Mass suspended by 3 ropes (midterm practice)

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SUMMARY

The problem involves a 100kg mass suspended by three ropes, with specific attachment points in a three-dimensional coordinate system. The ropes are anchored at (1m, 1m, -1m), (1m, -1m, -1m), and (-4m, 0, -1m). The tension T in the rope at (-4m, 0, -1m) is calculated to be 810N. To solve this, one must create a free-body diagram and apply equilibrium equations to determine the tensions in each rope.

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  • Familiarity with Newton's laws of motion
  • Basic skills in vector resolution and equilibrium analysis
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A 100kg mass is supended by 3 ropes. one rope is attached at a point 1m[itex]\hat{x}[/itex] + 1m[itex]\hat{y}[/itex], one is attached at 1m[itex]\hat{x}[/itex] - 1m[itex]\hat{y}[/itex] and one is attached at -4m[itex]\hat{x}[/itex]. The three ropes all connect at -1m[itex]\hat{z}[/itex], at which point the mass is attached. What is the tension T in the rope attached at -4m[itex]\hat{x}[/itex]?

I found this problem in my midterm study sheet, but I have no idea how to solve it.
I only know the answer is supposed to be 810N but I don't understand how to get there. Thanks
 
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First draw a picture, then construct the free-body diagram.

ehild
 

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