Question about uniforn circular motion and highway curves

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SUMMARY

The maximum speed at which a 1050-kg car can round a turn with a radius of 77 meters on a flat road, given a coefficient of static friction of 0.80, is determined using the formula F = mv² / r. The force of friction calculated is 8232 N, which represents the maximum force before sliding occurs. To find the maximum speed, one must rearrange the equation to solve for v, confirming that the static friction force is the limiting factor in maintaining circular motion.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with circular motion equations
  • Knowledge of static friction and its calculation
  • Basic algebra for rearranging equations
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  • Calculate maximum speed using the formula v = sqrt(F * r / m)
  • Explore the effects of varying the coefficient of static friction on maximum speed
  • Study the implications of road conditions on friction and vehicle dynamics
  • Learn about centripetal acceleration and its role in circular motion
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Students studying physics, automotive engineers, and anyone interested in the dynamics of vehicles on curved paths.

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Homework Statement


What is the maximum speed with which a 1050-kg car can round a turn of radius 77m on a flat road if the coefficient of static friction between tires and the road is .80?

Homework Equations


F = mv^2 / r
a = v2 / r
Ffr = mustatic x mg

The Attempt at a Solution



I found the force of friction to be 8232 N: .80 x 1050 x 9.8 = 8232 N
If someone could just tell me the next step that would help me out a lot; i don't know where to go from here. Thanks.
 
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Well that is the max force you can use before static friction gives upand the car slides. Therefore that is the max force you can use to turn the corner. All you need to do is solve for speed.
 

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