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Homework Help: Two hanging masses and three strings

  1. Jul 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Two masses m and M (where M = 2m) are attached with strings. One mass m is suspended from a single verticle string held by two strings each at 45 degrees to the horizontal. The suspending string to the left at 45 degrees is attached to a fixed point. The string on the right at 45 degrees is attached to another mass M which in turn is attached by a further to a fixed point above at an angle theta to the horizontal.
    If the system is in equilibrium, determine the tension in the three strings in terms of m and g, and calculate the angle theta.

    2. Relevant equations
    F = ma

    3. The attempt at a solution
    As the system is in equilibrium i can say a=0 and therefore ΣF = 0.
    The y component of the two tensions in the two diagonal strings supporting mass m should be equal to mg when summed. Assuming the tensions are still equal (not quite sure what effect the other mass M would have on this - mass M is what has thrown me) then the tension in the bottom two strings should be mg/√2 ?
    The tension in the 3rd string connecting mass M with the fixed point ? My best quest was to say it is equal to √2mg as 2mg sin45 = T ?
    I also dont know theta however and dont see a way of finding it, at this point im almost sure i have absolutely none of this right! Any help on a method to solve this would be much appreciated!

    P.s sorry for the lack of image, cant seem to find anything on the web which shows a similar situation.
  2. jcsd
  3. Jul 31, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor



    No need to assume that... prove it!

    Why guess? Apply ΣF = 0 to mass M and solve for the unknowns.

    You can use the whiteboard to slap something together yourself.
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