What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the μs between tires and track is 0.32?

r=20.6m

Explanation:

What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the μs between tires and track is 0.32?

the acceleration experienced by the bicycle will be the centripetal acceleration

which is given by a=v^2/r

v=velocity of the bicyclist 29km/h = 8.05m/s

the centripetal force is given as

f=mv^2/r

note the maximum value of the static frictional force

fmax=∪N

U=the coefficient of static friction

N=mg=normal reaction of the bicycle which is equal to the the weight of the bicycle

equating fmax=fcentripetal

mv^2/r=Umg

r=v^2/Ug

r=8.05^2 / (.32*9.81)

r=20.6m, is the smallest radius of an unbanked track