

Given Data / Assumptions:

• Before impact: the body (or system) possesses a certain kinetic energy based on its mass and speed.
• During impact: internal forces act over very short time intervals; deformation and heat may occur.
• After impact: speeds generally change; some energy may be lost to non-recoverable modes unless the collision is perfectly elastic.

Concept / Approach:
Momentum is conserved for an isolated system during an impact, but kinetic energy is conserved only in a perfectly elastic collision. In most practical engineering situations (vehicle bumps, hammer blows, drop tests), the impact is partially or highly inelastic, so kinetic energy decreases.

Step-by-Step Solution:

Verification / Alternative check:
Coefficient of restitution e characterizes elasticity. When 0 ≤ e < 1, relative speed of separation is less than relative speed of approach, implying a reduction in kinetic energy. Only when e = 1 is kinetic energy conserved.

Why Other Options Are Wrong:

• Remains constant / Equal before and after: True only for perfectly elastic collisions; not the general case.
• Before is less than after: Violates energy conservation without an external energy input.
• None of the above: Incorrect because the general case is a decrease in kinetic energy.

Common Pitfalls:
Confusing momentum conservation (almost always valid for isolated systems) with kinetic energy conservation (valid only for elastic impacts). Also ignoring dissipative effects like plastic deformation and sound.

Final Answer:
The kinetic energy of a body before impact is more than the kinetic energy of a body after impact.