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!

A Box is suspended by two strings, what is the tension?

  1. Feb 5, 2017 #1
    1. The problem statement, all variables, and given/known data
    Suppose a block is suspended by two strings, one, T1, is anchored at 30 degrees to the horizon, the other, T2, at 60 degrees to the horizon. If the block weighs 100 kg, what is the tension in the two strings?
    Assume that:
    The 30-degree angle is Phi.
    The 60-degree angle is Theta.
    M = 100 kg
    g = 10 m/s^s

    2. Relevant equations
    (I had to create them myself, so they will be shown in the attempt section.)

    3. The attempt at a solution
    This image details my attempt. I am fairly certain that I got the correct answers, but I would really appreciate confirmation as well as an explanation for why certain things may be sin or cos. Most of the formulas are ones the professor just gave to us in class, and instead of expecting us to know how to create them, he just wants us to memorize them, which I struggle with unless I know the basis behind it.

    7Sx1bqD.jpg
     
  2. jcsd
  3. Feb 5, 2017 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The key equation that you have is:

    ##T_1 = \frac{mg}{\tan(\theta) \cos(\phi) + \sin(\theta)}##

    Which is very good!

    In fact, if you then calculate a similar expression for ##T_2## you will see the symmetry of the solution.
     
  4. Feb 5, 2017 #3

    kuruman

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    To add to PeroK's answer, a useful thing to memorize is that if angles θ and φ are complementary, i.e. θ + φ = 90o, the sine of one is the cosine of the other. If you use this fact to express T1 in terms of one of the angles, say θ, your expression will simplify to a great extent. Do the same for T2 and you should recognize the expression relating the two tensions to the weight as something old and familiar.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted