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March 26, 2017

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A sign weighing 10N hangs from two ropes. Each rope is 45 degrees from the horizontal.
1. What is the tension in each rope?

  • Physics - ,

    Let T be the rope tension force in each. They are the same in each rope, due to symmetry.
    2 T cos45 = 10 N (vertical equilibrium)
    T = 10N * sqrt2 = 14.14 N

  • Physics - ,

    T1*sin(180-45) + T2*sin45 = -10*sin270.
    0.707T1 + 0.707T2 = 10.
    T1 = T2.
    0.707T1 + 0.707T1 = 10.
    1.414T1 = 10.
    T1 = 7.07 N. = T2.

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