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Statics: find tension/wrap angle for pulley

  1. Apr 7, 2015 #1
    1. The problem statement, all variables and given/known data
    Given: T(sub-B) plus T(sub-B) prime = 36. Both T(sub-C) values are 0. T (sub-D) =36 and T (sub-D) prime = 12. Find values of T (sub-B) and T (sub-B) prime



    2. Relevant equations
    OK, so we need to find the wrap angle, which should be 180 + 30 -22, which comes to 188 degrees, which is 1.04 pi radians.
    Then: T (tightside)/T (slackside) = e raised to wrap angle (in radians)
    This yields a T (tightside)/T (slackside) of 2.84.
    The book shows this ratio as 3.

    Also, confused: the values of T (sub-D) are in the same ratio (3 to 1) yet their wrap value is clearly 180 degrees or 1 pi


    Can someone point me in the right direction? Thank you.

    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Apr 7, 2015 #2
    This is a balance of moments problem, not a belt friction problem. But, in any event, in your equation for the ratio of the tensions, you left out the coefficient of friction.

    Chet
     
  4. Apr 8, 2015 #3
    Oh, so this is just a lever-arm problem? If we look at T (sub-D), it exerts a torque of (6 in)(36Lbs)=216 in-LB on the axle. Therefore, the tightside of the belt around pulley B, which is T (sub-B), must also exert 216 in-LB of force on the axle. We know its lever arm is 8 in, so the force must be 27LB. Is this the correct logic to apply here?

    Thank you for helping.....I am trying to wade through this statics course by myself, so I don't have access to professors or even other students to ask questions or debate logic.
     
  5. Apr 8, 2015 #4
    No. You need to include in the moment balance all four of these: TB, TB', TD, and TD'.

    Chet
     
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