A road with a radius of 75.0 m is banked so that a car can navigate the curve at a speed of 15.5 m/s without any friction. When a car is going 22.4 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?

Question

Physics

Avah Crawford

18 February, 07:38

A road with a radius of 75.0 m is banked so that a car can navigate the curve at a speed of 15.5 m/s without any friction. When a car is going 22.4 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?

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Scooter · Answer 1

Answer: 0.683

Explanation: The relationship between a car moving along a curve and the frictional force is given below as

us*g = v²/r

Where us = coefficient of static friction = ?, g = acceleration due to gravity = 9.8 m/s², v = 22.4 m/s and r = 75m

By substituting the parameters, we have that

us*9.8 = 22.4² / 75

us * 9.8 = 501.76/75

us * 9.8 = 6.690

us = 6.690/9.8 = 0.683