Question

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?

Answer 1

Mass of astronauts will be 119.77 kg

Step-by-step explanation:

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

Time taken by the chair to complete the 1 vibration
`T_1=1.3sec`

And
`T_2=2.54sec`

Let the mass of the astronaut is m kg

So total mass = m + 42.5

We know that 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+m)}`

Squaring both side

`0.2619=(42.5)/(42.5+m)`

m = 119.77 kg