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Proving trigonometric identities in a belt and pulley proble

  1. Mar 20, 2016 #1
    1. The problem statement, all variables and given/known data
    verify that theta in L = piD + (d-D)theta + 2Csin(theta) is equal to arc-cosine [(D-d)/2C]

    2. The attempt at a solution
    you can see my attempt in the second picture uploaded. i don't think i even got it right
     

    Attached Files:

  2. jcsd
  3. Mar 21, 2016 #2

    ehild

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    You are close, but you put A to the wrong place, and c is not the hypotenuse of a right triangle in your picture.
    The line x (the connecting belt) makes a right angle with the radius of both circles, and you need to draw a parallel with it from the centre of the smaller circle. You get the yellow rectangle and the green right triangle. Find x and theta from that. Prove both formulas in the OP.
    upload_2016-3-21_6-52-44.png
     
  4. Mar 21, 2016 #3
    wow! how did i not see that. thanks! 2(theta) equals to arccosine (D-d)/C right? so to further simplify... theta equals to arccosine[(D-d)/2C] did i got that right?
     
  5. Mar 21, 2016 #4

    ehild

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    Yes, cos(θ)=(R-r)/c, that is arccos((D-d)/(2c))=θ. But you also have to prove the other formula, for the length of the belt.
     
  6. Mar 22, 2016 #5
    one thing i learned is i really have to put all of my thoughts on paper to make things easier. thanks for the help i think i got! check the new image uploaded :)
     

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  7. Mar 22, 2016 #6

    ehild

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    It is correct now. And you really need sketches. I am very old and have much experience, but still my first thing is to make a sketch before starting to solve a Physics or Geometry problem.
     
  8. Mar 22, 2016 #7
    thank you a lot for responding to my thread! i will keep that in mind! :D best of luck
     
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