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Forces/Newton's Laws of Motion

  1. Jan 29, 2009 #1
    This problem really shouldn't be this difficult but for some reason I can't seem to find the answer.

    An arrow, starting from rest, leaves the bow with a speed of 26.0 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?

    net force= mass x acceleration

    Acceleration is unknown in this question. Velocity (I'm assuming it's the final V?) is known (26.0 m/s). Initial velocity is 0. I know that when force doubles, acceleration doubles. That's about as far as I could get.
     
  2. jcsd
  3. Jan 29, 2009 #2

    Doc Al

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    Good. What quantity remains the same? When they said "all else remaining the same", what could they have been talking about?
     
  4. Jan 29, 2009 #3
    The initial velocity remains the same. But the only other variable that is given is final velocity, which would not stay the same.
     
  5. Jan 29, 2009 #4

    Doc Al

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    Hint: The distance the arrow takes to reach the final speed is the same.

    How do distance, acceleration, and speed relate?
     
  6. Jan 29, 2009 #5
    V^2=Vo^2 + 2ax. But what is x? It isn't known.
     
  7. Jan 29, 2009 #6

    Doc Al

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    All you want to do is compare the final speeds. You don't need to know the actual distance. Just call it x.
     
  8. Jan 29, 2009 #7
    But what is the acceleration?
     
  9. Jan 29, 2009 #8

    Doc Al

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    Again, you don't need actual numbers. Call the original acceleration "a". What would be the new acceleration?
     
  10. Jan 29, 2009 #9
    It would be 2a
     
  11. Jan 29, 2009 #10

    Doc Al

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    Good. Now solve for the speeds in terms of "a" and "x" and compare. (You can also use ratios.)
     
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