Finding the Coefficient of Static Friction on a Banked Curve

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SUMMARY

The discussion focuses on calculating the coefficient of static friction required for a car to navigate a banked curve without skidding. Given a curve radius of 87.5 meters and a speed of 93.8 km/hr, the banking angle was determined to be 24.7 degrees using the equation tan θ = v² / (r * g). The key to solving the problem lies in analyzing the forces acting on the car, particularly the direction of the frictional force necessary to maintain stability on the incline.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Knowledge of the equations of motion, specifically tan θ = v² / (r * g)
  • Ability to draw and interpret free body diagrams
  • Familiarity with the concept of static friction
NEXT STEPS
  • Calculate the coefficient of static friction using the derived banking angle and forces involved
  • Explore the effects of varying speeds on the stability of vehicles on banked curves
  • Study the principles of centripetal force in relation to banking angles
  • Investigate real-world applications of banked curves in road design and safety
USEFUL FOR

Physics students, automotive engineers, and anyone interested in vehicle dynamics and road safety design will benefit from this discussion.

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 [tex]\theta[/tex] = [tex]v^{2}[/tex] / r*g

The Attempt at a Solution



I found the banking angle:

tan [tex]\theta[/tex] = 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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