Friction question (intro level)

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SUMMARY

The discussion focuses on calculating the minimum coefficient of friction required for vehicles to safely navigate a banked circular highway curve designed for 55 km/h traffic, with a radius of 213 m, while actual traffic moves at 49 km/h on a rainy day. The angle of the banked curve was determined to be approximately 6.38 degrees. Participants suggest using a free body diagram (FBD) to visualize the forces at play, including the frictional force necessary to prevent sliding. Algebraic calculations will follow to derive the coefficient of friction from the established parameters.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Knowledge of free body diagrams (FBD)
  • Familiarity with frictional force concepts
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of circular motion in physics
  • Learn how to create and analyze free body diagrams
  • Research the equations governing frictional forces
  • Practice algebraic manipulation for physics problems
USEFUL FOR

This discussion is beneficial for physics students, civil engineers, and anyone involved in traffic safety and roadway design, particularly those interested in the dynamics of vehicles on banked curves.

Fallinleave
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A banked circular highway curve is designed for traffic moving at 55 km/h. The radius of the curve is 213 m. Traffic is moving along the highway at 49 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road?

I found the angle to be 6.38 degree. Is it right? How do I go from here?
Thanks,
 
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Fallinleave said:
I found the angle to be 6.38 degree. Is it right?
That's pretty close to what I came up with, differing by only the 3rd significant digit. :cool:
How do I go from here?
Thanks,
A free body diagram (FBD) would be a good start. Your FBD should look pretty similar to the FBD in the first part, except there is now a frictional force involved, parallel to the surface of the road.

(Then prepare yourself for bit of algebra). http://www.websmileys.com/sm/cool/694.gif
 

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