Solving Equilibrium Problem: Find Forces in Ropes and Ball & Socket Joint

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SUMMARY

The discussion focuses on solving an equilibrium problem involving a rod weighing 180 lb and a 400 lb load at point A, suspended by two lines to points C and D, and supported by a ball and socket joint at E. Participants emphasize the importance of using static equilibrium equations, specifically summation(Fx) = 0, summation(Fy) = 0, summation(Fz) = 0, and summation(Mx) = 0, to find the unknown forces. The necessity of a free body diagram (FBD) is highlighted for visualizing the forces acting on the system, including the tensions in the lines and the forces at the ball joint. Accurate calculations with at least four significant digits are recommended for precision.

PREREQUISITES
  • Understanding of static equilibrium equations
  • Knowledge of free body diagrams (FBD)
  • Familiarity with tension forces in cables or ropes
  • Basic principles of mechanics related to forces and moments
NEXT STEPS
  • Study the principles of static equilibrium in three dimensions
  • Learn how to construct and analyze free body diagrams (FBD)
  • Explore tension calculations in systems with multiple supports
  • Review the mechanics of ball and socket joints in structural applications
USEFUL FOR

Engineering students, mechanical engineers, and anyone involved in analyzing forces in static systems, particularly those dealing with tension in cables and joints.

mj123
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A rod weighs 180 lb and has a 400 lb load located at point A is suspended in the air by two lines runningfrom point A to points C and D and a ball and socket joint at E. Find the forces for the tension in eachline (rope?, cable?) (A to C and A to D) and the forces at the ball and socket joint.


I figured out the tensions.. but the ball and socket its confusing
 
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mj123: The PF rules state we are not allowed to tell you how to approach or solve your homework problem. See the required homework template that appears when you start to create a new thread in the homework forums. You must list relevant equations yourself, and show your work; and then someone might check your math. Also, you would need to show a diagram of the problem.
 
sorry.. I figured out that TAD=TAD[-.6506-.390+.6509] and TAC=TAC[.394-.4728+.788]

then i know that i have to find Bx,By and Bz. But I am kind of stuck there 'cause I am not sure how the 180lb and the 400lb influence in the whole problem

http://www.mech.utah.edu/~me1300/CP1.pdf
 
Last edited by a moderator:
mj123: Maintain at least four, preferably five, significant digits for all your intermediate calculations. Use the static equilibrium equations, such as summation(Fx) = 0, summation(Fy) = 0, summation(Fz) = 0, summation(Mx) = 0, to solve simultaneously for the unknowns. If you show your work, someone might check your math.
 
Draw a free body diagram (FBD) similar to the given figure ( I assume there is a mistake and B is the same as E). On the FBD, draw all the forces that act on it, including at the ball joint. Then make equilibrium statements from which you can extract your answers.
 

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