Four passengers with combined mass 250 kg compress the springs of a car with worn out shock absorbers by 4.00cm when they enter it. Model th

Question

Four passengers with combined mass 250 kg compress the springs of a car with worn out shock absorbers by 4.00cm when they enter it. Model the care and passengers as a single body on a single ideal spring. If the loaded has a period of vibration of 1.08 s, what is the period of vibration of the empty car?

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Đan Thu 4 years 2021-08-04T02:23:27+00:00 1 Answers 75 views 0

Answers ( )

  1. trucchi
    0
    2021-08-04T02:24:57+00:00
    Reply

    Answer:

    The time period of the empty car will be “1.00 s“.

    Explanation:

    The given values in the question will be:

    Mass,

    m = 250 kg

    Loaded car’s time period will be:

    T = 1.08 s

    Shock absorbers compression,

    x = 4 cm

    or,

      = 0.04 m

    Now,

    Weight of passengers will be:

    ⇒  F=mg

             =250\times 9.8

             =2450 \ N

    The spring constant of shock absorbers will be:

    ⇒  k=\frac{F}{x}

            =\frac{2450}{0.04}

            =61.250 \ N/m

    As we know,

    Time period, T = 2 \pi\sqrt{\frac{M}{k} }

    On substituting the values, we get

                       1.08=2\pi \sqrt{\frac{M}{61250} }

                      \frac{M}{61250}=0.02955

                          M=0.02955\times 61250

                               =1809.6 \ kg (Total mass of car as well as its passengers)

    Now,

    The mass of the empty car will be:

    ⇒  m'=M-m

              =1809.6-250

              =1559.6 \ kg

    hence,

    The time period of empty car will be:

    ⇒  T'=2\pi\sqrt{\frac{m'}{k} }

             =2\pi\sqrt{\frac{1559.6}{61250} }

             =2\pi \sqrt{0.0254}

             =1.003 \ s

    or,

             =1.00 \ s

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