Question

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

Answer 1

Answer:

Mass of astronaut will be 119.7674 kg

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 $T=2\pi \sqrt{\frac{m}{k}}$

So $\frac{T_1}{T_2}=\sqrt{\frac{m_1}{m_2}}$

$\frac{1.3}{2.54}=\sqrt{\frac{42.5}{42.5+mass\ of\ astronaut}}$

Squaring both side

$0.2619={\frac{42.5}{42.5+mass\ of\ astronaut}}$

$11.13+0.2619\times mass\ of\ astronaut=42.5$

Mass of astronaut will be 119.7674 kg