How Do Astronauts Measure Mass and Speed Using a Spring in Space?

[bobbarkernar]

Homework Statement

Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure .

What is her mass if the spring constant is 240 ?

What is her speed when the spring's length is 1.2 ?

Homework Equations

image is http://session.masteringphysics.com/problemAsset/1001073/9/knight_Figure_14_36.jpg

The Attempt at a Solution

i got that the answer to the first question is 54.7kg

i just don't know how to find her velocity at that length
if someone can please help me

 

[Gokul43201]

Treating the astronaut on the spring as a simple harmonic oscillator, and using the plot, can you write down the equation that represents the position (x) of the astroanut as a function of time (t) ?

 

[Cyrus]

I would look at the natural frequency of the vibrations. This gives you the 'signature' of the system.

 

[bobbarkernar]

goku do u mean x(t)=Acos(wt+phase constant)?

 

[Gokul43201]

Yes, what are the values of A and w (look at the plot)? From x(t), can you find dx/dt?

If you haven't had calculus as yet, think about energy conservation. You can find the total energy (E) using the spring constant (k) and the maximum stretch (amplitude, A). Then at x=1.2m you can plug in the value of the PE and use the value of E to find the KE at this point.