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Energy and basic math (proportionality)

  1. Apr 26, 2014 #1
    1. The problem statement, all variables and given/known data

    A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same
    amount of work, her speed will be changed by a factor of
    a. 0.25
    b. 0.50
    c. 0.71
    d. 1
    e. 2

    2. Relevant equations

    E=1/2mv2

    3. The attempt at a solution

    Since m is doubled, v2 should be halved. I'm stuck now. But the correct answer is 0.71. Can someone explain how?
     
  2. jcsd
  3. Apr 26, 2014 #2
    You're correct that ##v^2## should be halved (multiplied by a factor of 1/2). So what does that say about the factor by which ##v## should be decreased?
     
  4. Apr 27, 2014 #3
    Well, 1/2 squared is 0.25, and 12 halved is 0.5. How do I get to 0.71?
     
  5. Apr 27, 2014 #4
    You know that her initial kinetic energy is ##\frac{1}{2}mv_{0}^2##, the final kinetic energy is ##\frac{1}{2}(2m)v_{1}^2##.

    You need to find what the relationship between v1 and v0 is. Ask yourself, how can you do so given the above equations?
     
  6. Apr 30, 2014 #5
    v12 = ((1/2)v0)2

    If I let v0 = 1, then v1 = sqrt(1/2), which equals 0.71 :)
     
    Last edited: Apr 30, 2014
  7. Apr 30, 2014 #6
    That's not true. Check your math. As you state above, you've simplified the equation to the following:

    ##v_{1}^2=\frac{1}{2}v_{0}^2##

    So just take the square root of both sides. What does that get you?
     
  8. Apr 30, 2014 #7
    Changed my previous post. Thanks!
     
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