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") end had It installed Suppose s 1800-kg car passes over a hump In a roadway that follows the arc of a circle of radius 20.2 m as In the figure below. If the car travels at 21.4 km/h what force does the road exert on the car as the car passes the highest point of the hump? magnitude direction What is the maximum speed the car can have without losing contact with the road as it passes this highest point?

Explanation / Answer

part(a)

along vertical

Fnet = N - Fg

from newtons second law Fnet = -m*a = -m*v^2/R

N - mg = -mv^2/R

N = mg - mv^2/R

m = mass = 1800 kg

v = 21.4 km/h = 21.4*5/18 = 5.94 m/s

N = 1800*9.81 - 1800*5.94^2/20.2

N = 14513.9 N

direction upwards

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part b

for maximum speed N = 0

mg = mv^2/R

v = sqrt(Rg)

v = sqrt(20.2*9.81)

v = 14.1 m/s

v = 14.1*(18/5) = 50.8 km/h

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