Find Coeff. of Static Friction of Car on Track

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SUMMARY

The discussion focuses on calculating the coefficient of static friction for a car on a flat circular track with a radius of 5 meters and a tangential acceleration of 1.7 m/s². The car travels 0.2 of the way around the track before skidding off, with gravity set at 9.8 m/s². The initial approach used the equations Fc=Ff and V²m/r=μmg, leading to an incorrect calculation of μ. The correct coefficient of static friction is determined to be approximately 0.436, but calculation errors were noted as a potential issue in achieving this result.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with Newton's second law (F=ma)
  • Knowledge of frictional forces and coefficients
  • Ability to manipulate kinematic equations
NEXT STEPS
  • Review the derivation of the centripetal force equation (Fc=V²m/r)
  • Study the relationship between tangential acceleration and velocity in circular motion
  • Learn about the role of static friction in preventing skidding
  • Practice solving problems involving coefficients of friction in circular motion scenarios
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of friction in circular motion.

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Homework Statement


A car traveling on a flat circular track of radius 5m accelerates uniformly from rest with a tangential acceleration of 1.7m/s^2. The car makes it 0.2 of the way around the track before skidding off. Acceleration of gravity=9.8m/s^s.
What is the coefficient of static friction between the car and the track?


Homework Equations


Fc=V^2m/r
F=ma

The Attempt at a Solution



So I tried this:
Fc=Ff
V^2m/r=\mumg
v^2/gr=\mu

To determine the velocity at which the car slips, I said V^2=2ax, where x is 2\pir/5.

So I get 4\pia/5g=\mu

It's not correct. Why is that?
 
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Nice solution. I get 0.436, but I'm prone to calculation errors.
 
The online homework system marks it wrong. I can't explain it. Is there another way to do this?
 

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