 #1
mncyapntsi
 38
 4
 Homework Statement:

Trying to solve this problem to study for an exam next week!
There are two masses : 2m and m and they collide with v and v. I need to find the final velocities (it is also a perfectly elastic collision).
 Relevant Equations:

KEi = KEf gives (1/2)(m1)(vi1)^2 + (1/2)(m2)(vi2)^2 = (1/2)(m1)(vf1)^2 + (1/2)(m2)(vf2)^2
pi = pf gives (m1)(vi1) + (m2)(vi2) = (m1)(vf1) + (m2)(vf2)
m1 = 2m
m2 = m
I know I need to look at the conversation of momentum, as well as the conservation of kinetic energy. However I get stuck with my equations. Any help would be greatly appreciated! I've already got (don't know where I am going wrong):
(v)^2 + (1/2)(m)(v)^2 = (vf1)^2 + (1/2)(m)(vf2)^2
(3/2)v^2 = (vf1)^2 + (1/2)(vf2)^2
3mv = 2m(vf1) + m(vf2)
3v = (vf1) + (vf2)
(vf1) = 3v  vf2
Plugging into KE conservation equation gives me:
(3/2)v^2 = (3v  vf2)^2 + (1/2)(vf2)^2
(3/2)v^2 = 9v^2 6v(vf2) + (vf2)^2 + (1/2)(vf2)^2
 6v (vf2) = (7.5)v^2 + (3/2)(vf2)^2
And this is where I get stuck – I indeed have two variables, however since there is a v multiplied by vf2 I don't know how to continue. I can't spot my error anywhere... Would anyone have any advice? Thank you!
(v)^2 + (1/2)(m)(v)^2 = (vf1)^2 + (1/2)(m)(vf2)^2
(3/2)v^2 = (vf1)^2 + (1/2)(vf2)^2
3mv = 2m(vf1) + m(vf2)
3v = (vf1) + (vf2)
(vf1) = 3v  vf2
Plugging into KE conservation equation gives me:
(3/2)v^2 = (3v  vf2)^2 + (1/2)(vf2)^2
(3/2)v^2 = 9v^2 6v(vf2) + (vf2)^2 + (1/2)(vf2)^2
 6v (vf2) = (7.5)v^2 + (3/2)(vf2)^2
And this is where I get stuck – I indeed have two variables, however since there is a v multiplied by vf2 I don't know how to continue. I can't spot my error anywhere... Would anyone have any advice? Thank you!