1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bungee Jumping Question

  1. Apr 8, 2014 #1
    1. The problem statement, all variables and given/known data

    A bungee jumper of mass m drops off a bridge and falls vertically downwards.
    The bungee cord is elastic with natural length L and stiffness k. Deduce that
    at the lowest point of the fall, the cord is stretched by an amount [tex] x = \frac {mg}{k} \Big( 1 + \sqrt {1+ \frac {2kL}{mg}} \Big) [/tex]



    2. Relevant equations

    [itex] mgh = \frac{1}{2} k x^2 [/itex]



    3. The attempt at a solution

    Energy considerations dictate that the gravitational potential energy of the jumper in the initial state is equal to the elastic potential of the cord in the final state

    [itex] mg ( L + x ) = \frac{1}{2} k x^2 [/itex]

    [itex] mgL + mgx = \frac{1}{2} k x^2 [/itex]

    [itex] 2mgL + 2mgx = k x^2 [/itex]

    [itex] x^2 - \Big( \frac{2mg}{k} \Big )x - \Big( \frac{2mgL}{k} \Big) = 0 [/itex]

    [itex] x = \frac{- \Big(- \frac{2mg}{k} \Big) + \sqrt{ \Big( - \frac{2mg}{k} \Big)^2 - 4 \Big( - \frac{2mgL}{k} \Big )}}{2} [/itex]

    [itex] x = \frac{1}{2} \Big( \frac{2mg}{k} + \sqrt{ \frac{4m^2g^2}{k^2} + \frac{8mgL}{k}} \Big) [/itex]

    [itex] x = \frac{mg}{k} + \frac{1}{2} \Big ( \sqrt{ \frac{4m^2g^2}{k^2} \Big ( 1 + \frac{2kL}{mg} \Big )} \Big ) [/itex]

    [itex] x = \frac{mg}{k} + \frac{1}{2} \Big( \sqrt{\frac{4m^2g^2}{k^2}} \sqrt{1+\frac{2kL}{mg}} \Big ) [/itex]

    [itex] x = \frac{mg}{k} + \frac{1}{2} \Big( \frac{2mg}{k} \Big) \sqrt{1 + \frac{2kL}{mg}} [/itex]

    [itex] x = \frac{mg}{k} + \frac{mg}{k} \sqrt{1 + \frac{2kL}{mg}} [/itex]

    [itex] x = \frac{mg}{k} \Big( 1 + \sqrt{1+ \frac{2kL}{mg}} \Big) [/itex]

    Is this the correct method? There is no solution online to this problem.
     
  2. jcsd
  3. Apr 8, 2014 #2

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Seems reasonable to me.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Bungee Jumping Question
Loading...