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Calculate tension and strain of wire

  1. Oct 27, 2016 #1
    1. The problem statement, all variables and given/known data
    TwoRopes_5.P.018.jpg
    A load of 1150 kg is suspended as shown in the figure. The angle θ1 = 57° and the angle θ2 = 36°.

    (a) Calculate the tension in all three wires (that is, the magnitude of the tension force exerted by each of these wires):
    Tension in left wire
    Tension in right wire
    Tension in bottom wire: 11270

    (b) These wires are made of a material whose value for Young's modulus is 1.7 × 1011 N/ m2. The diameter of the wires is 1.4 mm. What is the strain (fractional stretch) in each wire?
    Strain in the left wire
    Strain in the right wire
    Strain in the bottom wire: 4.3e-2

    2. Relevant equations
    I got the strain by using this equation:
    diameter= 1.4 radius= o.7mm= 7e-4
    pi(r)^2= pi(7e-4)^2 = 1.54e-6m^2
    11270/1.54e-6= 7.318181818= 7.3e9
    7.3e9/1.7e11= 4.3e-2

    3. The attempt at a solution
    I really have no idea how to use the angles to get the tension in the left and right wire. I have used equations with tension in the bottom wire and that got me the strain in the bottom wire.
     
  2. jcsd
  3. Oct 27, 2016 #2

    billy_joule

    User Avatar
    Science Advisor

    Draw a free body diagram of the point where the three wires meet. Apply the equations of static equilibrium and solve for the two unknown tensions.
     
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