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Astronauts and Spring question

  1. Dec 5, 2006 #1
    1. The problem statement, all variables and given/known data


    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 ?

    2. Relevant equations

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

    3. The attempt at a solution
    i got that the answer to the first question is 54.7kg

    i just dont know how to find her velocity at that length
    if someone can please help me
     
  2. jcsd
  3. Dec 5, 2006 #2

    Gokul43201

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    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) ?
     
  4. Dec 5, 2006 #3
    I would look at the natural frequency of the vibrations. This gives you the 'signature' of the system.
     
  5. Dec 5, 2006 #4
    goku do u mean x(t)=Acos(wt+phase constant)?
     
  6. Dec 8, 2006 #5

    Gokul43201

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    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.
     
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