Answer:0.077
Explanation:
Given
banked designed for traffic moving at [tex]58 km/h\approx 16.11 m/s[/tex]
Radius of the curve 201 m
Actual traffic velocity =[tex]37 km/h approx 10.27 m/s[/tex]
For banking of road
[tex]tan\theta =\frac{v^2}{rg}[/tex]
[tex]tan\theta =\frac{16.11^2}{201\times 9.81}[/tex]
[tex]\theta =7.49^{\circ}[/tex]
Centripetal acceleration is given by
[tex]a=\frac{v^2}{r}[/tex]
Taking component of centripetal acceleration
along and perpendicular to surface
[tex]a_{parallel}=\frac{v^2cos\theta }{r}[/tex]
[tex]a_{perpendicular}=\frac{v^2sin\theta }{r}[/tex]
From FBD
[tex]mgsin\theta -f_s=ma_{parallel}[/tex]
[tex]f_s=mgsin\theta -ma_{parallel}[/tex]----1
where [tex]f_s[/tex] is frictional force
[tex]N-mgcos\theta =ma_{perpedicular}[/tex]
[tex]N=mgcos\theta +ma_{perpedicular}[/tex]----2
and we know coefficient of friction is given by
[tex]\mu =\frac{f_s}{N}[/tex]
[tex]\mu =\frac{mgsin\theta -ma_{parallel}}{mgcos\theta +ma_{perpedicular}}[/tex]
[tex]\mu =\frac{gsin\theta -\frac{v^2cos\theta }{r}}{gcos\theta +\frac{v^2sin\theta }{r}}[/tex]
[tex]\mu =\frac{1.2804-0.5202}{9.726+0.068}[/tex]
[tex]\mu =0.077[/tex]
