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Question

A 1000 kg car carrying four 82 kg people travels over a "washboard” dirt road with corrugations 4.0 m apart. The car bounces with maximum amplitude when its speed is 16 km/h. when the car stops, and the people get out, by how much does the car body rise on its suspension?


A

10 cm

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B

3 cm

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C

5 cm

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D

None of these

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Solution

The correct option is C

5 cm


The time period between corrugations would be T=4m(16×518)910s

f=1T=109;ω=2π f=2π×109=20π9

since at this frequency the amplitude is maximum. So it got to be its natural frequency.

As we know ω=km k=ω2m

k=(20π29)2×(1000+(4× 82))=64659.5Nm1

when the people get out of the car the weight change is 4×82×10=3280N

we have ω=kx

3280=64659.5x

x=0.050m5 cm


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