Question

What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29.5 km/h and the μs between tires and track is 0.435?

Answer 1

Answer:

Radius=15.773 m

Explanation:

Given data

v=29.5 km/h=8.2 m/s

μs=0.435

To find

Radius R

Solution

The acceleration is a centripetal acceleration  which is experienced by the bicycle given by

$a=v^{2}/R$

This acceleration is only due to static force which given as

$f=ma\\f=m(v^{2}/R )$

The maximum value of the static force is given as

$Fs_{max}=u_{s}F_{N}$

where

FN is normal force equal to mass*gravity

Therefore when the car is on the verge of sliding

$f=fs_{max}\\ m(v^{2}/R )=u_{s}mg$

Therefore the minimum radius should be found by the bicycle move without  sliding

So

$v^{2}/R=u_{s}g\\ R=v^{2}/u_{s}g\\R=(8.2)^{2}/(0.435*9.8)\\R=15.773m$