Four people each with a mass of 72.4 kg are in a car with a mass of1130kg. an ea

Question

Four people each with a mass of 72.4 kg are in a car with a mass of1130kg. an earthquake strikes. The verticaloscillations of the ground surface make the car bong up and down onits suspension springs, but the driver manages to pull off the roadand stop. When the frequency of the shaking is 1.80Hz, thecar exhibits a maximum amplitude of vibration. The earthquakeends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car'sbody as the people get out?

Explanation / Answer

Wo = sqrt(k/m)

2 pi * 1.8 = Wo = 11.3 radians/s

11.3 = sqrt (k/(1130+4*72.5) )

127.69 = k/1420
k = 181,319.8 N/m

force lost = 4 * 72.5 * 9.81 = weight of people

force lost = 2844.9 N

elongation = F/k = 2844.9/181,319.8 = .01569 m = 1.569 cm

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