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

Radius=15.773 m

Step-by-step 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`