Elastic Collision of Two Particles: Solving for Final Velocity

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SUMMARY

The discussion focuses on solving for the final velocity of particle 2 after an elastic collision with particle 1. Particle 1 has mass m and initial speed v, while particle 2 has mass 3m and is initially at rest. The correct final speed of particle 2 is determined to be v1/2, derived from the conservation of momentum and kinetic energy equations. The participants clarify that both momentum and kinetic energy must be conserved in elastic collisions, leading to a system of equations that can be solved simultaneously.

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Homework Statement


Particle 1 of mass m moving with speed v in the +x direction has an elastic
collision with particle 2 of mass 3m which was originally at rest. After the collision,
particle 2 is moving in the +x direction. What is its speed?

Homework Equations


deltap = 0
pf1 + pf2 = pi1 + pi2

The Attempt at a Solution


Wouldn't it just be
pf2 = pi1
3mvf2 = mv1
vf2 = v1/3

How come the answer is v1/2 instead? Help please..
 
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v3r said:

The Attempt at a Solution


Wouldn't it just be
pf2 = pi1
You can't assume that the first particle stops and all its momentum goes to the second particle.

Hint: What does elastic mean?
 
Elastic means no change in internal energy
DeltaE = 0
DeltaK + DeltaEint = 0
DeltaK = 0
Kf1 - Ki1 + Kf2 = 0

0.5mvf1^2 - 0.5mvi1^2 + 0.5(3m)vf2^2 = 0
0.5(3m)vf2^2 = 0.5mvi1^2 - 0.5mvf1^2

There's two unknowns, vf2 and vf1
Is this setup wrong?
 
v3r said:
0.5mvf1^2 - 0.5mvi1^2 + 0.5(3m)vf2^2 = 0
0.5(3m)vf2^2 = 0.5mvi1^2 - 0.5mvf1^2

There's two unknowns, vf2 and vf1
Is this setup wrong?
No, it's fine. You just need another equation--conservation of momentum. Then you'll have two equations and two unknowns.

In any collision, momentum is conserved; in an elastic collision, kinetic energy is also conserved.
 

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