Answer :
Final answer:
The concept of centripetal force allows us to calculate the safe speed limit for cars on a highway curve, given the radius of the curve and the maximum static friction force. In this case, the safe speed limit comes out to be approximately 24.2 m/s.
Explanation:
The question refers to the concept of centripetal force and how it helps cars to safely navigate highway curves. Centripetal force is the force that keeps an object moving in a circular path. In this case, friction between the car's tires and the road surface provides the centripetal force, allowing the car to make a turn without slipping.
Given the radius of the curve (42 m) and the maximum force of static friction (8,327 N), you can calculate the safe speed for cars using the formula for centripetal force: F = mv^2/r, where m is the mass of the car, v is its speed, and r is the radius of the curve.
By rearranging the formula to solve for v (speed), we get v = sqrt(Fr/m). Substituting the given values, the safe speed comes out to approximately 24.2 m/s. Therefore, this should be the posted speed limit for the curve to ensure safe driving.
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