Question

A circular curve of highway is designed for traffic moving at 66 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 220 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 66 km/h?

Answer 1

(A)


first we know all forces are balanced so
considering the vertical direction we have,
\[n _{y}=F _{g}\]
\[n \times \cos \theta = mg\]
\[m = (n \times \cos \theta)/g\]

now horizontal direction,

\[n _{x}=F _{c}\]
\[n \times \sin \theta = mv ^{2}/r\]
\[m = (rn \times \sin \theta)/v ^{2}\]

the mass of the car is the same no matter the direction of force so equate, giving

\[ (n \times \cos \theta)/g=(rn \times \sin \theta)/v ^{2}\]
\[ ( \cos \theta)v ^{2}=(r\times \sin \theta)g\]
\[ (\sin \theta/ \cos \theta)=v ^{2}/(rg)\]
\[\theta = \tan^{-1} (v ^{2}/(rg))\]

then convert velocity to meters/second and sub in