In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least “massed”). One way in which this

Question

In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least “massed”). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 36.4-kg chair alone oscillates with a period of 1.40 s, and the period with the astronaut sitting in the chair is 2.22 s.

A)Find the force constant of the spring?
B)Find the mass of the astronaut ?

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Doris 2 months 2021-07-28T08:11:41+00:00 1 Answers 1 views 0

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    2021-07-28T08:13:39+00:00

    Answer:

    Explanation:

    This question is based on oscillation in spring – mass system

    time period is given by the relation T = 2π \sqrt{\frac{m}{k} }

    m is mass attached , k is spring constant of spring .

    In the first case

    mass m = 36.4 kg , T = 1.4

    Putting these values in the equation above

    1.4 = 2π\sqrt{\frac{36.4}{k} }

    1.4² = 4π² x \frac{36.4}{k}

    k = 732.42 N / m

    In the second case

    mass m = (36.4+m ) kg , T = 2.22s  , m is mass of astronaut

    Putting these values in the equation above

    2.22  = 2π\sqrt{\frac{36.4+m}{k} }

    2.22² = 4π² x \frac{36.4+m}{k}

    Putting the value of k

    2.22² = 4π² x \frac{36.4+m}{732.42}

    36.4 + m = 91.53

    m = 55.12.kg

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