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Conservation of energy problem

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Example: A 50 kg gymnast does giant circles around a horizontal bar. At the top of her swing her center of mass is 1.0 m above the bar travelling 1.2 m/s. what is the speed of her center of mass at the bottom of her swing where her center at mass is 1.0 m below the bar? ( No given diagram)


    2. Relevant equations

    [K + Eg + Es] = [K + Eg + Es + Ef]
    Initial Final

    K=1/2mv^2
    Eg=mgh
    Es= 1/2 kx^2
    Ef = uNd


    3. The attempt at a solution

    [K + Eg] = [K]

    1/2mv^(2) + mgh = 1/2mv^(2)
    1/2(50 kg)(1.2m/s)^(2) + (50kg)(9.8 Nt/kg)(1.0m) = 1/2(50 kg)(v)^(2)
    520 = 25(v)^(2)
    v=4.56 m/s

    is this right? If its not can someone please walk me through what I did wrong. Thank You so much. I'm just getting ready for a test soon.
     
  2. jcsd
  3. Oct 9, 2009 #2
    Hi farmguy

    youre using the right approach but you've left out information and made a calculation error:

    if E0=Ef ....Initial total mechanical energy = final tot mech enrgy

    then....

    remember that if u make final height 0, like u did, u have to make initial height 2m. From reading the problem statement u can conclude that there's 2m difference between her top height and bottom height, right? That has to reflect in your equation as well. Also u made a slight calculation error on the left. Should get 526, not 520.

    Tip: In calculating problems like these the values used for the initial and final heights doesnt matter as long as the difference is correct.
     
    Last edited: Oct 9, 2009
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