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Bungy jump problem

  1. May 22, 2010 #1
    You go bungee jumping from a bridge that is 65m high, the bungee cord has an unstretched length of 32m and a spring constant of k=107 N/m
    You have a mass of 75kg.

    Question: what is the acceleration at the bottom, closest to the ground?

    I`ve tried to use 1/2kA2=1/2mx+1/2kx2
    but it doesn´t seem to work for me :(

    please help, I´m not asking for U to solve it but at least give me a couple of hints!!
     
  2. jcsd
  3. May 22, 2010 #2

    Doc Al

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    Staff: Mentor

    Start by figuring out where the lowest point is. Use conservation of energy.
     
  4. May 22, 2010 #3
    should I use mgh=1/2kx2?

    x as how far it stretches from 32m?

    and then should I use F=-kx => F=ma and solve out a?
     
  5. May 22, 2010 #4

    Doc Al

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    Yes. Hint: Express h in terms of x. (Measure gravitational PE from the lowest point.)
     
  6. May 22, 2010 #5
    you mean mg(x+32)=1/2kx2?

    should I then continue with F=-kx => F=ma solve out a?
     
  7. May 22, 2010 #6

    Doc Al

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    Exactly.
    Be sure to include all forces when applying F=ma.
     
  8. May 22, 2010 #7
    mg(x+32)=1/2kx2 gives two answers but I can throw away the negative one, right?

    then I used F=-kx+mg => a= (-kx+mg)/m
    is that right?
     
    Last edited: May 22, 2010
  9. May 22, 2010 #8

    Doc Al

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    Right.

    Yes, that's fine.

    Don't get hung up with signs. You have an upward force of magnitude kx and downward force of magnitude mg. Which direction will the acceleration be in at the lowest point?
     
  10. May 22, 2010 #9
    the direction will be "up",negative
    right?
     
  11. May 22, 2010 #10

    Doc Al

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    Yes, the acceleration will be up. Which you happen to call negative. I suspect that they only care about the magnitude of that acceleration.
     
  12. May 22, 2010 #11
    thank you for the help!:smile:
     
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