# A force acting on a particle moving in the xy plane is given by

1. Oct 9, 2012

### AryRezvani

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

2. Relevant equations

W=∫ Fx dx

3. The attempt at a solution

I think you gotta split this one in terms of axis.

∫(2yi + x2j) dx

Pretty lost on it.

2. Oct 9, 2012

### 256bits

Well, they do not say in which direction the vectors i and j point, so let us assume that vector i is parallel to the x-axis and vector j is parallel to the y-axis, which is the usual convention.

To start you off,
Path OAC:
From O to A, can you find the force on the particle along this path knowing that y = 0. In what direction does the force point from the equation given for force.? Does the force do any work along this path? Note that the particle is moving along the x-axis which is what vector direction, i or j. Can you find an equation for the path of the particle in terms of vectors i oj or both?

from A to C, same questions.

You might want to review dot and cross product as that that is what this problem seems to be designed for.

PS. Your picture shows up a bit large.

3. Oct 9, 2012

### AryRezvani

Understood, so quick question, is the blue line the force? Then the other lines simply components of the force?

Still a little lost. We want to calculate the work required to mvoe the object to the right first. Force is constant right? So would you use fΔrCosθ?

4. Oct 9, 2012

### SammyS

Staff Emeritus
No, the force is not along the blue line.

No, the force is not constant.

The force depends upon the location of the particle according to $\displaystyle \vec{F}=2y\hat{\text{i}}+x^2\hat{\text{j}}\ .$

You are to calculate the work done by that force in moving the particle from point, O, to point, C, along each of the colored paths.