How Do You Solve the Moving Pulley Problem with a 100 kg Sack for Equilibrium?

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Homework Help Overview

The discussion revolves around a moving pulley problem involving a 100 kg sack and the equilibrium conditions of the system. Participants are tasked with determining the position x and the tension in the cable ABC, given the constraints of the problem.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equilibrium equations related to tension in the cables and explore the geometry of the system, including the introduction of new variables and the use of trigonometric relationships. There is also a focus on the implications of the free body diagram and the tension consistency across the pulley.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and observations. Some have introduced new variables and equations, while others are questioning the assumptions made regarding the tension and geometry. There is no explicit consensus yet, but various lines of reasoning are being explored.

Contextual Notes

Participants note the need to consider the height component and the implications of the rope's length in their calculations. There is also mention of the complexity introduced by the equations derived from similar triangles.

Jay9313
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Homework Statement


http://media.cheggcdn.com/media/76d/76dd5c56-43a5-44d3-b8b8-40ba63a9010a/phpYYNJyN.png

Cable ABC has a length of 5 m. Determine the position x and the tension developed in ABC required for equilibrium of the 100 kg sack. Neglect the size of the pulley


Homework Equations


TABCosθ + TBCCos\phi=0
TABSinθ + TBCSin\phi=980N
I also have the distance from C to the pulley (in x direction) is 3.5-x

The Attempt at a Solution


My attempt at the solution so far is
TABCosθ = TBCCos\phi
I can rearrange the trig functions themselves, but I'm missing a height component, but I don't even know if that's the right track.
 
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I have also managed to introduce a few new variables. I have introduced h+H=5 (The length of the rope) and y and y+0.75
 
Consider the 'free body' diagram for a thin vertical slice of the rope directly under the pulley (thin compared with radius of pulley). What does this tell you about the tension each side?
 
Tension is the same. I tried to find similar triangles and worked with them but I am getting equations with x^4.
 

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