The standard test to determine the maximum lateral acceleration of a car is to drive it around a 200-ft-diameter circle painted on a level asphalt surface. The driver slowly increases the vehicle speed until he is no longer able to keep both wheel pairs straddling the line. A 3000 lb car is traveling at 25 mi/hr when the driver applies the brakes, and the car continues to move along the circular path. What is the maximum deceleration possible if the tires are limited to a total horizontal friction force of 2400 lb?

is the maximum deceleration from this top speed keeping-up with the grip of friction.

Explanation:

Given:

diameter of the track,

mass of the car,

speed of the car,

maximum horizontal frictional force between the surfaces,

Now the maximum speed attained by the car according to the frictional force:

also

where:

is the maximum deceleration from this top speed keeping-up with the grip of friction.

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