Determine the maximum constant speed a race car

Determine the maximum constant speed a race car can have if the acceleration of the car cannot exceed 7.5 m/s^2 while rounding a track having a radius of curvature of 200 m.


Since the speed of the race car is constant, it has no tangential acceleration. Thus, we only need to worry about the normal acceleration. Normal acceleration is found by:


(Where a_n is normal acceleration, v is velocity, and \rho is the radius of the circle)

Knowing that the acceleration cannot exceed 7.5 m/s^2, let us find the velocity.



v=38.7 m/s
Thus, the car cannot exceed 38.7 m/s.


This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-115.

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