What Is the Required Coefficient of Static Friction for a Car on a Banked Curve?

AI Thread Summary
To determine the required coefficient of static friction for a car on a banked curve, one must consider the banking angle and the forces acting on the car. The problem involves calculating the maximum speed for a car on an 80m radius curve, initially designed for 70km/hr, and assessing the friction needed to prevent skidding at 90km/hr. Participants suggest deriving expressions for the banking angle and the maximum speed to understand the relationship between speed, angle, and friction. Drawing free body diagrams is recommended to visualize the forces and their directions in this scenario. Understanding these concepts is essential for solving the problem effectively.
cdawg201
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I am new to the forum and was hoping if someone could explain to me how to do this problem, give me some formulas, or even possibly give me an answer. :) It is from my Giancoli Fifth Edition High School Physics book.

If a curve with a radius of 80m is perfectly banked for a car traveling 70km/hr, what must be the coefficient of static friction for the car not to skid when traveling 90km/hr?

Any/all help is greatly appreciated.
 
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Welcome to pf cdawg201!

Consider an inclined section of a road with banking angle \alpha. Can you find an expression for the maximum speed that the car can have so that it moves in a circle of fixed radius without slipping and relate it to the angle of banking? Next, if the actual speed is different from this "correct" speed, then what are possible directions of frictional force? Will it aid motion down the incline or oppose it? Draw freebody diagrams to convince yourself.

Hope that helps...

Cheers
Vivek
 
How about just doing it the hard way eh ?
Try deriving an expression for the angle of banking. while doing so try to take your problem into it. Btw I'm new too...
 
pseudoNewtonian said:
How about just doing it the hard way eh ?
Try deriving an expression for the angle of banking. while doing so try to take your problem into it. Btw I'm new too...

Hello pseudoNewtonian (welcome to PF)

When I said "find" I meant derive. You're not supposed to know all the formulae by heart (thought it helps sometimes to know the value of pi correct to 30 decimal places...esp in a party or something :smile:)

Enjoy physics...

Cheers
 
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