Forces and Tensions: Two Masses Suspended from Cable System

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SUMMARY

The discussion focuses on calculating the tensions in a cable system involving two suspended masses of 50 kg and 20 kg. Participants utilized the law of cosines and the law of sines to analyze the forces acting on the masses. A critical observation highlighted the need for accurate free body diagrams to ensure that the sum of forces equals zero, particularly at point C where the forces acting on the 20 kg mass were misrepresented. The importance of correctly identifying angles and force directions was emphasized to achieve accurate tension calculations.

PREREQUISITES
  • Understanding of the law of cosines
  • Familiarity with the law of sines
  • Knowledge of free body diagram construction
  • Basic principles of static equilibrium
NEXT STEPS
  • Study the application of the law of cosines in tension problems
  • Learn how to construct accurate free body diagrams for multiple forces
  • Explore static equilibrium conditions in systems with multiple masses
  • Review examples of tension calculations in cable systems
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Physics students, engineering students, and anyone involved in mechanics or statics who seeks to understand tension in cable systems and the application of equilibrium principles.

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Homework Statement



Two masses, 50 kg and 20 kg, are suspended from a cable system. Determine tentions in cables AB, BC, CD, CE

Homework Equations



law of cosines
law of sines

The Attempt at a Solution



I tried by solving around point B first and have found Tab and Tbc.
Are my findings correct? See attache .pdf
 

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One question: Is the angle between CD and CE also 40o?

One observation: You have drawn three forces acting on the 20 kg mass at C. Tension CE is up and to the right, tension 196 is straight down and tension CD is only to the right. These three forces cannot possibly add up to give zero because the net force will surely have a non-zero component to the right. You need to redraw the diagram using arrows to indicate the direction of each force.

One suggestion: Draw two separate free body diagrams, one for each mass saying that the sum of all the forces in each diagram must be zero.
 

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