Question

If a curve with a radius of 88m is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95km/h? ac=v^2/r

Answer 1

find the bank angle from \[ncos(\theta)=mg\]and\[nsin(\theta)=mv^{2}/r\]or\[\theta=\tan^{-1}(v^{2}/rg)\]Now, since the car is traveling faster than the design speed, the frictional force will be down the slope, so \[ncos(\theta)-f _{s}\sin(\theta)-mg=0\]where the static frictional force is\[f _{s}=u _{s}n\]so, substituting\[ncos(\theta)-\mu _{s}ncos(\theta)\sin(\theta)-mg=0\]Find the coefficient from here

Answer 2

Oh, we also know \[nsin(\theta)+f _{s}\cos(\theta)=mg\]