(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 1000 kg steel beam is supported by two ropes. What is the tension in each?

2. Relevant equations

F = ma = mg

3. The attempt at a solution

I labeled the left tension as [tex]T_{1}[/tex] and the right tension as [tex]T_{2}[/tex].

[tex]\sum{F_{y}} = T_{1,y} + T_{2,y} -mg = 0[/tex]

[tex]T_{1,y} = T_{1} cos(20^{o})[/tex]

[tex]T_{2,y} = T_{2} cos(30^{o})[/tex]

[tex]T_{1,y} = T_{2,y}[/tex]

[tex]\sum{F_{y}} = T_{2,y} + T_{2,y} -mg = 0[/tex]

[tex]\sum{F_{y}} = 2T_{2,y} -mg = 0[/tex]

[tex]2T_{2,y} = mg[/tex]

[tex]2T_{2,y} = (1000kg)(9.8 m/s^2)[/tex]

[tex]2T_{2,y} = 9800 N[/tex]

[tex]T_{2,y} = 4900 N[/tex]

[tex]T_{2} cos(30^{o}) = 4900 N[/tex]

[tex]T_{2} = 5658 N[/tex]

For [tex]T_{1}[/tex], I get [tex]5214 N[/tex].

That answer is wrong. The answer should be [tex]6397 N[/tex] and [tex]4376 N[/tex].

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# Homework Help: Force Problem and steel beam

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