Question

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 330 km/h in a semicircular arc with a radius of 230 m

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?

Answer 1

Here,

initial speed , u = 0 m/s

final speed , v = 330 km/hr = 91.7 m/s

Now , for the tangential acceleration at

total distance , d = pi * R = pi * 230

using third equation of motion

v^2 - u^2 = 2 *at * d

91.7^2 - 0 = 2 * at * (pi * 230)

at = 5.82 m/s^2

the tangential acceleration of the car is 5.82 m/s^2

Now, for the speed at half way

again using third equation of motion

v^2 - u^2 = 2 *at * d

v^2 - 0 = 2 * 5.82 * (pi * 230/2)

v = 64.84 m/s

radial acceleration = v^2/R

radial acceleration = 64.84^2/230

radial acceleration = 18.27 m/s^2

the radius acceleration is 18.27 m/s^2

the radial acceleration is 18.27 m/s^2

B)

net acceleration = sqrt(18.27^2 + 5.82^2)

net acceleration = 19.2 m/s^2

now, for the coefficient of friction u

u * g = 19.2

u = 19.2/.9.8

u = 1.96

the coefficient of friction needed is 1.96