I need some Physics B help (banking curve problems)?A car is rounding a curve with a radius of curvature 103 meters. The road surface is banked at an angle of 83 degrees. The coefficient of friction used in this problem is 0.331597, and the mass of the vehicle is 1450 kg. I need help finding the maximum safe speed with which the car can round the curve but with... | |
Your banking angle of 83 degrees is too steep for there to be a solution.
This can be seen by looking at the equation for Vmax at Reference 1:
(1) Vmax = √ [ r * g * (μs * cos(θ) + sin(θ) ) / (cos(θ) - μs * sin(θ)) ]
In particular, look at the denominator:
(2) (cos(θ) - μs * sin(θ))
If you evaluate this using your values of 83 degrees and 0.331597 :
(3) (cos(83) - 0.331597 * sin(83)) = - 0.207 . . .,
or a negative number.
That means that the curve is so steeply banked that no amount of speed will cause it to skid out. After all, 83 degrees is nearly a right angle!
Typical banking angles are less than 20 degrees.
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