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srg
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Homework Statement
Consider the diagram below. A 1000 kg block being suspended in equilibrium by cables c and a. Cable c is on a pulley which can vary the length of the cable. Write the constraints of equilibrium. Find the tension in each cable based on varying lengths of cable c between 1.2 m and 2.2 m.
http://srg.sdf.org/images/PF/MassVarLength.png
Homework Equations
Law of Cosines: [itex]c^2=a^2+b^2-2ab\cos{C}[/itex]
Constraints of Equilibrium: [itex]\sum{F_x}=\sum{F_y}=0[/itex]
The Attempt at a Solution
I drew a free body diagram:
http://srg.sdf.org/images/PF/VarLengthDiagram.png
I used the law of cosines to begin writing the constraints of equilibrium.
[itex]\sum{F_x}=0 \rightarrow T_c(\frac{b^2+c^2-a^2}{2bc})-T_b(\frac{a^2+b^2-c^2}{2ab})=0[/itex]
[itex]\sum{F_y}=0 \rightarrow T_c\sin{\arccos{\frac{b^2+c^2-a^2}{2bc}}}+T_b\sin{\arccos{\frac{a^2+b^2-c^2}{2ab}}}-9810=0[/itex]
Since everything is known except for [itex]T_c[/itex] and [itex]Tb[/itex], they can be solved for. However, this system of equations doesn't seem easily solved for. I suspect I went wrong when I took the [itex]sin(arccos())[/itex], but I needed the sine of the angle when all I had was the law of cosines.
This course has been incredibly frustrating, and I'm only 5 weeks in. I'm beginning to feel I'm not really cut out for this.
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