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Weighing Astronauts. This procedure actually has been used to "weigh" astronauts in space. A 42.5kg chair is attached to a spring and allowed to oscillate. When it is empty, the chair takes 1.30 s to make on complete vibration. But with an astronaut sitting in it, with her feet off the floor, the chair takes 2.54 s for one cycle. What is the mass of the astronaut?

Respuesta :

Answer:

Mass of astronauts will be 119.77 kg

Explanation:

We have given mass of the chair [tex]m_1=42.5kg[/tex]

Time taken by the chair to complete the 1 vibration [tex]T_1=1.3sec[/tex]

And [tex]T_2=2.54sec[/tex]

Let the mass of the astronaut is m kg

So total mass = m + 42.5

We know that time period is given by

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

So [tex]\frac{T_1}{T_2}=\sqrt{\frac{m_1}{m_2}}[/tex]

[tex]\frac{1.3}{2.54}=\sqrt{\frac{42.5}{42.5+m}}[/tex]

Squaring both side

[tex]0.2619=\frac{42.5}{42.5+m}[/tex]

m = 119.77 kg

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