# Two Cars on an Air Track

1. Mar 16, 2009

### gregcor

1. The problem statement, all variables and given/known data
Two carts are set up on an air track with a rubber band connecting them. The carts are pulled just slightly more than the length of the relaxed rubber band. Upon release, mass 1 travels a distance of x1 and mass 2 travels a distance of x2. Show that $$\frac{x_1^2}{x_2^2}=\frac{m_2}{m_1}$$

2. Relevant equations

$$F_s=-kx$$

$$x=x_1+x_2$$

$$p=mv$$

3. The attempt at a solution
I'm not exactly sure where the first two equations come in. However, I noticed:
$$m_1 v = m_2 v$$

$$m_1 \frac{x_1}{t} = m_2 \frac{x_2}{t}$$

$$\frac{m_1^2}{x_2^2} = \frac{m_2^2}{x_1^2}$$

Though that's clearly not the original equation. I'm a bit lost at where I should go from here.

Thanks!