10. The newest formula 1 cars employ spoilers and wings both front and back to g

Question

10. The newest formula 1 cars employ spoilers and wings both front and back to generate more “downward” force based on their speed. Since the force is similar to drag, it is proportional to v^2 which means at 64m/s it may be = mg (the car + driver’s weight) but at 90m/s is twice mg. a) At the track a 200m radius curve is banked at 25. Ignoring Wing effects, what is the design speed for this curve? b) If an Indy driver can negotiate a flat turn of radius 200 meters while traveling at 64m/s because of the mg of downward force caused by the wing, what must the minimum frictional coefficient of his/her tires be? (yes they are sticky tires.) c) Given the coefficient of friction in part b (or assume 1.0 if you didn’t get it) and at a speed of 90m/s, determine the smallest radius 25 banked curve this Indy driver can negotiate without sliding off the track? Assume the wing tilts so that its force is still vertically downward!

Explanation / Answer

here,

(A)

radius , r = 200 m

theta = 25 degree

let the speed be v

m*g*sin(theta) = m*v^2*cos(theta)/r

9.8* tan(25) = v^2/200

v = 30.23 m/s

the maximum velocity of the car is 30.23 m/s

(B)

r = 200 m

speed of car , v = 64 m/s

let the coefficient of friction be u

equating the forces

m*v^2/r = u*m*g

64^2/200 = u * 9.8

u = 2.09

the coefficient of friction must be 2.09

(C)

u = 1

v = 90 m/s

theta = 25 degree

u*m*g*cos(theta) + m*g*sin(theta) = m*v^2 * cos(theta) /r

1 * 9.8 * cos(25) + 9.8 * sin(25) = 90^2 * cos(25) /r

r = 563.68 m

the smallest radius of the curve is 563.68 m

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