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Minimize the Tension

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    A package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle 40 degrees with the horizontal; cord 2 is at angle, theta.

    a) for what value of theta is the tension in cord 2 minimized?
    b)in terms of mg, what is the minimum tension in cord 2?

    (here's the link of the problem with the picture http://www.unc.edu/~rowan/phys26/P26recit/p26-12-b.htm )

    I know I have to figure out the force diagram first. I'm just having trouble with where to start.

    I'm not asking for the solution, i just need some direction,
     
  2. jcsd
  3. Oct 31, 2009 #2

    tiny-tim

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    Hi munchy35! :wink:

    You can solve this either with a vector triangle, or by taking components in a convenient direction.

    Choose one method, and show us how far you get. :smile:
     
  4. Nov 1, 2009 #3
    i used the component method so

    for horizontal component i said t1cos40=t2cosx

    (i'm just using x for theta)

    t2=t1cos40/cosx

    and t1 = t2cosx/cos40

    so for part a, i used the t2 equation and just assumed for t2 to be a minimum cos x had to be maximum, the maximum cosx=1, so x= 0 degrees

    ^ can i just assume that?

    for part b, i used vertical component

    t1sin40 + t2sinx = mg

    after plugging in t1

    t2 = mg/ tan40cos0 + sin0

    and eventually get 1.192mg

    is that right
     
  5. Nov 1, 2009 #4

    tiny-tim

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    Hi munchy35! :smile:
    Nooo … stop trying to take short-cuts! :rolleyes:

    Your two equations are correct :smile:

    now eliminate t1 to find t2 …

    then minimise t2. :wink:
     
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