Will Either Rope Break Supporting a 1000kg Steel Beam?

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SUMMARY

The discussion centers on the tension analysis of a 1000kg steel beam supported by two ropes, each with a maximum tension capacity of 6000N. The calculations indicate that Rope 1 experiences a tension of 5638N and Rope 2 experiences 5196N, both of which are below their maximum limits. However, the consensus is that Rope 1 will break first due to incorrect initial calculations and the need for a more comprehensive approach using F=ma for both x and y components. The correct method involves solving two equations with two variables to accurately determine the tension distribution.

PREREQUISITES
  • Understanding of basic physics concepts, particularly tension and forces.
  • Familiarity with trigonometric functions, specifically cosine and sine.
  • Knowledge of Newton's second law (F=ma).
  • Ability to solve systems of equations, either through matrix methods or calculators.
NEXT STEPS
  • Study the application of F=ma in static equilibrium problems.
  • Learn about tension distribution in multi-rope systems.
  • Explore trigonometric functions in physics, focusing on their application in force resolution.
  • Practice solving systems of equations using matrix algebra.
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This discussion is beneficial for physics students, engineering students, and anyone involved in structural analysis or mechanics, particularly those studying tension in static systems.

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Homework Statement


A 1000kb steel beam is supported by two ropes. Each rope as a maximum sustained tension of 6000N. Does either rope break? If so, which one(s)?

http://img101.imageshack.us/img101/3930/diagramgm2.jpg

Homework Equations


Tension = M cos/sin theta
(in this case it is cos)

The Attempt at a Solution


Rope1 = 6000cos20 = 5638N
Rope2 = 6000cos30 = 5196N
W=1000*9.8 = 9800N / 2 = 4900N so no It does not break, but the answer says rope 1 breaks first and then rope 2
 
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the equations you used are wrong. as well as the angles you used.

you need to use F=ma for the x and y components and you will get 2 equations of 2 variables which you can solve as a matrix or plugging it into your calculator.

for the x-component the tensions cancel out right?
and for the y-component the tensions will equal to the weight of the beam?
 

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