Finding the mass ratio in a 2-particle elastic collision

[I Like Pi]

Hey, just doing some homework, and can't figure this one out

Homework Statement

Two particles go through an elastic collision. One particle has mass, m, and is initially at rest, while the other particle has initial velocity, v, and final velocity, -v/5. What is the mass of the second particle relating to m.

Answer: 2m/3

Homework Equations

The Attempt at a Solution

What I'm confused about is because you have two unknowns, the final velocity of the resting particle, and the mass of the second particle..

i tried using

m1v1 + m2v2 = m1v1' + m2v2'
and .5m1(v1)² + .5m2(v2)² = .5m1(v1)²' + .5m2(v2)²'

that seems waay too confusing for a question with no values..

 

[ehild]

You can imagine that m and v are numerical values. Just plug in m1=m, v1=0 (initially in rest), v2=v, v2' = -v/5 into your equation and solve for m2/m.

ehild

 

[I Like Pi]

You can imagine that m and v are numerical values. Just plug in m1=m, v1=0 (initially in rest), v2=v, v2' = -v/5 into your equation and solve for m2/m.

ehild

yes i figured it out last night, and when I have time I'll post the answer up here, it's really long haha

thanks ehild!

 

[ehild]

Is it long really?

m₂ v=m v'-m₂v/5
m₂ v²=m v'²+m₂v'²/25

mv'=6/5 m₂ v *
mv'²=24/25 m₂v² **

Divide equation ** by eq. *

v' = 4/5 v

Substitute for v' in eq.*.

ehild