A car\'s wheels are connected to the automobile by four springs. When six 68 Kg

Question

A car's wheels are connected to the automobile by four springs. When six 68 Kg teenagers get into the automibile, it settles closer to the road by 3.2 centimeters. What is the spring constant of each of the springs? If the automobile has a mass of 1400 Kg when empty, what would be its oscillation frequency when carrying this load of people.

The wheel, hub , brake and outer part of the driveshaft has a total mass of 83 Kg What is the oscillation frequency of the wheel assembly? If the driver drives one wheel over a 9.4 centimeter high curb, how much energy must be absorbed by the damper (shock absorber) attached to the wheel assembly in order to prevent the wheel from bouncing (oscillating) and making control of the vehicle difficult?

Explanation / Answer

Total mass is
M = 1400 kg + 6(68kg)
= 1808 kg
Acceleration due to gravity is g = 9.8 m/s^2
Extension in the string is x = 3.2 cm
                                      = 0.032 m
Then the spring constant (k) is

        (4k)(x) = Mg
k = Mg / 4x
  = (1808kg)(9.8 m/s^2) / 4(0.032m)
= 138425 N/m


Please post the second question as separate.

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