Answer:
[tex]R=17.4m[/tex]
Explanation:
Given data
Speed v=23 km/h =6.4 m/s
Coefficient of static friction μs=0.24
The acceleration experienced by bicycle is centripetal acceleration by:
[tex]\alpha =\frac{v^2}{R}[/tex]
This acceleration is only due to static friction force given by:
[tex]f=m\frac{v^2}{R}[/tex]
The maximum value of the static friction force given by
[tex]f_{s.max}=u_{s}F_{N}\\Where\\F_{N}=mg[/tex]
Therefore when the car is on verge of sliding:
[tex]f=f_{s.max}\\m\frac{v^2}{R}=u_{s}mg[/tex]
Therefore the minimum radius the bicycle can move without sliding is:
[tex]R=\frac{v^2}{u_{s}g}\\ R=\frac{(6.4m/s)^2}{0.24(9.8m/s^2)} \\R=17.4m[/tex]
