Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Co

Question

Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1 800-kg car passes over a hump in a roadway that follows the are of a circle of radius 20.8 m as in the figure below. If the car travels at 25.0 km/h what force does the road exert on the car as the car passes the highest point of the hump? magnitude N direction What is the maximum speed the car can have without losing contact with the road as it passes this highest point? km/h

Explanation / Answer

a)

25.0 km/h = 25.0 * 10^3 m / 3600s = 6.944 m/s

Fn = mg - mv²/R
Fn = m(g - v²/R)

800kg (9.80 - 6.944²/20.8)

Fn = 5985.4 N (upwards)

b)

mg = mv²/R

v² = Rg

20.8m x 9.80 = 203.84(m/s)²

v = 203.84 = 14.27 m/s

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