1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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)


    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


    User Avatar
    Science Advisor
    Homework Helper

    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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook