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Reading Variable Force Graph

  1. Nov 4, 2006 #1
    Behold Halliday's Question and Halliday's answers:

    The only force acting on a 2.0 kg body as it moves along the x axis varies as shown in Figure 7-41 (see attatchment). The velocity of the body at x = 0 is 4.0 m/s.

    (a) What is the kinetic energy of the body at x = 3.0 m?
    12 J
    (b) At what value of x will the body have a kinetic energy of 8.0 J?
    4.0 m
    (c) What is the maximum kinetic energy attained by the body between x = 0 and x = 5.0 m?
    18 J

    I am stumped. I've only tried to figure out (a) and (b), but my method does not give me correct answers. My train of thought was that Delta KE=W=area under curve. So for part (a), I said that area under graph is (triangle-triangle-rectangle) = -4 Nm. Well, gee.
    Maybe since KE is always positive, take the absolute value of various areas! I think that is very poor reasoning, because Delta KE and W can both be negative. And even when I do that, I get 8 Nm, which is still wrong.
    Similar reasoning applied to (b) also gives the incorrect answer, which is comforting.

    A hint from the wise gurus perhaps?
     

    Attached Files:

  2. jcsd
  3. Nov 5, 2006 #2

    ehild

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    Homework Helper
    Gold Member

    Correct.

    The change of KE is equal to the work done on the body. If the work is negative, the kinetic energy will decrease. Final KE - initial KE = W. You know the initial KE, (16 J) you know W,(-4 J) what is the problem?

    ehild
     
  4. Nov 5, 2006 #3
    Problem is that I thought initial Kinetic Energy was 4J. Wups!
    Thank you.
     
  5. Nov 11, 2007 #4
    I'm doing the same problem. Does anyone know the answers?
    I got 12J for (a) but I'm lost on (b) and (c)
     
  6. Nov 11, 2007 #5
    Edit: this is what I got after some thought...

    (a) 12 J
    (b) x=4
    (c) 28 J

    anyone agree?
     
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