Discover the Bicyclist's Paradox for a Memorable Holiday Adventure

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The discussion highlights the significance of friction as a non-conservative force in the context of cycling during holidays. It emphasizes that air resistance varies with velocity, leading to different energy losses depending on the travel path. The conversation suggests setting up equations of motion that incorporate frictional forces to analyze these effects. The proposed equation of motion is x'' - bv² + x = F(v), where x'' represents acceleration. Understanding these dynamics can enhance the experience of a holiday cycling adventure.
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Good Hollidays
 
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Friction is a nonconsertive force and must be accounted for. Typically, air resistance is not a linear function of velocity. So, different amounts of energy are lost to air friction for the different paths of travel. To prove this, set up an equation of motion for each direction incorporating the frictional force and assume the applied force is a funtion of velocity.

x'' - bv2 + x = F(v)

where x'' is the second time derivative of x.
 

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