Centripetal Acceleration of car

AI Thread Summary
Two cars are driving in circular paths, with Car B's circle being twice the radius of Car A's and its centripetal acceleration three times greater. The centripetal acceleration formula, a = (v^2/r), is used to relate the velocities and radii of both cars. By establishing equations for the centripetal accelerations of both cars and their respective radii, a relationship between their speeds can be derived. The solution indicates that Car B is driving approximately 2.45 times faster than Car A. Understanding these relationships is crucial for solving the problem effectively.
bgrove
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Homework Statement


Two cars drive around in circles at constant speeds. Car B's circle is twice as large as car A's, but its centripetal acceleration is three times as large. How many times faster is car B driving than car A?

Homework Equations


I'm trying to use a=(v^2/r) for centripetal acceleration.

The Attempt at a Solution


I don't really know where to start on this one.

Per our answer key, the answer should be: 2.45 times faster.
 
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You want to find a relation between the velocity of car A and car B, and you're given a relation between the radii of their circular paths and a relation between their centripetal accelerations. Try to write down some equations.
 
Use subscripts to represent the parameters for A and B. Thus, rA, vA, and aA are the radius, velocity, and acceleration of A, respectively, and similarly for B. Now, in terms of these parameters, write the centripetal acceleration equations for A and B respectively. How is rA related to rB? How is aA related to aB? This should give you enough to solve the problem.

Chet
 
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