Consider a test driving course as shown in the figure below. The driving course

Question

Consider a test driving course as shown in the figure below. The driving course is a sinusoidal function which is given by y = 4 sin (pi/L x + pi/2 Note that the coefficients of static and kinetic friction between the tires and the track are mu_s = 0.3 and mu_k = 0.25, respectively. Between the points A and B, choose the most critical point to the car for slipping off the track and explain the reason. Assume that at the critical point that you chose in (a), the track has a slope which has an angle of theta = 15 degree as shown in below figure. Determine the required cone spacing L to have the maximum driving speed of 54 km/h at the critical point.

Explanation / Answer

Answer A:

A is the most crictical point to slip off the car from the track.

at point A, y=4

y=4 sin ((pi/L)*x+(pi/2))

sin ((pi/L)*x+(pi/2)) = 4/4 = 1

((pi/L)*x+(pi/2)) = pi/2

x=0

Vmax = square root of (µ(static) g r)

V max = square root of (0.3X 9.8X4) = 3.4 m/s

at point B, y=0

sin ((pi/L)*x+(pi/2)) = 0

x = - (pi/2)*(L/pi)

x = - (L/2)

Vmax = square root of (µ(static) g r)

V max = square root of (0.3X 9.8X0) = 0 m/s

Answer B:

Vmax = square root of (µ(static) g r)

54 = square root of (0.25X9.8X sin 15) X L)

L = (54 X 54) X (1000/3600)^2 /0.25X9.8XSin 15)

L = 354 m

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