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Verifying conservative field

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Verify the following force field is conservative.
    F = 2xcos2yi - (x2+1)sin2yj

    2. Relevant equations

    ∇xF=0

    3. The attempt at a solution
    I'm pretty sure this is just a mistake in the book, but according to my calculations, this isn't a conservative force.
    I used the determinant method to do the curl of F to find -2xsin(2y) + 4xsinycosy. Unless those two terms cancel each other to equal 0, then the force isn't conservative and there's a mistake in the book.

    What do you think? Thanks.
     
  2. jcsd
  3. Oct 7, 2013 #2

    dextercioby

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    You should brush up your HS trigonometry before doing anymore maths/physics. How do you expand sin 2y ?
     
  4. Oct 7, 2013 #3
    Oh.
    Is there a way to expand sin2y manually, or is it just one of those things you have to memorize?
     
  5. Oct 7, 2013 #4

    dextercioby

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    Trigonometry generally appeals to memory even though some proofs can be visual. sin (x+y) = ? then take x=y.
     
  6. Oct 8, 2013 #5
    [tex]\sin(2y) = 2\sin y \cos y[/tex] for any angle [itex]y[/itex]. So yes, the terms cancel out and the force is conservative.
     
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