anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
integrate along the path F.dr
anonymous
  • anonymous
Don't you need to Integrate?
anonymous
  • anonymous
ya

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anonymous
  • anonymous
vector integral
anonymous
  • anonymous
vector is how would you do it when the path is a straight line?
anonymous
  • anonymous
give us the question..well see
anonymous
  • anonymous
between point (3,0,0) to point (0,pi/2,3)
anonymous
  • anonymous
when the path between those two points is a straight line
anonymous
  • anonymous
I'm having trouble knowing what to do when it's path dependent.
anonymous
  • anonymous
whats the force?
anonymous
  • anonymous
F(x,y,z)= z i + x j + y k
anonymous
  • anonymous
gotcha
anonymous
  • anonymous
so dr is the distance between the two points?
anonymous
  • anonymous
first write the eqn of a line in cartesian form like x=3+3k y=k(pi)/2 z=3k
anonymous
  • anonymous
parametric representation of the line segment right?
anonymous
  • anonymous
the work done is F.dr which is right
anonymous
  • anonymous
sorry write y=-k(pi)/2 and z = -3k
anonymous
  • anonymous
got it till here??
anonymous
  • anonymous
Kinda it's just hard to remember how to find the parametric equations of a line
anonymous
  • anonymous
no bt ive written em down fr u nw
anonymous
  • anonymous
kk so use dot product of the vector with dr right?
anonymous
  • anonymous
so you just replace x y z with the parametric equations right?
anonymous
  • anonymous
so here goes dot prod gives zdx + xdy + ydz for zdx write (-3k)(dx) (-3k)(3dk)
anonymous
  • anonymous
now integrate this -9k^2 dk from k =0 to k=-1
anonymous
  • anonymous
coz k=-1 gives u ur final point
anonymous
  • anonymous
got it?
anonymous
  • anonymous
yup
anonymous
  • anonymous
now similarly compute it for xdy and ydz and then add all three/
anonymous
  • anonymous
got it?
anonymous
  • anonymous
Yes so my area of integration is going to change because I reperamatize right?
anonymous
  • anonymous
yes integrate all three frm 0 to -1
anonymous
  • 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
  • anonymous
that should do it i spose
anonymous
  • anonymous
yup my book shows it but in two dimensions....
anonymous
  • 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
  • anonymous
wt hapnd??
anonymous
  • anonymous
nothing I got the answer

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