How Does Pulley Radius Affect Car Movement in a Mechanical Engineering Project?

[ennova]

First, this isn't really a "homework" problem, it is more to help me with my design for an engineering project for ME1000. I'm am trying to model how my "car" will move with my current design. The aim being to power and move a car forward and then launch a projectile using a set weight and allowing the weight to be displaced 2 meters, a torsion spring, an extension spring and a compression spring. We've decided to use the compression spring to fire the projectile and we will try and use the other springs and the displacement of the weight by 2 meters to power the drive train of the car. I'm trying to set up equations to get an estimate of the distance that the car will travel in 1 minute as a function of the radii of the pulleys I'll be using for my design.

Homework Statement

we "know" everything but we need to solve for "how far" the car will go. I say we "know" everything because I have a finite set of pulleys that I can choose from and once I know how to find the distance as a function of these pulleys (ie with their radii and mass), I can plot them in excel and find the design that I want etc. So I guess the variables would be the radii.

Homework Equations

sum(torque) = I*alpha
sum(force) = m*a
torque = -k*theta (for a torsion spring)
force = -k*x (for the extension spring)
W = m*g
a = alpha*r
I = (1/2)MR^2
d = vi*t + (1/2)*a*t^2

The Attempt at a Solution

I'm a bit lost on how to set this up. If anyone has any ideas/comments as a better way to approach this problem let me know. I guess I don't understand how to set up the (torque)force-diagrams for each pulley when I'm trying to balance the equations. Thanks for any help.

http://img228.imageshack.us/img228/4083/img021nc.th.jpg

[PLAIN]http://img839.imageshack.us/img839/2415/examplea.jpg

 

[nvn]

Perhaps see if post https://www.physicsforums.com/showthread.php?t=285915#post2042315" might help.