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!

How do you work out the tension and angle of this block in equilibrium?

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    A block that has a weight of 20N, is in equilibrium. It is attached to 3 strings, A, B and C. String A has a tension of 15N to the right of the block. Between String A and B is the angle (a) and between B and C is 90degrees. The tension in String B and C is the same. Calculate the tension and the angle (a).


    2. Relevant equations

    sum of the forces=0


    3. The attempt at a solution

    For the horizontal forces I got:
    15+Tcos(a)=Tcos(90+a)

    And then for the vertical:
    20=Tsin(a)+Tsin(90+a)

    But I don't know how to figure it out from there, or whether they are even right. Any help at all would be greatly apprecaited!
     
  2. jcsd
  3. Apr 1, 2009 #2
    cos(90+a) = sin(a)
    sin (90+a) = -cos(a)

    But, why the angle is 90+a?
     
  4. Apr 1, 2009 #3
    The angle of String C is 90degrees plus (a) away from the 15N to the right. I've attached a diagram of the situation, sorry I aren't very good at expalining. Am I totally wrong with the angles??

    Thanks by the way!
     

    Attached Files:

  5. Apr 1, 2009 #4
    It is easier to visualize if you use 90-a (triangle left to the force vector C).

    I would recommend to divide both equations and eliminate T. Then you will get Acos (a) = B sin(a) relationship..which is easier to solve
     
  6. Apr 1, 2009 #5
    So my two equations are:

    15+Bcos(a)=Ccos(90-a)
    20=Bsin(a)+Csin(90-a)

    Which because the tension is the same in both means the A and C can be replaced by T:

    15+Tcos(a)=Tcos(90-a)
    20=Tsin(a)+Tsin(90-a)

    From this do I rearrange to get Tcos(a) and Tsin(a) as the subjects? And if they are divided they equal tan(a), or is this wrong?
     
  7. Apr 3, 2009 #6

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I would next simplify the cos(90-a) and sin(90-a). You can use the trig formulas for sin(x-y) and cos(x-y) to do this.
     
    Last edited: Apr 3, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How do you work out the tension and angle of this block in equilibrium?
Loading...