Calculating Radius for Stone in Rotating Tire with Static Friction

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SUMMARY

The discussion focuses on calculating the radius of a tire based on the dynamics of a stone wedged in its tread. Given a stone mass of 3.0 x 10-3 kg and a coefficient of static friction of 0.71, the stone experiences a normal force of 1.8 N from the tread. At a tire surface speed of 16 m/s, the maximum centripetal force provided by static friction is calculated, leading to the determination of the tire's radius.

PREREQUISITES
  • Understanding of uniform circular motion
  • Knowledge of static friction and its coefficients
  • Familiarity with centripetal force calculations
  • Basic physics concepts related to forces and motion
NEXT STEPS
  • Calculate the maximum centripetal force using the formula Fc = μ * FN
  • Explore the relationship between linear velocity and radius in circular motion
  • Study the effects of varying coefficients of friction on centripetal force
  • Investigate real-world applications of static friction in automotive engineering
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the mechanics of circular motion and frictional forces.

TastyTyr
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please help...uniform circular motion..I am STUMPED:frown:

A stone has a mass of 3.0 10-3 kg and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.71. When the tire surface is rotating at 16 m/s, the stone flies out of the tread. The magnitude FN of the normal force that each side of the tread channel exerts on the stone is 1.8 N. Assume that only static friction supplies the centripetal force, and determine the radius r of the tire.
 
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Show what you've done so far. (Hint: What's the maximum possible centripetal force that the friction can supply?)
 

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