Finding Work done under a graph?

[juju1]

Homework Statement

[/B]
A force acts on an object along an x axis. The force varies with position as shown in the graph below. On the graph, F = 52.0 N. Find the work done by the force as it moves the object from x = 0 to x = 15.0 m.

Homework Equations

[/B]

The Attempt at a Solution

So what I tried to do was separate the graph into triangles and squares..and then use it's area (i.e. for triangle i did (1/2 x b x h)

I tried this and it didn't work. So then i tried separating them into trapezoids...still didn't work. What am I doing wrong?

The answers i got were 936 and 1044[/B]

 

[Charles Link]

If you do a quick count of the squares, what do you get? i.e. How many positive squares and how many negative ones? Meanwhile, how much work does a single square represent?

 

[magoo]

Why don't you show how you got 936 and 1044. Then we can see if there's a math error or have another suggestion.

 

[juju1]

ROUGHLY 26 positive and 9 negative

 

[Charles Link]

ROUGHLY 26 positive and 9 negative

Now answer my second question=see my post above=I edited it...

 

[juju1]

Why don't you show how you got 936 and 1044. Then we can see if there's a math error or have another suggestion.

Okay so i separated the 'postive' into 2 triangles and one square. One triangle had a base of 3 height of 4 and the another triangle had a base of 2 height of 4. To calculate the work for each triangle, I used a triangle's area formula. And for the square the base was 4 and height was 4. I used bxh formula.

Did the same for 'negative.' just separated everything

 

[juju1]

Now answer my second question=see my post above=I edited it...

One square does 52 J?

 

[Charles Link]

One square does 52 J?

$F=52$, but that is 2 units high. 52 is incorrect.

 

[PhanthomJay]

Homework Statement

[/B]
A force acts on an object along an x axis. The force varies with position as shown in the graph below. On the graph, F = 52.0 N. Find the work done by the force as it moves the object from x = 0 to x = 15.0 m.

Homework Equations

[/B]

The Attempt at a Solution

So what I tried to do was separate the graph into triangles and squares..and then use it's area (i.e. for triangle i did (1/2 x b x h)

I tried this and it didn't work. So then i tried separating them into trapezoids...still didn't work. What am I doing wrong?

The answers i got were 936 and 1044[/B]

Hard to say what you did wrong unless you show your workings. You might have goofed on finding areas, or forgot to note that part of the area is negative, or both.

 

[juju1]

AH so 26 J.

 

[Charles Link]

ROUGHLY 26 positive and 9 negative

How does that compare with your more precise arithmetic with the triangles? I get 26 and 8, so your rough count was quite close.

 

[juju1]

I don't quite get the question you're asking...but I re-did it again, now knowing that it's 26J per square and got 468..

 

[Charles Link]

I don't quite get the question you're asking...but I re-did it again, now knowing that it's 26J per square and got 468..

Very good. What I was asking is, your rough estimate (post 4) was 26 and 9, but what was your exact count with the triangle method? You got the correct answer now, so I presume your exact counts were an area of +26 and the other area was -8.

 

[juju1]

Ahhhh, I get it. Yes, my exact count was positive 26 and negative 8! Thank you, Charles!