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Kinetic Energy problem

  1. Nov 11, 2011 #1
    Jogger A has a mass m and a speed v, jogger B has a mass m/2 and a speed 3v, jogger C has a mass 3m and a speed v/2 and jogger D has a mass 4m and a speed v/2. Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate

    I started with KE formula, KE=1/2mv^2 and plugged in values for each jogger
    Jogger A KE=1/2mv^2
    Jogger B KE=1/2(m/2)(3v)^2 which = 2.25mv^2
    Jogger C KE=1/2(3m)(v/2)^2 which =6mv^2
    Jogger D KE=1/2(4m)(v/2)^2 which =8mv^2

    Based on this I ranked them in increasing order A,B,C,D
    The answer given is, D<A = D<B
    I'm not sure I understand the answer, and I don't see where I went wrong.
    Thank you for any help.
     
  2. jcsd
  3. Nov 11, 2011 #2

    gneill

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    Staff: Mentor



    Check your math for joggers C and D.
     
  4. Nov 11, 2011 #3

    Doc Al

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    Good.
    Redo these.
     
  5. Nov 11, 2011 #4
    Jogger C KE=1/2(3m(v/2)^2 = 3/2m(v^2)/4 = 3/8mv^2
    Jogger D KE= 1/2(4m)(v/2)^2 = 1/2mv^2
    Which means D=A and both > C > B
    Which still isn't the given answer
     
  6. Nov 11, 2011 #5

    gneill

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    List all four results now that you've recalculated.
     
  7. Nov 11, 2011 #6

    Doc Al

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    Right.
    OK.
    Rethink that.
     
  8. Nov 11, 2011 #7
    Jogger A KE= 1/2mv^2
    Jogger B KE= 2.25mv^2
    Jogger C KE= 3/8mv^2
    Jogger D KE=1/2mv^2

    Oh C< D=A < B Still not the answer
    Thanks again for all this help
     
  9. Nov 11, 2011 #8

    Doc Al

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    Obviously a typo here. Better check it. (that first D should be a C)
     
  10. Nov 11, 2011 #9
    I really don't understand the format of the given answer, could one of you translate, why don't they give value of C in the answer?
     
  11. Nov 11, 2011 #10
    ahhhhh, Typo is in book. Thanks for the help
     
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