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Energy stored in a bow and arrow

  1. Dec 19, 2008 #1
    The following was a question from a Work/Energy high school test.
    "3. An archer is shooting at a hay bale target. The archer pulls back on his bow string with 500 N of force to draw it back a distance of 80 cm. He releases the string, and the arrow (m= 1 Kg) flies straight to its target (neglect air resistance).
    a) How fast is the arrow traveling when it leaves the bow?"
    Some students used the work-energy theorem (W=delta KE in this case) and got an answer of 28.3 m/s. However, many students used the info given to determine a spring constant (k) for the bow (k = F/x), and then applied Conservation of Energy (Elastic PE = KE in this case) to the system. This yields an answer of 20 m/s for the arrow.
    My question is "Why doesn't the spring constant method work?"
     
  2. jcsd
  3. Dec 19, 2008 #2

    Doc Al

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    Staff: Mentor

    They messed up.
    That's fine.
    Both methods, done correctly, yield the same answer. Note that the spring force varies from 500 N at first to zero at the release. You can't just use W=Fx = 500*0.8.
     
  4. Dec 19, 2008 #3
    THANKS!!!
    I feel a little stupid now.
     
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