# WOrk done by a variable force (in two dimension)

1. Oct 10, 2012

### daivinhtran

1. The problem statement, all variables and given/known data

How to find the work done by a variable force in (two dimension)

When
F = ax^2 i + b y^3 j

If a subject move from (x1,y1) to (x2, y2)

2. Relevant equations

F = dW/dr

3. The attempt at a solution

I tried to solve them separately by x-direction and y-direction, and then I added them up
like Wx + Wy = W
Am I right?

Last edited: Oct 10, 2012
2. Oct 10, 2012

### Spinnor

In this problem the path taken from (x1,y1) to (x2, y2) is important, different paths taken give different results. In this problem I assume the path is a straight line. If you solve the problem as you suggested I'm not sure you took into account the path taken? Can you scan your work and post it?

Hopefully others will help.

3. Oct 10, 2012

### daivinhtran

https://www.physicsforums.com/attachment.php?attachmentid=51764&stc=1&d=1349922834

I hope I solve it right

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4. Oct 11, 2012

### Spinnor

I don't think what you did is right. You did not take the path into account only the end points. Start from the diffinition of infitesimal work, dW = vector F dot vector dr and plug and chug. You must come up with a vector expression for dr for the straight line path. You can do this as you know the endpoints.

5. Oct 11, 2012

### daivinhtran

as I stated before, the particle goes from (x1,y1) to (x2, y2)
so the end point is (x2, y2)

So, am I doing this right?

P/s: however, the path between the two points is straight line

6. Oct 11, 2012

### Spinnor

I don't think so. Hopefully others will confirm.