# How do I solve elastic collisions?

1. Oct 18, 2015

### Brainiac11

• Member warned to use the formatting template for homework posts.
A 2-kg ball is moving at 3 m/s toward the right. It elastically collides with a 4-kg ball that is initially at rest. Calculate the velocities of the balls after the collision.

I know that kinetic energy is conserved in elastic conditions, but I don't know how to use that to calculate this. I tried solving this using the conservation of momentum, but i ended up with 2(3) + 4(0) = 2vf1 + 4vf2 and I can't solve for both variables. I know PE = mgh and KE = (1/2) mv2

2. Oct 18, 2015

### HallsofIvy

Staff Emeritus
Yes, in all collisions, in which there is no external force, momentum is preserved and that is what your equation, 2(3)+ 4(0)= 6= 4vf1+ 2vf2 or, dividing through by 2, 2vf1+ vf2= 3. And, as you say, in an elastic collision, kinetic energy is conserved. Since this doesn't involve change in height, the "potential energy" equation is irrelevant. And, as you say, kinetic energy is "$(1/2)mv^2$" the total kinetic energy before the collision is $(1/2)(2)(9)+ (1/2)(4)(0)= 9$. After the collision, with speeds vf1 and vf2, the kinetic energy is $(1/2)(2)(vf1^2)+ (1/2)(4)(vf2^2)= vf1^2+ 2vf2^2$. Since the kinetic energy does not change, $vf1^2+ 2vf2^2= 9$.

Solve the two equations $2v1+ vf2= 3$ and $vf1^2+ 2vf2^2= 9$ for vf1 and vf2.

3. Oct 18, 2015

### Brainiac11

Thank you so much. I follow all of your work and understand it!

Last edited: Oct 18, 2015