Finding tension of support cables

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SUMMARY

The discussion centers on calculating the tension in support cables for a 30 kg mass in static equilibrium. The tension in the vertical cable is established at 126 N. Using the formula for tension in the first cable, the calculated tension is 142.45 N, while the tension in the second cable is determined to be 179.62 N. The calculations utilize trigonometric functions based on the angles of the cables, specifically 15 degrees and 40 degrees.

PREREQUISITES
  • Understanding of static equilibrium principles
  • Knowledge of trigonometric functions (sine, cosine, tangent)
  • Ability to perform calculations involving forces and tension
  • Familiarity with free body diagrams
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn how to create and analyze free body diagrams
  • Explore advanced tension calculations in multi-cable systems
  • Investigate the effects of varying angles on tension in cables
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Students in physics, engineering students, and anyone involved in mechanics or structural analysis who needs to understand cable tension calculations.

ARJewell
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Homework Statement


A 30 kg hanging mass is supported by three cables and is in static equilibrium. The tension in the center of the vertical cable is 126 N. A free body diagram is given with the one cable making an angle of 15 deg and another cable making an an angle of 40 deg. Determine the tension in the other two cables.


Homework Equations


I'm not sure.


The Attempt at a Solution



Tension of the first cable = mg/(sin theta1 + cos theta1 + tan theta2)
So t1=30kg*9.8m/s^2/(sin 15 + cos 15 + tan 40) = 142.45 N

Tension of the second cable = T1cos theta1/cos theta2
So t2=142.45Ncos15/cos40 = 179.62 N

Does this look correct?
 
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Please show the free body diagram.
 

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