What Speeds Are Safe for a Banked Curve in Wet Conditions?

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SUMMARY

The discussion focuses on calculating safe speeds for a banked curve with a radius of 300 meters and a banking angle of 10 degrees. For part (a), the speed at which no friction is required is determined using the formula Fc=mv²/r. In part (b), with a coefficient of friction of 0.4 due to wet conditions, participants explore how to derive both maximum and minimum speeds for safe navigation of the curve. The key insight is understanding the dual role of friction in preventing sliding either down or up the banked curve.

PREREQUISITES
  • Understanding of centripetal force (Fc=mv²/r)
  • Knowledge of banking angles in physics
  • Familiarity with coefficients of friction
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the no-friction speed for different banking angles
  • Explore the effects of varying coefficients of friction on curve navigation
  • Learn about the dynamics of vehicles on banked curves
  • Investigate real-world applications of banked curves in civil engineering
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the dynamics of vehicles on banked curves, particularly in wet conditions.

a.wright
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Homework Statement


the curve has a radius of 300m and is banked at an angle of 10.0degrees. (a) what speed is no friction required? (b)suppose it is raining and the coefficient of friction is 0.4, what are the maximum and minimum speeds at which the curve can be travelled


Homework Equations



Fc=mv2/r
Fnet=0

The Attempt at a Solution


i attached my work. i think i have the right answer to part (a) and think I'm on the right track for part (b) but i don't know how to get two speeds, i only end up wit one.
any help would be great. thanks
 

Attachments

  • banked curve.JPG
    banked curve.JPG
    47.1 KB · Views: 535
Physics news on Phys.org
Consider what the friction can keep the car from doing, it can either be used to keep the car from sliding down the ramp, but it could also be the reason it doesn't slip up the ramp.
 

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