Banked curves, coefficient of friction problem

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SUMMARY

The discussion centers on calculating the minimum coefficient of static friction required for a car navigating a banked curve with a radius of 74.8 meters at a speed of 21.1 m/s. The angle of the bank is determined using the formula (v^2)/(gr), where 'v' is the speed and 'g' is the acceleration due to gravity. Participants emphasize the importance of drawing a free-body diagram to visualize the forces acting on the car, ensuring that the resultant forces equal the necessary centripetal force to prevent slipping.

PREREQUISITES
  • Understanding of centripetal force dynamics
  • Knowledge of static friction and its coefficient
  • Familiarity with free-body diagrams
  • Basic physics equations related to motion and forces
NEXT STEPS
  • Study the derivation of the formula for the angle of a banked curve
  • Learn how to calculate the coefficient of static friction in various scenarios
  • Explore the concept of centripetal acceleration and its applications
  • Review examples of free-body diagrams in physics problems
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for practical examples of friction and motion in curved paths.

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Homework Statement



A road with a radius of 74.8 m is banked so that a car can navigate the curve at a speed of 15 m/s without any friction. When a car is going 21.1 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?

Homework Equations





The Attempt at a Solution



I figured out the angle by doing (v^2)/gr but I don't know how to find the coefficient of static friction. PLEASE HELP!
 
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Draw a free-body diagram. The resultant of all forces has to be equal to the centripetal force. ehild
 

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