Help with elastic equations?

Question

I need to turn the equation 1/2m1v0^2+1/2m2v0^2=1/2m1v1f^2+1/2m2v2f^2 into
v2f=[(2m1)/(m1+m2)]v0

I have been working on this problem for a while now and I feel like my head is going to explode. I can't figure it out and my teacher won't help me. Can you please show me how to do it step by step.

I don't know why it didn't include the whole equation, so here it is.

1/2m1v0^2+1/2m2v0^2=1/2m1v1f^2+1/2m2v2f^2

Okay it did it again, heres the last part
+1/2m2v2f^2

Answer 1

I think you had trouble getting the whole equation to show because you didn't allow any spaces. With spaces, text is allowed to wrap. We'll see how it treats what I'm doing.

In this question you are starting with conservation of KE. In your other elastic question you start with conservation of momentum. You need to combine both types of conservation in the solution of this problem. And in eleastic collisions, that is valid. The result you are supposed to get is only valid if one of the masses is stationary before the collision. Did you leave that detail out?

Assuming yes:
Starting with the general case - I'm going to use u1 and u2 for the original velocities and v1 and v2 for the final velocities. That's the way my book does it and it'll help keep me straight.

1/2m1u1^2 + 1/2m2u2^2 = 1/2m1v1^2 + 1/2m2v2^2
From conservation of momentum we also know
m1u1 + m2u2 = m1v1 + m2v2
rewriting that
m1(u1-v1) = m2(v2-u2) [Eq 1]
Doing something similar to the KE equation,
m1(u1^2-v1^2) = m2(v2^2-u2^2) [Eq 2]

Dividing Eq 2 by Eq1 some factoring required
u1+v1 = v2+u2
Rearranging a couple times
u1-u2 = v2-v1
v1 = v2+u2-u1
Plugging that into Eq1 and solving for v2
v2 = (2m1/(m1+m2))*u1 + ((m2-m1)/(m1+m2))*u2
Now, if u2=0, then you have your required result.

I hope I got this to you before your head exploded - if not, sorry bout that.

Answer 2

i think the answer is pie