Find the work done by the force field F that is not conservative. The distance is between two points. How would you approach this problem since the Fundamental Rules of Calculus do no apply.

- anonymous

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- anonymous

integrate along the path F.dr

- anonymous

Don't you need to Integrate?

- anonymous

ya

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## More answers

- anonymous

vector integral

- anonymous

vector is how would you do it when the path is a straight line?

- anonymous

give us the question..well see

- anonymous

between point (3,0,0) to point (0,pi/2,3)

- anonymous

when the path between those two points is a straight line

- anonymous

I'm having trouble knowing what to do when it's path dependent.

- anonymous

whats the force?

- anonymous

F(x,y,z)= z i + x j + y k

- anonymous

gotcha

- anonymous

so dr is the distance between the two points?

- anonymous

first write the eqn of a line in cartesian form like
x=3+3k
y=k(pi)/2
z=3k

- anonymous

parametric representation of the line segment right?

- anonymous

the work done is F.dr
which is
right

- anonymous

sorry write y=-k(pi)/2 and z = -3k

- anonymous

got it till here??

- anonymous

Kinda it's just hard to remember how to find the parametric equations of a line

- anonymous

no bt ive written em down fr u nw

- anonymous

kk so use dot product of the vector with dr right?

- anonymous

so you just replace x y z with the parametric equations right?

- anonymous

so here goes
dot prod gives zdx + xdy + ydz
for zdx
write (-3k)(dx)
(-3k)(3dk)

- anonymous

now integrate this
-9k^2 dk from k =0 to k=-1

- anonymous

coz k=-1 gives u ur final point

- anonymous

got it?

- anonymous

yup

- anonymous

now similarly compute it for xdy and ydz and then add all three/

- anonymous

got it?

- anonymous

Yes so my area of integration is going to change because I reperamatize right?

- anonymous

yes integrate all three frm 0 to -1

- anonymous

bcoz remmbr on ur line k=0 gives the initial pt and k=-1 givs d final pt...so as our integrating variable is k, we use the lim its fr k

- anonymous

that should do it i spose

- anonymous

yup my book shows it but in two dimensions....

- anonymous

js get the answer and tally it..its complicated enough...ur book mightve represented it in 2d..fr me dis is d way i thot dis cld be done

- anonymous

wt hapnd??

- anonymous

nothing I got the answer

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