Question

Homework 13 Item 13 < 13 of 17 > Part A Your friend helps you place a 115 kg sofa in the back of a 2600 kg truck. Your keen vision tells you that the truck sinks 3.75 cm on its springs when you place the sofa. With what frequency (in Hz) will the truck and the sofa oscillate on the springs? IVO ALV O a ? Hz Submit Request Answer Provide Feedback Next >

Answer 1

First, find the spring constant of the spring

Given that the springs compress 0.0375m when a 115kg sofa is placed on the truck

Use Hooke's Law

$F=kx$

$W=kx$

$mg=kx$

$\frac{mg}{x}=k$

$\frac{115kg*9.81m/s^{2}}{0.0375m}=k$

$\frac{115*9.81}{0.0375}=k$

${\color{Red} k=30084N/m}$

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Frequency, $f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

$f=\frac{1}{2\pi }\sqrt{\frac{k}{m_{truck}&plus;m_{sofa}}}$

$f=\frac{1}{2\pi }\sqrt{\frac{30084N/m}{2600kg&plus;115kg}}$

$f=\frac{1}{2\pi }\sqrt{\frac{30084}{2600&plus;115}}$

ANSWER: ${\color{Red} f=0.53Hz}$

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