Theory for acceleration of a cart: lab experiment

[Ascrapper]

Homework Statement

In a lab experiment in my introductory physics class, we are asked to verify Newton's Second Law by taking data from an experiment and then comparing that data to a theory. We are given a cart of unknown mass m_{}1 is put on a horizontal track with a string attached over a pulley to a hanging mass m_{}2. It is given that both masses are moving as one system and therefore have the same acceleration. My problem lies with the theory part of this experiment: how am I supposed to solve for the acceleration with known values? Let the acceleration of the system be a, the rolling frictional force f_{}r, the coefficient of rolling friction μ_{}r, the normal force F_{}N, the tension in the string T, and the acceleration due to gravity g.
This picture is similar to what our experiment looks like: http://www.physicssource.ca/images/cart_forcesensor_track.gif

Homework Equations

Newton's Second Law, F=ma

The Attempt at a Solution

Perhaps there is something intuitive about the mass of the cart and the coefficient of rolling friction that I am not seeing but I just can't figure it out. Here is what I have so far:

First I set up a free body diagram of the mass of the cart m_{}1 to show that:
ƩF_{}x=f_{}r-T=m_{}1*a (Equation 1)
ƩF_{}y=F_{}N-m_{}1*g=0, So F_{}N=m_{}1*g
Also, we know that f_{}r=μ_{}r*F_{}N, So f_{}r=μ_{}r*m_{}1*g

Now I set up a free body diagram of the hanging mass to show:
ƩF_{}x=0
ƩF_{}y=T-m_{}2*g, so T=m_{}2*(g+a)

Substituting all back into Equation 1:
μ_{}r*m_{}1*g-m_{}2*(g+a)=m_{}1*a
μ_{}r*m_{}1*g-m_{}2*g-m_{}2*a=m_{}1*a
g*(μ_{}r*m_{}1-m_{}2)=a*(m_{}1+m_{}2)
(g*(μ_{}r*m_{}1+m_{}2))/(m_{}1+m_{}2)=a

This is where I am stuck: How am I to get rid of or solve for these two unknown values μ_{}r and m_{}1?

 

[Spinnor]

Except for a minus sign I got what you have. I'm guessing you measure acceleration and are supposed to figure out m1? Without knowing μ_r you have done as much as you can.