The smell of burned rubber

Race car tracks bank their turns so that cars can go faster without sliding off the track. Consider a banked race car track. The track is in the shape of a circle of radius \(300~\mbox{m}\) and the track is banked at an angle of \(20^\circ\) with respect to the horizontal. The maximum speed of race cars around this track is \(v_b\). The maximum speed of race cars around a non-banked (flat) track of the same radius is \(v_f\). What is \(v_b/v_f\)?

Details and assumptions

  • The coefficient of static friction \(\mu\) between car tires and the track can be taken to be one. Tires don't like to slide.
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