Answer to Question #280508 in Physics for Faith

Question

Rick wants to know Morty's mass in space. He conducted an experiment by attaching an empty chair to a spring and set it to oscillate, and measured the time after one cycle. Afterwards, he asked Morty to sit on this chair not letting his feet touch the ground, then measured the time after one vibration. Calculate Morty's mass by referring to the data gathered by Rick below:

Empty chair

Time after one cycle: 0.65

Mass: 16.97

Morty sitting on the chair

Time after one cycle: 1.93

Mass: ?

Answer 1

Let's first find the spring constant:

$$T=2\pi\sqrt{\dfrac{m_{ch}}{k}},$$ $$k=\dfrac{4\pi^2m_{ch}}{T^2}=\dfrac{4\pi^2\times16.97\ kg}{(0.65\ s)^2}=1586\ \dfrac{N}{m}.$$

Then, we can find total mass of Morty and chair:

$$M_{tot}=\dfrac{T^2k}{4\pi^2}=\dfrac{(1.93\ s)^2\times1586\ \dfrac{N}{m}}{4\pi^2}=150\ kg.$$

Finally, we can find the Morty's mass:

$$M_{Morty}=M_{tot}-m_{ch}=150\ kg-16.97\ kg=133\ kg.$$