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anonymous

  • 5 years ago

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.

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  1. anonymous
    • 5 years ago
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    integrate along the path F.dr

  2. anonymous
    • 5 years ago
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    Don't you need to Integrate?

  3. anonymous
    • 5 years ago
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    ya

  4. anonymous
    • 5 years ago
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    vector integral

  5. anonymous
    • 5 years ago
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    vector is <z,x,y> how would you do it when the path is a straight line?

  6. anonymous
    • 5 years ago
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    give us the question..well see

  7. anonymous
    • 5 years ago
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    between point (3,0,0) to point (0,pi/2,3)

  8. anonymous
    • 5 years ago
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    when the path between those two points is a straight line

  9. anonymous
    • 5 years ago
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    I'm having trouble knowing what to do when it's path dependent.

  10. anonymous
    • 5 years ago
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    whats the force?

  11. anonymous
    • 5 years ago
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    F(x,y,z)= z i + x j + y k

  12. anonymous
    • 5 years ago
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    gotcha

  13. anonymous
    • 5 years ago
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    so dr is the distance between the two points?

  14. anonymous
    • 5 years ago
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    first write the eqn of a line in cartesian form like x=3+3k y=k(pi)/2 z=3k

  15. anonymous
    • 5 years ago
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    parametric representation of the line segment right?

  16. anonymous
    • 5 years ago
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    the work done is F.dr which is <zdx, xdy, ydz> right

  17. anonymous
    • 5 years ago
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    sorry write y=-k(pi)/2 and z = -3k

  18. anonymous
    • 5 years ago
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    got it till here??

  19. anonymous
    • 5 years ago
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    Kinda it's just hard to remember how to find the parametric equations of a line

  20. anonymous
    • 5 years ago
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    no bt ive written em down fr u nw

  21. anonymous
    • 5 years ago
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    kk so use dot product of the vector with dr right?

  22. anonymous
    • 5 years ago
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    so you just replace x y z with the parametric equations right?

  23. anonymous
    • 5 years ago
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    so here goes dot prod gives zdx + xdy + ydz for zdx write (-3k)(dx) (-3k)(3dk)

  24. anonymous
    • 5 years ago
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    now integrate this -9k^2 dk from k =0 to k=-1

  25. anonymous
    • 5 years ago
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    coz k=-1 gives u ur final point

  26. anonymous
    • 5 years ago
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    got it?

  27. anonymous
    • 5 years ago
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    yup

  28. anonymous
    • 5 years ago
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    now similarly compute it for xdy and ydz and then add all three/

  29. anonymous
    • 5 years ago
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    got it?

  30. anonymous
    • 5 years ago
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    Yes so my area of integration is going to change because I reperamatize right?

  31. anonymous
    • 5 years ago
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    yes integrate all three frm 0 to -1

  32. anonymous
    • 5 years ago
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    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

  33. anonymous
    • 5 years ago
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    that should do it i spose

  34. anonymous
    • 5 years ago
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    yup my book shows it but in two dimensions....

  35. anonymous
    • 5 years ago
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    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

  36. anonymous
    • 5 years ago
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    wt hapnd??

  37. anonymous
    • 5 years ago
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    nothing I got the answer

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