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Show that the following force is conservative 
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#1
Feb1512, 10:10 AM

P: 8

1. The problem statement, all variables and given/known data
Fx = K(2x + y), Fy = K(x + 2y) 2. Relevant equations 3. The attempt at a solution I think what is confusing me is that it is two different forces (Fx and Fy). I know that the curl has to be zero for it to be conservative, and I am assuming I will have to figure out a value for the constant K for that too happen. 


#2
Feb1512, 10:32 AM

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P: 11,617

Fx and Fy represent two components of a vector, so they describe a vector field. It might be written as:
## \vec{F} = Fx\;\hat{i} + Fy\;\hat{j} ## How would you form the curl of that? 


#3
Feb1512, 10:37 AM

P: 8

I think that is one thing that is confusing me. How else could you determine that the force is conservative? Would you have to determine the work done by both Fx and Fy are equal to 0?



#4
Feb1512, 10:47 AM

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P: 11,617

Show that the following force is conservative



#5
Feb1512, 10:56 AM

P: 8

When you do the curl of Fx and Fy, I think the constant K becomes useless because it equals to zero. What is the meaning of K in the problem then?



#6
Feb1512, 11:11 AM

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P: 11,617




#7
Feb1512, 11:19 AM

P: 8

Curl = d/dx(Fy) i  d/dy (Fx) j
= d/dx [K(x + 2y)] + d/dy [K(2x + y)] = K(1+ 0)  K (0+1) = 0 So K  K = 0? 


#8
Feb1512, 11:41 AM

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#9
Feb1512, 11:44 AM

P: 8

Is it correct? Is my calculation of the curl and the value of K being meaningless correct?



#10
Feb1512, 11:52 AM

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#11
Feb1512, 11:53 AM

P: 8

Ok thank you.



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