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Crossbow bolt velocity 
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#1
Sep1708, 12:56 PM

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I should preface this, this may be the stupidest question yet on this forum. But I can't get it to work out right so I'm going wrong somewhere obvious I'm sure...
1. The problem statement, all variables and given/known data A crossbow is readied for release. Suppose it takes 45.0 pounds of force to draw the arrow back by 13.0 inches, and the weight of the arrow is 2 ounces. What is the speed of the arrow when it is released? (1 lb = 4.448 N; 1 in = 2.54 cm; 1 oz = 28.35 grams) 2. Relevant equations PE=KE Force*Distance=.5*mass*velocity^2 3. The attempt at a solution 45lb=200.16N 13in=.3302M 2oz=.0567kg 66.092832NM=66.09832J 66.09832J=.5*.0567*v^2 66.09832J=.02835*v^2 2331.5104=v^2 v=48.2857 Any help is appreciated. Thanks 


#2
Sep1708, 01:11 PM

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The force is only 45lbs at the end of the pull but it is zero at the point where the arrow leaves the string.
If you draw a force/distance diagram it's easy to see that you only get half the energy you calcualted. 


#3
Sep1708, 01:15 PM

P: 24

Ah geez, me and my linear thinking. Yep, that was it.
Final answer: 34.141740036184633488266425671601 m/s Thanks for the help mgb_phys! I appreciate it. 


#4
Sep1708, 02:32 PM

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Crossbow bolt velocity
Knowing why that is a ridiculous answer is as important as knowing how to get it. 


#5
Sep1708, 02:43 PM

P: 24

I guess I don't understand what you mean. The homework system I'm using gives feedback after you complete a problem and tells you whether you're correct or not. The answer I posted here was MScalc's output that I just copy & pasted. I inputted 34.142 m/s and it returned "You are correct. The computer's answer is 34.14 m/s"
What am I missing here? I understand there will never be 100% conservation of energy to give to the bolt, however this is a pretty basic physics course and most of the questions don't deal with any outside energy losses. 


#6
Sep1708, 03:04 PM

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As an example, the size of an atom is about 0.0000000001m, you are quoting distance to an accuracy of 0.0000000000001 of a proton! This isn't just being picky  it is completely unphysical to quote an answer like that. 


#7
Sep1708, 03:09 PM

P: 24

Was my extremely lengthy answer "correct", no. But was it, in it's rounded form that is, the answer I needed, yes. In the future I'll attempt to answer in a more realistic format. Sorry about that. 


#8
Sep1708, 03:51 PM

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It's like getting the units right, there is an attitude of "thats what the calcualtor said  it must be right" that you have to get beyond. 


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