Question

given 2 masses traveling at independent velocities. How can you find the resultant velocities after an elastic collision?

I tried to combine the equation for conservation of momentum and conservation of kinetic energy but i'm having trouble isolating any variables

Answer 1

It depends on the information given in the question you are dealing with. Since the collision is elastic, both momentum and kinetic energy are conserved. Here are the relevant equations. Note that momentum is a vector quantity.
For the conservation of momentum of the two independent masses:
\[\color{green}{m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1^` + m_2\vec{v}_2^`}\]
For the conservation of kinetic energy in the elastic collision, use:\[\color{green}{\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 = \frac{1}{2}m_1v_1^{`2} + \frac{1}{2}m_2v_2^{`2}}\]

Answer 2

right and i've gotten that far, what i don't understand is how to get V1f and V2f

Answer 3

given m1, m2, and both of their velocities

Answer 4

found it http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html
thanks though

Answer 5

what grade are u in

Answer 6

this is AP physics C, probably in AP physics B, 12th grade

Answer 7

thats why i dont know what u are doing because i am in ninth grade

Answer 8

yea i didn't start physics till junior year

Answer 9

hello oO

Answer 10

oh i said that wrong, i'm a freshman in college, retaking physics cause i got a 3 on the ap exam in high school and nobody accepts 3's

Answer 11

given m1, m2, and both of their velocities ...

That will allow you to find the initial total momentum and the initial total kinetic energy. You know those things will be conserved. Do you know ANYTHING at all about the final conditions after the collision? If you have some other information about what happens after the collision, that would be very helpful.

Answer 12

no there is no final information given, but you can find the final velocities with these equations

\[V_{2f} = \frac{2m_{1}}{m_{1}+m_{2}}v_{1i} - \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{2i}\]
\[V_{1f} = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}V_{1i} - \frac{2m_{2}}{m_{1}+m_{2}}V_{2i}\]

Answer 13

those are the combined Ke and P equations i was looking for

Answer 14

those only work in an elastic collision though