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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 35.6 kg chair alone oscillates with a period of 1.30 s , and the period with the astronaut sitting in the chair is 2.23 s.

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

Respuesta :

Answer:

Explanation:

mass of chair, m = 35.6 kg

Time period, T = 1.3 s

Time period when the astronaut is sitting, T' = 2.23 s

Let the mass of astronaut is M.

Let the force constant is K.

(a)

The formula for the time period of a loaded spring

[tex]T=2\pi \sqrt{\frac{m}{K}}[/tex]

[tex]1.3=2\pi \sqrt{\frac{35.6}{K}}[/tex]

0.043 = 35.6 / K

K = 830.7 N/m

(b)

[tex]T'=2\pi \sqrt{\frac{m+M}{K}}[/tex]

[tex]2.23=2\pi \sqrt{\frac{35.6+M}{830.7}}[/tex]

0.126 x 830.7 = 35.6 + M

M = 69.15 kg

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