Elastic Collision of Two Particles: Solving for Final Velocity

AI Thread Summary
In an elastic collision involving two particles, momentum and kinetic energy are conserved. The problem involves particle 1 of mass m moving with speed v colliding with particle 2 of mass 3m, initially at rest. The initial attempt to solve for the final speed of particle 2 incorrectly assumes that particle 1 comes to a complete stop. To find the correct final velocities, both conservation of momentum and conservation of kinetic energy equations must be used, resulting in two equations with two unknowns. The final speed of particle 2 is determined to be v1/2, highlighting the importance of using both conservation principles in elastic collisions.
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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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