Impulse–momentum — comparing rebounds and stops: A lead ball and a rubber ball of the same mass strike a rigid wall with the same speed. The lead ball falls down (almost stops), whereas the rubber ball rebounds. Which statement correctly compares their changes in momentum (magnitude)?

Introduction / Context:This classic comparison illustrates impulse, coefficient of restitution, and how rebound affects momentum change. It links to collision analysis, sports physics, and materials selection for impact absorption.

Given Data / Assumptions:

• Both balls have the same mass m and approach the wall with the same speed u.
• Lead ball: comes nearly to rest after impact (final speed ≈ 0).
• Rubber ball: rebounds with some speed v (v > 0) in the opposite direction.

Concept / Approach:Change in momentum Δp = p_final − p_initial (vector). Take the approach direction as positive. Lead: initial momentum = +mu; final ≈ 0 ⇒ |Δp_lead| ≈ mu. Rubber: initial = +mu; final = −mv ⇒ Δp_rubber = −mv − (+mu) = −m(u + v) ⇒ magnitude |Δp_rubber| = m(u + v), which is greater than mu because v > 0.

Step-by-Step Solution:Lead: |Δp| ≈ mu.Rubber: rebounds ⇒ |Δp| = m(u + v) > m*u.Therefore, the rubber ball experiences a larger magnitude of momentum change.Impulse equals change in momentum, so the wall delivers a larger impulse to the rubber ball.

Verification / Alternative check:Coefficient of restitution e > 0 for rubber; e ≈ 0 for lead. Higher e implies a more negative final velocity relative to the incident direction, increasing |Δp|.

Why Other Options Are Wrong:

• Equal change: only true if both stop dead or both rebound equally, which is not the case.
• Rubber less than lead: contradicts the rebound reversal which adds to the momentum change.
• None of the above: incorrect because a valid comparison exists.

Common Pitfalls:

• Comparing forces rather than impulse; the relevant measure is the integral of force over contact time.
• Ignoring direction in momentum; the rubber ball’s reversal makes the change larger.

Final Answer:the change in momentum suffered by rubber ball is more than the lead ball