Explanation:
(a) radius of the curve, r = 100 m
Angle of banking, [tex]\theta=15^{\circ}[/tex]
The angle of banking is given by the formula as :
[tex]\tan\theta=\dfrac{v^2}{rg}\\\\v=\sqrt{gr\ \tan\theta} \\\\v=\sqrt{9.8\times 100\times \ \tan(15)} \\\\v=16.2\ m/s[/tex]
(b) Let [tex]\mu[/tex] is the minimum coefficient of friction. The force of friction is given by :
[tex]f=\mu mg[/tex]
v = 20 km/h = 5.56 m/s
The first centripetal force is given by :
[tex]F_1=\dfrac{mv_1^2}{r}\\\\F_1=\dfrac{m(16.2)^2}{100}=2.62\ m[/tex]
The second centripetal force is given by :
[tex]F_2=\dfrac{mv_2^2}{r}\\\\F_2=\dfrac{m(5.56)^2}{100}=0.309\ m[/tex]
The additional friction force is given by :
[tex]f=|F_2-F_1|\\\\\mu=\dfrac{2.62-0.3}{9.8}\\\\\mu = 0.23[/tex]
Hence, this is the required solution.
