# Work problem: force vs distance curve for compound bow

#### Angela_vaal

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?

2. Homework Equations
area= work

total work=sum of all areas

3. 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.

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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#### phinds

Gold Member
But the area is NOT "two triangles and a rectangle". Do you see why I say that?

#### Angela_vaal

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?

#### gneill

Mentor
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!

#### Angela_vaal

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?

#### gneill

Mentor
the smaller triangle is sitting on a small rectangle between .5m to .6m?
Right.

#### Angela_vaal

the smaller triangle is sitting on a small rectangle between .5m to .6m?
That was tricky, but I got it now. Thanks!!

"Work problem: force vs distance curve for compound bow"

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