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Work problem: force vs distance curve for compound bow

  1. Nov 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A compound bow in archery allows the user to hold the bowstring at full draw with considerably less force than the maximum force exerted by the string. The draw force as a function of the string position x for a particular compound bow is shown in (Figure 1) .

    Part A
    How much work does the archer do on the bow in order to draw the string from x=0 to x=0.60m?
    Express your answer to three significant figures and include appropriate units.

    fig_7-26.png

    2. Relevant equations
    area= work

    total work=sum of all areas

    3. The attempt at a solution

    (.2m x 350 N)/2 + (.3m x 350 N) + (.1m x 250 N)/2 = 152.5J

    153J for three sig figs.


    Apparently the answer is wrong, but I do not know what I did wrong? I found the area of the two triangles, and the rectangle in the three equations above.
     
  2. jcsd
  3. Nov 9, 2016 #2

    phinds

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    Gold Member
    2016 Award

    But the area is NOT "two triangles and a rectangle". Do you see why I say that?
     
  4. Nov 9, 2016 #3
    No I do not. Is it because from .5m to .6m it is not a complete triangle?
     
  5. Nov 9, 2016 #4

    gneill

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    Staff: Mentor

    Your thread title is too general. I've modified it to better identify the type of problem.

    You've missed a bit of the area under the curve. Take a closer look at the region of the smaller triangle: what's it "sitting" on?


    edit: Ah. Phinds got in there before me!
     
  6. Nov 9, 2016 #5
    the smaller triangle is sitting on a small rectangle between .5m to .6m?
     
  7. Nov 9, 2016 #6

    gneill

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    Staff: Mentor

    Right.
     
  8. Nov 9, 2016 #7
    That was tricky, but I got it now. Thanks!!
     
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