Nature of Impact – Lead Spheres Approximation The impact between two lead spheres is typically approximated as which type of impact?

Introduction / Context: Real materials dissipate energy during impact through plastic deformation, internal friction, and heat. Lead is soft and exhibits significant plasticity, so its collision behavior helps illustrate the difference between elastic and inelastic impacts.

Given Data / Assumptions:

• Two lead spheres collide along a line of impact.
• Material properties of lead: low yield strength and high plasticity.
• No external impulses during the very brief collision.

Concept / Approach: In elastic impact, kinetic energy is conserved (e = 1). In inelastic impact, some kinetic energy converts into deformation and heat, giving 0 ≤ e < 1. For very soft, plastically deforming bodies like lead, e is well below 1, hence collisions are modeled as inelastic (often close to perfectly inelastic for rough estimates).

Step-by-Step Solution: Identify material behavior: lead deforms plastically on impact. Plastic deformation absorbs kinetic energy. Therefore, the relative speed of separation is much less than relative speed of approach. Hence e is significantly less than 1 ⇒ inelastic impact.

Verification / Alternative check: Practical drop tests with lead balls show poor bounce heights compared with steel or glass, reflecting low restitution and significant energy loss at contact.

Why Other Options Are Wrong: elastic / perfectly elastic: would require negligible energy loss, which contradicts lead’s plastic response. super-elastic / rebound amplification: requires energy input during impact; not applicable.

Common Pitfalls: Assuming all metals behave elastically at impact; material hardness matters.

Final Answer: inelastic