Elastic collisions formula help

[GreenPrint]

Homework Statement

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?

Homework Equations

momentum

The Attempt at a Solution

I don't even know were to start

 

[GreenPrint]

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

and V_o is the intial velocity

 

[ideasrule]

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

 

[GreenPrint]

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... let's see.. um..

 

[GreenPrint]

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

 

[ideasrule]

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.

 

[GreenPrint]

oh ok hold up

 

[GreenPrint]

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)

 

[GreenPrint]

i'm not really sure were this problem is going