Calculating Work and Determining Conservativity for a Force F=(xy)i+(2*y^2)j

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Homework Help Overview

The problem involves calculating the work done by a force F defined as F=(xy)i+(2*y^2)j as an object moves from (0,0) to (1,3) along the line y=3x. The inquiry also includes determining whether the force is conservative.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of calculating work along different axes and question the implications for conservativity. Some suggest using the integral of F along the path, while others mention the need to check the curl of F to determine if it is conservative.

Discussion Status

The discussion is ongoing with various approaches being explored. Some participants have provided insights into calculating work and checking for conservativity, but no consensus has been reached on the methods or interpretations.

Contextual Notes

There are mentions of specific paths and integrals, as well as corrections to previous posts, indicating that participants are refining their understanding of the problem setup and calculations involved.

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Homework Statement


A force F=(xy)i+(2*y^2)j,an object (mass=m) is move from (0,0) to (1,3) along y=3x , how much work does F do? Is F a conservative force?

Homework Equations



3. The Attempt at a Solution [/B]
Can I do it on the two axes?I mean ∫Fdx+∫Fdy , and because the work differ from the different road I take , F isn't a conservative force.
∫x*ydx=∫x*(3x)dx=1/3
∫2*y^2dy=36
 
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If F be a conservative force yo can get work ∫Fdx+∫Fdy
 
Do I have to do ∫F⋅dr , where r=(1,3)/√10 ?
 
You can calculate curl of F if it will be zero F is conservative otherwise it isn't.

Path is clear and work is ∫F.dr, dr=dTI+3dtj and 0<t<1 whatever F be a conservative force or not.
 
Correction: 'dr=dti+3dtj'
 
I forgot tell you which x=t and y= 3t in above integral.
 

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