What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29.0 km/h and the coefficient of static friction between tires and track is 0.320? The bicyclist, bicycle and tires are all to the right of the center of the track. Treat the bicyclist, bicycle and tires as one object.

Question

Sebastian Boyd

Physics

10 September, 22:37

What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29.0 km/h and the coefficient of static friction between tires and track is 0.320? The bicyclist, bicycle and tires are all to the right of the center of the track. Treat the bicyclist, bicycle and tires as one object.

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Answers (1)

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Micah Werner · Answer 1

Let the radius of track required be r.

Centripetal force will be provided by frictional force which will be equal to

m v² / r

Frictional force = mg x μ

So

m v² / r = mg μ

r = v² / μ g =

v = 29 km / h = 8.05 m / s

r = (8.05 x 8.05) / (.32 x 9.8) = 20.66 m