- #1
jonah
- 3
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Homework Statement
A town wants to build a banked curve to join to large roads. The maximum speed they would like cars travel on this curve is 51m/s. The angle of the banked curve is to be 19o and the radius is to be 1.8x102 m.
a) What does the coefficient of static friction need to be for the material being used to build this bank curve to achieve these parameters?
b) If the banked curve mentioned above is covered in ice (you can assume it is then a frictionless surface), what does a driver need to do to sure they make around they make it around a banked curve without slipping? Explain also what happens if they don’t do this (hint: there two scenarios if they slip, our answer should include a specific value relating to this exact situation and an equation for general banked curves).
Homework Equations
FN = M g = (M) (9.8 m/s2)
Fc = M v2 / r
The Attempt at a Solution
The net force must be horizontal--pointing toward the center of the circle--and only the friction force is available to provide it. The normal force and the weight simply cancel each other.
Fc = M v2 / r
= (M (51 m/s)2)/350 m
Fc = 14.45 M (m/s2)
FN = M g = (M) (9.8 m/s2)
For this flat curve, the centripetal force is supplied by the friction force, Ff,
Ff = FN
F f = M 9.8 m/s 2
Ff = Fnet = Fc
M 9.8 m/s 2 = 14.45 M (m/s2)
= 0.68
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I think my calculation of static friction is correct for part a). Although, I don't understand how to finish part b).