A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 310 km/h in a semicir arc with a radius of 210m.?

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A) Determine the tangential and radial acceleration of the car when it is halfway through the arc, assuming constant tangential acceleration.

B) If the curve were flat, what would the coefficient of static friction would be necessary between the tires and the road to provide this acceleration with no slipping or skidding?

At the end of the semicircle, the speed is
310km/h = 86 m/s
and the distance covered was
d = πr = π*210m = 660 m
and so from
v² = u² + 2as
we get (when initial speed u = 0)
a = v² / 2s = (86m/s)² / 2*660m = 5.62 m/s² ◄
That's the tangential acceleration the entire time.

To calculate the radial acceleration at the halfway point, we need the velocity at the halfway point, where D = d/2 = 330 m:
V = √(2as) = √(2 * 5.62m/s² * 330m) = 60.9 m/s
and so the radial acceleration is
a' = V²/r = (60.9m/s)² / 210m = 17.66 m/s² ◄ radial

B) So the overall acceleration is
a" = √(a² + a'²) = 18.5 m/s²

The minimum coefficient of friction would be
µ = a" / g = 18.5m/s² / 9.8m/s² = 1.89

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