Basic Statics/Dynamics System of Equations (help)

[kroq]

Homework Statement

Hi there, I'm working on a simple model vehicle (powered by a twisted rubber band) applying torque to a drive wheel. I just want to understand the loads going through the member bodies.

I've mocked up the enclosed free body diagrams and attempted to outline the systems of equations. Can I get a sanity check on my logic.

The static considerations sum to zero for forces and moments in the vertical direction.
The vehicle will accelerate horizontally as its powered by the band. Sum of forces equal ma. Sum of moments equal I•alpha.

A sanity check would be appreciated. It's not solving out correctly, and it seems weird to have a system of 9 equations and 6 unknowns.

Homework Equations

See jpeg.

The Attempt at a Solution

See jpeg.

 

[mrmiller1]

Havn't studied your jpeg but if your equations are all linear then you should only need the 6 equations with the 6 unknowns. You might be over-specifying. If you think it's an algebraic mistake maybe you could try solving via matrix (6x6^-1 * 6x1)?