Vector Components: Equal Force of Two Wires Suspending 500N Sign

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SUMMARY

The problem involves two wires suspending a 500N sign, forming an angle of 100 degrees between them. Each wire exerts an equal force, calculated to be 389N. To solve this, one must analyze the forces acting on the sign using a free body diagram and apply trigonometric principles to determine the vertical components of the forces. The symmetry of the situation simplifies the calculations, allowing for a straightforward application of vector resolution.

PREREQUISITES
  • Understanding of free body diagrams
  • Basic knowledge of trigonometry
  • Familiarity with vector resolution
  • Concept of equilibrium in static systems
NEXT STEPS
  • Study vector resolution techniques in physics
  • Learn how to draw and analyze free body diagrams
  • Explore the principles of static equilibrium
  • Review trigonometric functions and their applications in physics problems
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Students in physics or engineering, particularly those studying statics and force analysis, as well as educators looking for examples of vector components in real-world applications.

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Homework Statement


two wires are used to suspend a sign that weighs 500N. the two wires make an angle of 100 degrees between each other. If each wire is exerting an equal amount of force, how much force does each wire exert?


Homework Equations





The Attempt at a Solution


The answer is 389.. but I don't understand how to get that.. Can someone please explain. Thanks
 
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Draw a free body diagram for the sign. What are ALL the forces that act on it? Since the sign is not moving, what must be true about the vector sum of these forces? Now pay attention to the vertical components of those forces...how would you use trigonometry to figure out what these are?
 
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Also note, that both wires are exerting equal force. Exploit symmetry.
 

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