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Finding Spring Constant

  1. Dec 19, 2009 #1
    1. The problem statement, all variables and given/known data

    The left side of the figure shows a light (`massless') spring of length 0.330 m in its relaxed position. It is compressed to 71.0 percent of its relaxed length, and a mass M= 0.210 kg is placed on top and released from rest (shown on the right).

    The mass then travels vertically and it takes 1.50 s for the mass to reach the top of its trajectory. Calculate the spring constant, in N/m. (Use g=9.81 m/s2). Assume that the time required for the spring to reach its full extension is negligible.

    2. Relevant equations

    3. The attempt at a solution
    I'm not too sure about how I consider the time it takes for the mass to go back up.
    I know that the energy while the mass is on the spring is mg (downwards) and -kx upwards.

    Then when the ball goes back up - its KE + mgh is equal to mg-kx?

  2. jcsd
  3. Dec 19, 2009 #2
    Calculate the maximum height of the object above the compressed spring, then you'll have a value of gravitational potential energy that is equal to the potential energy initially stored in the compressed spring.

    Then you simply solve for k.
  4. Dec 19, 2009 #3
    if so then why do i need the t=1.5 sec? it doesn't make any sense...

    is this what you suggest:
    mgh = 0.21*0.71*0.33*9.81= -k(0.29*0.33)
  5. Dec 19, 2009 #4
    The mass flies free of the spring and reaches an unknown height. use t to determine that height and the relation

    mgh = 1/2 K*x^2

    where x is the displacement of the spring which we are not given directly, but can be figured fout rom the data given.
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