A curve of radius 2.10 x 10^2 m is banked at an angle of 13 degree . If an autom

Question

A curve of radius 2.10 x 10^2 m is banked at an angle of 13 degree . If an automobile with wheels with mu= 0.90 is to round this curve without skidding, what is the maximum permissible speed? Textbook Reference: See worked Examples 10 and 11 in Chapter 6 of Physics for Engineers and Scientists. Incorrect Solution Strategy: Did you check your calculations? Does your answer make physical sense? Did you draw a free-body diagram and label all relevant forces? In what direction does the friction force act? The centripetal force acts inward toward the center of the circle and along the horizontal line. What forces or components of forces act toward the center of the circle in this situation?

Explanation / Answer

here,

r = 210 m

here,

using Newton's second law of motion

ma = mg*sin(theta) + u*mg*cos(theta)

v^2/210 = 9.8*(sin(13) + 0.90*cos(13) )

solving for v

v = 47.62 m/s

the maximum permissible speed is 47.62 m/s

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