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Math Help - forces and tension

  1. #1
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    forces and tension

    A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:
    http://i26.tinypic.com/28h0a6v.jpg

    What is the tension in each string?
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  2. #2
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    Quote Originally Posted by checkmarks View Post
    A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:
    http://i26.tinypic.com/28h0a6v.jpg

    What is the tension in each string?
    Try using Lami's Theorem: Lami's theorem - Wikipedia, the free encyclopedia
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    The way I am being taught

    it in Honors Physics is saying that \sum{F_x}=0 and \sum{F_y}=0 since this is a statics problem...you set up two equations with two variables based on this and solve them simultaneously...
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    Quote Originally Posted by checkmarks View Post
    A mass (10 kg) hangs from two strings which are attached to the ceiling shown in this picture:

    What is the tension in each string?
    The 2 strings must pull together with the same force as the weight of the mass.

    Draw the parallelogram of forces. You already know all angles in the marked triangle and the length of the third side. Thus use Sine rule here:

    \frac{|\overrightarrow{F_1}|}{10}=\frac{\sin(40^\c  irc)}{\sin(80^\circ)} ~\implies~ |\overrightarrow{F_1}|=10 \cdot \frac{\sin(40^\circ)}{\sin(80^\circ)} \approx 6.527036... kg By the way: You are dealing here with forces and therefore the unit kg is very, very inappropriate.

    \frac{|\overrightarrow{F_2}|}{10}=\frac{\sin(60^\c  irc)}{\sin(80^\circ)} ~\implies~ |\overrightarrow{F_2}|=10 \cdot \frac{\sin(60^\circ)}{\sin(80^\circ)} \approx 8.79385... kg
    Attached Thumbnails Attached Thumbnails forces and tension-forceandtension.gif  
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