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Block pull, Problems with trig to isolate for theta.

  1. Jul 28, 2013 #1
    1. The problem statement, all variables and given/known data
    block_pull.png
    What value(s) of θ will result in the block being accelerated 9.0m/s2 to the right?

    2. Relevant equations
    ƩFx = max
    N = mg - P sin(θ)


    3. The attempt at a solution
    P cos(θ) - μkN = max
    P cos(θ) - μk(mg - P sin(θ)) = max
    P cos(θ) + μk P sin(θ) = max + μkmg
    cos(θ) + μk sin(θ) = (1/P)(max + μkmg)

    From here I can't find a trig identity that will help me isolate for theta.
     
  2. jcsd
  3. Jul 28, 2013 #2
    ## a \cos \theta + b \sin \theta = r (\cos \alpha \cos \theta + \sin \alpha \sin \theta) ##, where ## r = \sqrt {a^2 + b^2} ## and ## \cos \alpha = a/r , \ \sin \alpha = b/r ##.
     
    Last edited: Jul 28, 2013
  4. Jul 28, 2013 #3

    gneill

    User Avatar

    Staff: Mentor

    Another approach is to replace one of the trig functions (say cos) using the identity sin2 + cos2 = 1. Rearrange the resulting expression so that squaring both sides eliminates the square root.
     
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