Banked Curve Problem: Solve Bicycle Speed & Friction Coefficient

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SUMMARY

The discussion centers on solving a banked curve problem involving a bicycle navigating a 20-meter radius circle. The resultant force from the surface on the bicycle forms a 15° angle with the vertical, requiring the application of centripetal acceleration formulas. The speed of the bicycle can be determined using the formula ac = v²/r, while the coefficient of static friction can be calculated given that the frictional force is half its maximum value. Key principles include Newton's second law and the relationship between friction and normal forces.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula (ac = v²/r)
  • Knowledge of Newton's second law of motion
  • Familiarity with static friction and its maximum value
  • Basic trigonometry to analyze angles and forces
NEXT STEPS
  • Calculate bicycle speed using centripetal acceleration principles
  • Determine the coefficient of static friction in practical scenarios
  • Explore the effects of different angles on banked curves
  • Study real-world applications of friction in cycling dynamics
USEFUL FOR

Physics students, mechanical engineers, and cycling enthusiasts looking to understand the dynamics of banked curves and frictional forces in motion.

dansmith46
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Hey guys I know this is probably easy for most of you but I need help with a banked curve problem. The problem is as follows "Suppose you ride a bicycle in a 20-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle (normal force plus frictional force) makes an angle of 15° with the vertical. (a) What is your speed? (b) If the frictional force on the bicycle is half its maximum possible value, what is the coefficient of static friction?"
 
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remember the formula for centripetal acceleration:

hint: ac = v2/r

where a is the centripetal acceleration, v is the velocity and r is the radius, that might get you started, and remember Newton's second law.
 

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