Perfectly elastic, head-on impact: equal masses Two balls of equal mass and perfectly elastic material lie on a smooth floor. One ball moving with speed v strikes the other, initially at rest. Choose the correct value among the options to represent the non-zero speed after impact.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
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Av
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Bv/2
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Cv/4
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Dv/8
Answer
Correct Answer: v
Explanation
Given dataEqual masses, perfectly elastic, one-dimensional impact; ball 1 speed initially = v, ball 2 initially at rest.
Concept/ApproachFor a perfectly elastic, head-on collision of equal masses, the velocities are exchanged.
Step-by-step calculationConservation of momentum: m·v + m·0 = m·v1′ + m·v2′ ⇒ v = v1′ + v2′Coefficient of restitution e = 1: v2′ − v1′ = vSolving the two linear equations ⇒ v1′ = 0 and v2′ = v.
InterpretationThe non-zero speed after impact equals v (the struck ball moves with v; the striker comes to rest).
Common pitfallsAssuming both move with the same speed after impact violates energy conservation for elastic collisions.
Final Answerv