Final answer:
The maximum speed of the car in circular motion is given by v = sqrt(μsgR)
Step-by-step explanation:
To find the maximum speed of the car in circular motion, we need to consider the relationship between the maximum static friction and the centripetal force. The maximum static friction can be represented as μsN, where μs is the static coefficient of friction and N is the normal force.
The normal force is equal to the weight of the car on level ground, so N = mg. Therefore, the centripetal force in this situation is Fc = f = μsN = μsmg.
Since the centripetal force can also be expressed as Fc = mv² / r, we can equate the two expressions: μsmg = mv² / r. Solving for v, we find that the maximum speed of the car in circular motion is v = sqrt(μsgR).