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 arc of a circle of radius 19.2 m as in the figure below. (a) 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 (b) 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) lets call into the circle positive 25 km/hr = 6.94 m/s mg - N = m v^2/r so N = mg - mv^2/r = 1800 ( 9.81 -6.94^2/19.2)=13142.66 N b) max speed means N = 0 mg = mv^2/r v = sqrt(gr) = sqrt(9.81*19.2)=13.724 m/s=49.4064 km/hr

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