Work problem: force vs distance curve for compound bow

In summary, the archer uses a compound bow to hold the string at full draw with considerably less force than the maximum force exerted by the string. The draw force as a function of the string position x for a particular compound bow is shown in Figure 1.
  • #1
Angela_vaal
59
1

Homework Statement


A compound bow in archery allows the user to hold the bowstring at full draw with considerably less force than the maximum force exerted by the string. The draw force as a function of the string position x for a particular compound bow is shown in (Figure 1) .

Part A
How much work does the archer do on the bow in order to draw the string from x=0 to x=0.60m?
Express your answer to three significant figures and include appropriate units.

fig_7-26.png


Homework Equations


area= work

total work=sum of all areas

The Attempt at a Solution



(.2m x 350 N)/2 + (.3m x 350 N) + (.1m x 250 N)/2 = 152.5J

153J for three sig figs.[/B]

Apparently the answer is wrong, but I do not know what I did wrong? I found the area of the two triangles, and the rectangle in the three equations above.
 
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  • #2
But the area is NOT "two triangles and a rectangle". Do you see why I say that?
 
  • #3
phinds said:
But the area is NOT "two triangles and a rectangle". Do you see why I say that?
No I do not. Is it because from .5m to .6m it is not a complete triangle?
 
  • #4
Your thread title is too general. I've modified it to better identify the type of problem.

You've missed a bit of the area under the curve. Take a closer look at the region of the smaller triangle: what's it "sitting" on?edit: Ah. Phinds got in there before me!
 
  • #5
gneill said:
Your thread title is too general. I've modified it to better identify the type of problem.

You've missed a bit of the area under the curve. Take a closer look at the region of the smaller triangle: what's it "sitting" on?edit: Ah. Phinds got in there before me!

the smaller triangle is sitting on a small rectangle between .5m to .6m?
 
  • #6
Angela_vaal said:
the smaller triangle is sitting on a small rectangle between .5m to .6m?
Right.
 
  • #7
Angela_vaal said:
the smaller triangle is sitting on a small rectangle between .5m to .6m?

That was tricky, but I got it now. Thanks!
 

What is a force vs distance curve for a compound bow?

A force vs distance curve for a compound bow is a graphical representation of the relationship between the amount of force exerted on the bow and the distance the bowstring is pulled back. This curve shows the amount of force required to draw the bowstring back at different distances, and can be used to determine the strength and efficiency of the bow.

How does the force vs distance curve differ between different compound bows?

The force vs distance curve can vary between different compound bows due to differences in design, materials, and manufacture. Some bows may have a steeper or flatter curve, indicating a higher or lower amount of force required at different draw distances. The shape of the curve can also be affected by the type and weight of arrows used with the bow.

What factors can affect the shape of the force vs distance curve for a compound bow?

The shape of the force vs distance curve can be influenced by several factors, including the draw weight of the bow, the cam design, the length of the bow, the type and weight of arrows used, and the draw length of the archer. These factors can all impact the amount of force required to draw the bowstring back at different distances.

What can the force vs distance curve tell us about a compound bow?

The force vs distance curve can provide valuable information about the performance and efficiency of a compound bow. It can indicate the maximum amount of force that the bow is capable of producing, as well as the amount of force needed to draw the bowstring back to different distances. This can help archers choose a bow that is best suited for their strength and shooting style.

How can the force vs distance curve be used to improve bow performance?

The force vs distance curve can be used to optimize the performance of a compound bow by adjusting the draw weight and draw length to achieve the desired curve shape. By finding the ideal balance between force and distance, archers can increase the power and accuracy of their shots. Additionally, monitoring the force vs distance curve over time can help identify any changes or issues with the bow's performance.

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