Equilibrium Question With Ropes and Weight

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SUMMARY

The discussion centers on solving a physics problem involving three tensions (T1, T2, T3) in a system with a weight of 1000 N at the end of a rope. The participant correctly identifies that T1 equals 1000 N, while T2 and T3 must sum to 1000 N to maintain equilibrium. Using vector addition, T2 is calculated to be 577 N, leading to T3 being 423 N. The solution emphasizes the importance of analyzing both vertical and horizontal force components to achieve equilibrium.

PREREQUISITES
  • Understanding of the Law of Cosines for vector calculations
  • Familiarity with SOH-CAH-TOA for trigonometric functions
  • Basic knowledge of equilibrium conditions in physics
  • Ability to perform vector addition and resolve forces
NEXT STEPS
  • Study the application of the Law of Cosines in multi-force systems
  • Learn about vector resolution techniques in physics
  • Explore equilibrium conditions in static systems
  • Practice problems involving tension in ropes and pulleys
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Students studying physics, particularly those focusing on mechanics and equilibrium problems, as well as educators looking for examples of tension calculations in real-world applications.

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Homework Statement


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The weight at the end of the rope is 1000 N. Find tensions in T1, T2, and T3.

Homework Equations



Law of Cosine: a^2+b^2-2ab(cosC)=c^2
SOH-CAH-TOA

The Attempt at a Solution



T1 has to be 1000N. I figured T2 and T3 have to add up to the weight of 1000 N. I ended up added the vectors head to tail and found T2 to be 577 N and T3 would have to be 1000-577=423 N since both ropes have to add up to 1000 N to be in equilibrium. I honestly do not have a clue how to do the problem (it was on a test today and it's really bugging me what the answer is or how to even achieve the answer)
 
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Consider vertical and horizontal force components. Start by analyzing the vertical forces acting on the junction of the ropes.
 

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