The force function is using Cartesian coordinates.

Find the work done from (1,1) to (4,4) using the following path:

So, what I did was:

Is this right?

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- September 18th 2008, 07:18 PMArythWork: Vector Integration
The force function is using Cartesian coordinates.

Find the work done from (1,1) to (4,4) using the following path:

So, what I did was:

Is this right? - September 18th 2008, 07:34 PMicemanfan
It seems to me that if you are heading in the x-direction the work done will only depend on the x component of the force, and if you are heading in the y direction the work done will only depend on the y-component of the force, so you can add where f(y) is the y-component of force and f(x) is the x-component of force. Your answer looks right to me.

- September 18th 2008, 07:54 PMJhevon
i agree. your answer is correct. i've never seen that method before, though. it seems to make sense

- September 18th 2008, 08:07 PMAryth
I've never seen this method either... But it's the way me and my friends interpreted it given this example:

The force exerted on a body is . The problem is to calculate the work done going from the origin to the point (1,1):

Separating the integrals, we obtain:

The first integral cannot be evaluated until we specify the values of x as y ranges from 0 to 1. Likewise, the second integral requires x as a function of y. Consider the first path:

Then:

since y = 0 along the first segment of the path and x = 1 along the second. If we select the path:

then the integral gives . For this force the work done depends on the choice of path.

That's pretty much all we had to go by. No professor, no class, just us and a book...

We did have this relation:

Using that, the separation of the integrals follows.