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.

Answer 1

119.74437 kg

Step-by-step explanation:

Mass of astronaut = x

Mass of chair = 42.5 kg

Time period is given by

`T=2\pi\sqrt{(m)/(k)}`

So,

`T\propto √(m)`

`\\\Rightarrow (T_1)/(T_2)=\sqrt{(m_1)/(m_2)}\\\Rightarrow (1.3)/(2.54)=\sqrt{(42.5)/(42.5+x)}\\\Rightarrow (1.3^2)/(2.54^2)=(42.5)/(42.5+x)\\\Rightarrow 42.5+x=(42.5* 2.54^2)/(1.3^2)\\\Rightarrow x=(42.5* 2.54^2)/(1.3^2)-42.5\\\Rightarrow x=119.74437\ kg`

The mass of the astronaut is 119.74437 kg is the required answer.