a car is traveling around a 150 m radius curve at 18 m/s. Answer the following,

Question

a car is traveling around a 150 m radius curve at 18 m/s. Answer the following, being sure to show all of your work. A) What is the minimum coefficient of static friction needed to keep the car from sliding? B) Imagine that the roadway is now covered in sheer ice (u_s=0), but has a bank to it. What banking angle is required to allow the car to make the turn? C) If the curve is banked at the angle you found in Part B, and friction is added back in with the coefficient you found in Part A, with what maximum speed could the car now travel and still make the turn?

Explanation / Answer

A) Use equation

Ffriction = Fcentri

us*mg=mv^2/r

us= v^2/gr = (18^2)/(9.8*150) = 0.22

B) Use equation,

tanq= v^2/gr

q= tan^-1(v^2/gr) = tan^-1[(18^2)/(9.8*150)]= 12.430

C) Use equation,

v = sqrt[((tanq+us)/(1-us*tanq))gr] = sqrt[((tan12.43+0.22)/(1-0.22tan12.43))*9.8*150] = 10.9 m/s

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