# Homework Help: Elastic collisions formula help

1. Jan 18, 2010

### GreenPrint

1. The problem statement, all variables and given/known data

After some messey algebra it can be said that

V_B = (2 m_A V_o_A)/(m_A + m_B)

V_A = ( (M_A - M_B ) V_o_A )/(M_A + M_B)

were did this come from???

2. Relevant equations

momentum

3. The attempt at a solution

I don't even know were to start

2. Jan 18, 2010

### GreenPrint

Re: Momentum

were _B indicates a quantity realtive to B
and _A indicates a quantity realitve to A

and V_o is the intial velocity

3. Jan 18, 2010

### ideasrule

Re: Momentum

That's for elastic collisions. It comes from solving the conservation of momentum and conservation of energy equations simultaneously.

4. Jan 18, 2010

### GreenPrint

Re: Momentum

ummm... hmm

ok... um so there is just kinetic energy??? no potential and you had to solve for the velocities becasue these are the only terms the same in momentum and kinetic energy so... lets see.. um..

5. Jan 18, 2010

### GreenPrint

Re: Momentum

ok then

m_A V_o_A + m_B V_o_B = m_A V_A + m_B V_B

.5 m_A V_o_A^2 + .5 m_B V_o_B^2 = .5 m_A V_A^2 + .5 m_B V_B^2

Last edited: Jan 18, 2010
6. Jan 18, 2010

### ideasrule

Re: Momentum

Yes. Now bring the terms that start with "m_A" to the left in both equations, bring the terms that start with "m_B" to the right in both equations, and see what you get.

7. Jan 18, 2010

### GreenPrint

Re: Momentum

oh ok hold up

8. Jan 18, 2010

### GreenPrint

Re: Momentum

m_A V_o_A + m_B V_o_B = m_A V_A + m_B V_B
m_A V_o_A - m_A V_A = m_B V_B - m_B V_o_B
m_A(V_o_A - V_A) = m_B (V_B - V_o_B )

.5 m_A V_o_A^2 + .5 m_B V_o_B^2 = .5 m_A V_A^2 + .5 m_B V_B^2
.5 m_A V_o_A^2 - .5 m_A V_A^2 = .5 m_B V_B^2 - .5 m_B V_o_B^2
.5 m_A (V_o_A^2 - V_A^2) = .5 m_B (V_B^2 - V_o_B^2)

9. Jan 18, 2010

### GreenPrint

Re: Momentum

i'm not really sure were this problem is going