# Two masses colliding

1. Jun 27, 2011

### kraigandrews

1. The problem statement, all variables and given/known data
A mass m with initial velocity v0 collides head on with a mass 2m initially at rest. What is the final velocity of the smaller mass, as a ratio to v0?

What is the final velocity of the larger mass, as a ratio to v0?

2. Relevant equations

Pi=Pf

KE=.5mv^2

3. The attempt at a solution

for part a I am confused as to what I am doing wrong:

mvo=mv1+2mv2
it wants to find v1 in terms of vo so:

v2=.5(vo+v1)

then plug into KE equation:

vo2=v12+.25(v12+vo2)
and simplify to get

(3/4)vo2=(5/4)v12

then v1=(3/5)1/2vo

2. Jun 27, 2011

### ehild

That + should be minus.

ehild

3. Jun 27, 2011

### tiny-tim

hi kraigandrews!
hmm …

i] v2=.5(vo minus v1)

ii] you need to put m or 2m in the KE equation

iii] (vo+v1)2 is not v12+vo2

4. Jun 27, 2011

### kraigandrews

yeah wow that was a dumb mistake not foiling, for the KE part I just cancelled the masses:

but now im left with
(3/4)Vo^2=(5/4)V1^2-(1/2)Vo*V1
and I am not quite sure how to solve this for V1

5. Jun 27, 2011

### tiny-tim

erm … it's a quadratic equation!

(and anyway, v0 = v1 is obviously going to be a solution, since that corresponds to the masses not colliding!)