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

[AryRezvani]

Homework Statement

Homework Equations

W=∫ F_x dx

The Attempt at a Solution

I think you got to split this one in terms of axis.

∫(2yi + x²j) dx

Pretty lost on it.

 

[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.

 

[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?

 

[SammyS]

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 move the object to the right first. Force is constant right? So would you use fΔrCosθ?

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.