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Energy Conversion Problem

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data

    A very short 100 kg acrobat steps off a 10 m high platform and
    starts falling. The acrobat falls 9 m, then encounters a 1 m long
    spring connected at one end to the ground below. (a) What’s the
    spring constant so the acrobat just touches the ground (that is, so the
    spring contracts 1 meter)? The spring-with-acrobat system rebounds
    and launches the acrobat back into the air. (b) How high off the
    ground does the acrobat go above the ground before falling back?


    2. Relevant equations

    (1/2)k(x-x0)^2
    mgΔh

    3. The attempt at a solution

    To solve this, wouldn't one set the gravitational potential energy (mgh) to the spring potential energy (1/2kx^2) because the energy converts to one another, then solve for k? 1.96 * 10^4 N/m is the answer I got.

    For the second part of the problem, the acrobat will be the same exact height above the ground because the energy is conserved, right?

    Am I missing something in this problem? This was unexpectedly simple.
     
  2. jcsd
  3. Oct 15, 2013 #2

    CompuChip

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    Science Advisor
    Homework Helper

    You are on the right track, but be careful: you wrote Δh in the second formula, not h. What is the difference in this case?

    Part two seems to be that simple, unless I'm also missing something :)
    Let's hope for the acrobat that there is some loss due to friction (or the spring won't fully extend after having been crushed to length 0) otherwise it may be a long evening for him!
     
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