Finding the Coefficient of Static Friction on a Banked Curve

AI Thread Summary
To determine the coefficient of static friction for a car on a banked curve, the banking angle was calculated to be 24.7 degrees using the formula tan θ = v² / (r*g). The problem involves a car traveling at 93.8 km/hr on a curve with a radius of 87.5 m, and the goal is to find the necessary friction to prevent skidding. It is important to analyze the forces acting on the car, including the direction of friction, to ensure there is no vertical acceleration. A free body diagram can help visualize these forces and establish the conditions needed for the car to maintain its path without sliding.
mparsons06
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Homework Statement



If a curve with a radius of 87.5 m is perfectly banked for a car traveling 71.8 km/hr, what must be the coefficient of static friction for a car not to skid when traveling at 93.8 km/hr?

Homework Equations



tan \theta = v^{2} / r*g

The Attempt at a Solution



I found the banking angle:

tan \theta = 19.9^2 / 87.5 * 9.81 = 24.7 deg.


But I'm not sure on how to find what the question is asking for. Help?!
 
Physics news on Phys.org
If there were no friction, would the car at that speed slide up or down the incline? The answer gives you the direction of the frictional force that is needed. Once you have the direction, draw a free body diagram and require that the acceleration have no vertical component.
 

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