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Homework Help: Energy problem on bungee jumper

  1. Oct 16, 2004 #1
    I'm having trouble solving this problem. can n e one help me?

    A bungee jumper of mass 64.5 kg (including safety gear) is
    standing on a platform 48.0 m above a river. The length of
    the unstretched bungee cord is 10.1 m. The force constant
    of the cord is 65.5 N/m. The jumper falls from rest and just
    touches the water at a speed of zero. The cord acts like an
    ideal spring. Use conservation of energy to determine the
    jumper’s speed at a height of 12.5 m above the water on
    the first fall.

    I used the work equation to find the total energy, then subtracted the elastic potential energy and gravitational potential energy at 12.5m above ground. Then i solved for Ek, and used THAT equation to solve for speed.
    i got 9.29m/s, but the answer is 6.37m/s.

    What did i do wrong?
     
  2. jcsd
  3. Oct 16, 2004 #2
    What were the numbers that you put into the term for elastic potential energy?
     
  4. Oct 16, 2004 #3
    elastic potential energy is E = 0.5 kx^2, right?

    I put: k = 65.5, x = 35.5 FIRST, but then i ended up getting a negative answer, so i used x = 12.5.

    But is what i tried to do correct, did i miss anything? I'm starting to think that i calculated the total energy wrong. What did you get for total energy?
     
  5. Oct 16, 2004 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Correct.
    Both x = 35.5 m and x = 12.5 m are wrong. How much is the cord stretched (beyond its unstretched length) when the jumper is 12.5 m above the water?
     
  6. Nov 1, 2004 #5
    you should find the "delta X", by this equation: mgh=.5kx^2, I got 30.45 m for delta X,
    then you should put this value in the equation: mgh=.5kx^2+mgh`+.5mv^2 and find the velocity..the initial X, 10.1, is extra in the given problem.
     
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