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Halfway measures

  1. Nov 23, 2007 #1
    [SOLVED] Halfway measures

    Am I doing this right?

    You stretch the spring of a certain mass-spring system 14.0 cm from its relaxed state; this requires 21.2J of work. You then release the system. What is its Kinetic energy when the stretch of the spring is 7 cm?

    W = F*s
    21.2 = F(.14)
    F = 151.4N

    W = 151.4(.07)
    W = 10.6J
    W = change in KE
    KE = 10.6J
     
  2. jcsd
  3. Nov 23, 2007 #2

    Doc Al

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    Staff: Mentor

    No, you cannot assume that the spring force is constant, which is what you are doing when you set the work equal to F*s. Hint: What's the energy stored in a stretched spring? (Look it up or derive it.)
     
  4. Nov 23, 2007 #3
    Is this close?

    W = 1/2(kx^2)
    21.2 = (1/2)k(.14^2)
    21.2(2) = k(.14^2)
    k = 216.3J

    W = (1/2)(216.3)(.07^2)
    W = .053J
    KE = .053J
     
  5. Nov 23, 2007 #4

    Doc Al

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    Much better. (You are close.)

    You have a typo (or arithmetic error) in that last step: k = 2163 J.

    Realize that this is the total energy stored in the system. After you release it, some of that initial spring potential energy will be transformed to KE. But at all times, Total energy = KE + PE.
     
  6. Nov 24, 2007 #5
    Thanks for replying.
    I do not see the error though. I changed it from cm to meters.

    21.2 = (1/2)k(0.14^2)
    21.2(2) = k(0.196)
    ((21.2)(2))/(0.196) = k am I calculating wrong?

    U1 = (1/2)k(x1^2)
    U2 = (1/2)k(x2^2)
    KE1 = (1/2)mv1^2
    KE2 = (1/2)mv2^2

    KE2 = KE1 + U1 - U2

    Is that the right Idea?
     
  7. Nov 24, 2007 #6

    Doc Al

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    Staff: Mentor

    0.14^2 = 0.0196 (not 0.196)

    Yes, exactly the right idea.
     
  8. Nov 24, 2007 #7
    Thank you so much.
    I wrote the equation down wrong.
     
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