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Re: Physics Quiz
Without using any "special" observations what you really should do is draw the Free Body Diagram and sum moments about the pivot point (in the plane normal to the sketch). This gives one equation and one unknown.
Then when reconstructing the total friction force from the longitudinal (given/known/by inspection) and lateral (unknown) components on the wheel, some sines and cosines will cancel out for you. This then makes clear the "two force" member observation which Ether has stated. If you see this right away, then you can jump straight to the answer without any diagrams.
A useful analogy to this system is a static screw. The wheel angle (incline) acts similar to the pitch of a thread. Following this you should watch out when reporting any answer for theta = N*pi (for N any integer neg, 0, or positive). This should also be clear from initial observations.
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