Minimizing Tension: Solving for Unknown Angle in Hanging Package Problem

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SUMMARY

The discussion focuses on solving the hanging package problem, specifically determining the unknown angle of cord 2 that minimizes tension. The mass of the package is denoted as m, with cord 1 at a fixed angle of 40 degrees to the horizontal. The key equations involve the forces acting on the mass, expressed as mg = FT1 + FT2, where FT1 and FT2 represent the tensions in cords 1 and 2, respectively. The solution requires applying Newton's second law and analyzing the free-body diagram to derive the minimum tension in cord 2 in terms of mg.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Ability to draw and interpret free-body diagrams
  • Basic knowledge of trigonometric functions related to angles
  • Familiarity with tension forces in static equilibrium
NEXT STEPS
  • Study the principles of static equilibrium in physics
  • Learn how to derive equations for tension in multiple cord systems
  • Explore trigonometric identities and their applications in force analysis
  • Investigate optimization techniques for minimizing forces in mechanical systems
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics or engineering, particularly those studying static equilibrium and tension analysis in systems with multiple forces.

mdoucette225
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Homework Statement


A package of mass m hangs from a short chord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at an angle 40 degrees with the horizontal cord two is at an unknown angle.
-For what value of the unknown angle of cord two is the tension minimized?
-In terms of mg, what is the minimum tension in cord 2?


Homework Equations





The Attempt at a Solution


mg= FT1 +FT2. I attempted to find the minimum tension first, but honestly I have no idea where to start
 
Physics news on Phys.org
First, draw a free-body diagram for every mass. Draw out all forces and write down Newton's second law for both the x and the y components.
 

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