The maximum tangential speed that the car can take the corner at w/o slipping when dry is 65.82m/s
The maximum tangential speed that the car can take the corner at w/o slipping when wet is 39.46m/s
In order to get the maximum tangential speed of the car, we must know that the centripetal force would be equal to the force of friction.
The centripetal force is expressed as:
\(F_c=\frac{mv^2}{r}\\\)
The force of friction is expressed as;
\(F_f=\mu R\\F_f= \mu mg\)
Equating both expressions
\(F_c=F_f\\\frac{mv^2}{r} = \mu mg\\\frac{v^2}{r} = \mu g\)
Given the following parameters
mass m = 1000kg
radius r = 690 meters
g = 9.81m/s²
\(\mu_d\) = 0.64
\(\mu_w\) = 0.23
Get the maximum tangential speed that the car can take the corner at w/o slipping when dry.
\(\frac{v^2}{r} = \mu_d g\\\frac{v^2}{690} =0.64(9.81)\\v^2=4,332.096\\v=\sqrt{4,332.096}\\v= 65.82 m/s\)
Hence the maximum tangential speed that the car can take the corner at w/o slipping when dry is 65.82m/s
Get the maximum tangential speed that the car can take the corner at w/o slipping when wet.
\(\frac{v^2}{r} = \mu_d g\\\frac{v^2}{690} =0.23(9.81)\\v^2=1,556.847\\v=\sqrt{1,556.847}\\v= 39.46 m/s\)
Hence the maximum tangential speed that the car can take the corner at w/o slipping when dry is 39.46m/s
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