Bill Va, What I think you are asking a few simple physics problems.
The coefficient of friction is a ratio of the pulling force (traction) to the weight acting perpendicular on wheels. The coefficient of friction depends on tires, surface, weight and angle of hill.
The second part of your question seems to be a torque problem. When you add weight to a 3 pt hitch you transfer weight off the front wheels and apply the weight to the rear wheels. The opposite is also true when you try to lift something with a front loader. The torque created by lifting with a front loader will put more weight on front wheels and remove it from rear wheels. Torque is a simple thing to calculate, it's the weight, perpendicular, you are trying to lift times the distance the weight is from the fulcrum, which happens to be either your front wheels when using a loader or the rear wheels when lifting with 3 pt.
So yes there is a rule, Torque and coefficient of friction, but it a little more complicated. Get your high school physics book out and look up first class lever and coefficient of friction. George
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