Answer:
The minimum coefficient of friction is 0.22
Explanation:
Suppose If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve.
We need to calculate the ideal speed to take a 85 m radius curve banked at 15°.
Given that,
Radius = 85 m
Angle = 15°
Speed = 20 km/h
We need to calculate the ideal speed
Using formula of speed
[tex]\tan\theta=\dfrac{v^2}{rg}[/tex]
[tex]v=\sqrt{rg\tan\theta}[/tex]
Put the value into the formula
[tex]v=\sqrt{85\times9.8\tan15}[/tex]
[tex]v=14.9\ m/s[/tex]
We need to calculate the minimum coefficient of friction
Using formula for coefficient of friction
[tex]v^2=\dfrac{rg(\sin\theta-\mu\cos\theta)}{\mu\sin\theta+\cos\theta}[/tex]
Put the value into the formula
[tex](5.55)^2=\dfrac{85\times9.8(\sin15-\mu\cos15)}{\mu\sin15+\cos15}[/tex]
[tex]\dfrac{30.8025}{85\times9.8}=\dfrac{0.2588-\mu0.966}{\mu0.2588+0.966}[/tex]
[tex]0.9754462\ mu-0.223541=0[/tex]
[tex]\mu=\dfrac{0.223541}{0.9754462}[/tex]
[tex]\mu=0.22[/tex]
Hence, The minimum coefficient of friction is 0.22
