Before 1960, people believed that the maximum attainable coefficient of static f

Question

Before 1960, people believed that the maximum attainable coefficient of static friction for an automobile tire on a roadway was ?s = 1. Around 1962, three companies independently developed racing tires with coefficients of 1.6. This problem shows that tires have improved further since then. The shortest time interval in which a piston-engine car initially at rest has covered a distance of one-quarter mile is about 4.43 s. (A) Assume the car's rear wheels lift the front wheels off the pavement as shown in the figure above. What minimum value of ?s is necessary to achieve the record time?

Explanation / Answer

Assuming the front wheels are off the ground for the entire ¼ mile = 402.3 m, the acceleration a = µs·9.8 m/s². For a constant acceleration, distance = 402.3 m = ½at² = .

804.6 m / (4.43 s)² = a = µs·9.8 m/s²

µs = 804.6 m / (4.43s)² / 9.8 m/s² = 4.18

or
assume a 1kg mass with an accelerating force equal to 1.6*1kg*9.8m/s^2 = 15.68 newtons
(the maximum supported by the tires)
15.68 n = 1kg*a
a = 15.68 m/s^2
distance travelled = 1/2 *a*t^2 = 7.84*t^2 max for the tires
1/4 mi = 5280ft/4 = 1320 ft = 402.336m
402.336 = 1/2*a*4.43^2
402.336 = 1/2*a* 19.625
a = 41m/s^2
41/15.68 = frict/1.6
friction = 4.184

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