Forces/Newton's Laws of Motion

  • Thread starter Amber430
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  • #1
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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.
 

Answers and Replies

  • #2
Doc Al
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I know that when force doubles, acceleration doubles.
Good. What quantity remains the same? When they said "all else remaining the same", what could they have been talking about?
 
  • #3
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The initial velocity remains the same. But the only other variable that is given is final velocity, which would not stay the same.
 
  • #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?
 
  • #5
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V^2=Vo^2 + 2ax. But what is x? It isn't known.
 
  • #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.
 
  • #7
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But what is the acceleration?
 
  • #8
Doc Al
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But what is the acceleration?
Again, you don't need actual numbers. Call the original acceleration "a". What would be the new acceleration?
 
  • #9
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It would be 2a
 
  • #10
Doc Al
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It would be 2a
Good. Now solve for the speeds in terms of "a" and "x" and compare. (You can also use ratios.)
 

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