Finding the Coefficient of Static Friction on a Banked Curve

In summary, to find the coefficient of static friction needed for a car not to skid when traveling at 93.8 km/hr on a perfectly banked curve with a radius of 87.5 m, you must first find the banking angle using the equation tan \theta = v^{2} / r*g and then do a free body diagram to determine the direction of the frictional force needed to prevent skidding. The coefficient of static friction can then be calculated using this information.
  • #1
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?!
 
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  • #2
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.
 

What is static friction on a curve?

Static friction on a curve refers to the force that prevents an object from sliding or moving on a curved surface. It is caused by the microscopic bumps and imperfections on the surface of the object and the surface it is resting on.

What factors affect static friction on a curve?

The amount of static friction on a curve is influenced by the weight of the object, the coefficient of static friction between the object and the surface, and the angle of the curve. The greater the weight and the steeper the curve, the more static friction is required to prevent the object from sliding.

How is the coefficient of static friction determined on a curve?

The coefficient of static friction on a curve can be determined by dividing the maximum force of static friction by the weight of the object. This value is dependent on the materials of the object and the surface it is resting on, and can vary based on the texture and smoothness of the surfaces.

What is the difference between static friction on a curve and on a straight surface?

The main difference between static friction on a curve and on a straight surface is the direction of the force. On a curve, the force of static friction is directed perpendicular to the curve, while on a straight surface it is directed parallel to the surface.

How can static friction on a curve be reduced?

Static friction on a curve can be reduced by decreasing the weight of the object, increasing the coefficient of static friction through the use of a different material or surface treatment, or by decreasing the angle of the curve. Additionally, adding lubricants or reducing the roughness of the surfaces can also decrease the amount of static friction on a curve.

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