Basic Statics/Dynamics System of Equations (help)

AI Thread Summary
The discussion revolves around a model vehicle powered by a twisted rubber band, focusing on understanding the loads through its member bodies. The user has created free body diagrams and outlined equations, noting that static forces and moments sum to zero in the vertical direction, while horizontal acceleration is governed by the equation sum of forces equals mass times acceleration. They express confusion over having nine equations and only six unknowns, suggesting a potential over-specification in their system. A suggestion is made to solve the equations using matrix methods to identify any algebraic mistakes. The user seeks a sanity check on their logic and equations to ensure accuracy.
kroq
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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.
 

Attachments

  • systemofequations.jpg
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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)?
 

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