Maximizing Speed on a Curved Road: Calculating Safe Speed with Varying Radii

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SUMMARY

The discussion centers on calculating the maximum safe speed for a car negotiating a curved road with a radius of 200 meters (2.00 x 10^2 m) and a coefficient of static friction of 0.20. The confusion arises from the mention of two different radii, specifically 50 meters and 200 meters. The correct radius for calculations is 200 meters, which is essential for determining the maximum speed using the formula derived from centripetal force and friction. The maximum speed can be calculated using the equation v = sqrt(r * g * μ), where g is the acceleration due to gravity and μ is the coefficient of friction.

PREREQUISITES
  • Understanding of centripetal force and its relation to circular motion
  • Familiarity with the concepts of friction and coefficients of friction
  • Basic knowledge of physics equations involving speed, radius, and gravitational acceleration
  • Ability to perform calculations involving square roots and basic algebra
NEXT STEPS
  • Research the formula for centripetal acceleration and its application in real-world scenarios
  • Learn about the effects of different coefficients of friction on vehicle handling
  • Explore advanced topics in vehicle dynamics, including tire performance on curves
  • Study the impact of road conditions on maximum safe speeds for vehicles
USEFUL FOR

Automotive engineers, physics students, and anyone involved in vehicle safety and performance analysis will benefit from this discussion.

Alexs45
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A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negoitate the curve if the radius of the curve 2.00 x 10^2?


please help
 
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Start by reading the problem carefully. It makes no sense to say "roadbed of radius 50 m" and then say "the radius of the curve 2.00 x 10^2".
 
that confused me also. two radii for one object.
 

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