Calculating Crossbow Bolt Velocity

In summary, the conversation revolved around finding the speed of an arrow released from a crossbow using given force, distance, and mass values. The initial calculation by the student was incorrect due to not taking into account the decrease in force as the arrow is released. The final answer was determined to be 34.14 m/s, although it was noted that the use of excessive significant figures was not necessary. The student acknowledged this and apologized for any confusion.
  • #1
haxxorboi
24
0
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...

Homework Statement


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)


Homework Equations


PE=KE
Force*Distance=.5*mass*velocity^2


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
 
Physics news on Phys.org
  • #2
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
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
haxxorboi said:
Final answer: 34.141740036184633488266425671601 m/s
No it isn't
Knowing why that is a ridiculous answer is as important as knowing how to get it.
 
  • #5
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
34.141740036184633488266425671601
You know the force and distance to 3 significant figures and the mass to 1, where do the 32 significant figures in the answer come from?

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
haxxorboi said:
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"

I was just copy and pasting the rough answer I got from the calculator. This wasn't the actual answer I used. I really don't remember too much of Sig. Digits as the only time I used them was about 3 years ago in high school chemistry but either way my professor doesn't use them.

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
haxxorboi said:
In the future I'll attempt to answer in a more realistic format. Sorry about that.
No problem - it wasn't anything personal I was just trying to make a point!
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.
 

1. What is crossbow bolt velocity?

Crossbow bolt velocity refers to the speed at which a bolt, or arrow, is launched from a crossbow. It is typically measured in feet per second (fps) and can vary depending on factors such as the weight of the bolt, the draw weight of the crossbow, and the distance the bolt is being shot.

2. Why is crossbow bolt velocity important?

The velocity of a crossbow bolt is important because it affects the accuracy and distance of the shot. A higher velocity usually results in a flatter trajectory and longer range, making it easier to hit the target. It also impacts the penetration power of the bolt, which is important for hunting game.

3. How is crossbow bolt velocity measured?

Crossbow bolt velocity is typically measured using a chronograph, which is a device that uses sensors to measure the speed of an object passing through it. The crossbow is fired directly over the chronograph, and the speed is recorded in feet per second.

4. What factors affect crossbow bolt velocity?

The main factors that affect crossbow bolt velocity include the weight of the bolt, the draw weight of the crossbow, and the type of crossbow used. Other factors that can impact velocity include the type of bowstring, the condition of the crossbow, and the weather conditions.

5. Can crossbow bolt velocity be increased?

Yes, crossbow bolt velocity can be increased by using a higher draw weight crossbow, a lighter bolt, or by using a more powerful bowstring. However, it is important to follow the manufacturer's guidelines and not exceed the recommended draw weight as it can damage the crossbow and be unsafe for the user.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
2K
Replies
52
Views
10K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
13K
  • Introductory Physics Homework Help
Replies
3
Views
2K
Back
Top