Question

This procedure has been used to "weigh" astronauts in space:

A 42.5 kg chair is attached to a spring and allowed to oscillate. When it is empty, the chair takes 1.30 s to make one complete vibration. But with an astronaut sitting in it, with her feet off the floor, the chair now takes 2.54 s for one cycle.
What is the mass of the astronaut?

Answer 1

Mass of astronaut will be 119.7674 kg

Step-by-step explanation:

We have given mass of the chair
`m_1=42.5kg`

When there is chair alone then time period of osculation
`T_1=1.30sec`

Now when astronaut sit on the chair then total mass
`m_2=m_1+mass\ of\ astronaut=42.5+mass\ of\ astronaut`

Now with astronaut time period is
`T_2=2.54sec`

For spring time period is given by
`T=2\pi \sqrt{(m)/(k)}`

So
`(T_1)/(T_2)=\sqrt{(m_1)/(m_2)}`

`(1.3)/(2.54)=\sqrt{(42.5)/(42.5+mass\ of\ astronaut)}`

Squaring both side

`0.2619={(42.5)/(42.5+mass\ of\ astronaut)}`

`11.13+0.2619* mass\ of\ astronaut=42.5`

Mass of astronaut will be 119.7674 kg