Consider the design of a banked curve. What is the maximum speed of a car going

Question

Consider the design of a banked curve. What is the maximum speed of a car going around
a banked curve as a function of the angle of the bank (), coefficient of friction (?), mass
of car (m), radius of curve (r), and acceleration due to gravity (g)? Use Mathematica to
plot this maximum veloity as a funtion of for regular rubber on cement (? = 4/5) and for
a wet road (? = 2/5) given a curve radius of r = 100 m. Then plot this maximum veloity
as a funtion of r for regular rubber on cement (? = 4/5) and for a wet road (? = 2/5)
given a panking angle of = 30 . use LogLogPlot to plot over a range of r from 10 to
1000 m.

Explanation / Answer

? Fx= Fnx= Fnsin10=Fc = mv^2/r (No Ffrictionx because it should =0) equation 1 ? Fy= Fny -Ffrictiony-mg=0 Ffrictiony= 0.140 sin 10 Fny= Fncos10 ?Fy= Fncos10-0.140Fnsin10=mg equation 2 Divide equation 1 by equation 2: (mv^2/r =Fnsin10)/(mg=Fn(cos10-0.140sin10): m's cancel and Fn's cancel then solve for v: v=v(rg(sin10/cos10-0.140sin10) v=18.8 m/s

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