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

AI Thread Summary
To calculate the work done by the force F=(xy)i+(2*y^2)j as an object moves from (0,0) to (1,3) along the path y=3x, the integral of the force along the specified path must be evaluated. The work done can be computed using the line integral ∫F⋅dr, where dr is parameterized based on the path. The discussion indicates that the work differs depending on the path taken, suggesting that F is not a conservative force. Additionally, calculating the curl of F can confirm its conservativity; if the curl is zero, F would be conservative. Ultimately, the analysis shows that F does not meet the criteria for being a conservative force.
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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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