A civil engineer wishes to redesign the curved roadway in the figure in such a w

Question

A civil engineer wishes to redesign the curved roadway in the figure in such a way that a car will not have to rely on friction to round the curve without skidding. In other words, a car moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a ramp is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the road is to be 14.0 m/s (31.3mi/h) and the radius of the curve is 39.0 m.

a) At what angle should the curve be banked?

b) For the above example, suppose that the coefficient of static friction between the tires and the road is 0.54. What maximum speed could a car negotiate the exit ramp without skidding?

Explanation / Answer

a) vmax = sqrt [r g tan theta]

tan theta = v2max / r g

tan theta = 142 / (39 * 9.81)

theta = 27.126 deg

b)  maximum speed could a car negotiate the exit ramp without skidding

vmax = sqrt [r g (sin theta + muk costheta) / (cos theta - muk sin theta)]

= sqrt [39 * 9.81(sin 27.13 + 0.54 cos 27.13) / (cos 27.13 - (0.54 * sin27.126))]

= 23.6 m/s

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