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Pendulum Harmonic Motion Help Needed Asap ( work is shown)

  1. May 8, 2006 #1
    A bungee jumper with mass 66.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 35.5 s. He finally comes to rest 28.0 m below the level of the bridge.

    Calculate the spring stiffness constant of the bungee cord.
    N/m


    For this part i figured i could solve for period (T) which would be the 35.5 sec /8 whihc is 4.4375 s
    and then i used T=2pi* (m/k)^1/2

    and with that i thought i could solve for K

    that comes out to be ....k=(4pi^2*mass) / T^2

    so k=132.3 N/m



    Calculate the unstretched length of the bungee cord

    I could either use T= 2*PI*(L/G)^1/2


    L=(4.4375 s^2 * 9.8)/4*pi^2-4.88 m ....but thats wrong

    OR I COULD USE ---f= 1/2*pi *(g/l)^1/2 ...

    L=(2.46*g)/f^2=477.69 m


    and just solve for L ...rite?

    but when i plug everything in i keep getting it wrong
     
  2. jcsd
  3. May 8, 2006 #2

    Chi Meson

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    Homework Helper

    No no no no.

    The first part (finding k) was correct. Exactly right. But then you start using other formula to find L simply becuase they have an L in them.

    Here's a hint. You have just found the "k," and you are given a distance and a mass (from which you can find a force). What kind of relationship is there for stretchy things that relates force, distance and a "k" ?
     
  4. May 8, 2006 #3
    ok i know that Force = - kx
    could x=length of the bungee cord....

    and which would lead me to believe that M*g=force also equals -Kx

    so...should i be using 66kg (9.8)=-132.3(x) and solve for x?
     
  5. May 8, 2006 #4

    Doc Al

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    Yes, you should solve for x, but realize that x is not the unstretched length of the cord.

    The x in Hooke's law (F = -kx) refers to the amount by which the spring (or cord) is stretched from its unstretched position.
     
  6. May 8, 2006 #5
    so how do i figure out the unstretched length...now im confused
     
  7. May 8, 2006 #6

    Doc Al

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    Staff: Mentor

    Make full use of the information provided in the problem statement, namely:
    "He finally comes to rest 28.0 m below the level of the bridge."​
     
  8. May 8, 2006 #7
    ok i think i got it...so ....66*9.8=-(132.3)x
    X in this case is -4.8 ms.. so if i add that to the 28 meters the unstretched cord should be in length equal to 23.1 meters ...that should be rite
     
  9. May 8, 2006 #8

    Chi Meson

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    Science Advisor
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    That's what I get.
     
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