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

AI Thread Summary
To solve the moving pulley problem with a 100 kg sack, the equilibrium conditions require analyzing the forces acting on the system. The equations TABCosθ + TBCCosφ = 0 and TABSinθ + TBCSinφ = 980N are essential for determining the tensions in the cables. The length of cable ABC is 5 m, and the horizontal distance from point C to the pulley is given as 3.5 - x. The tension in the cable remains constant on both sides of the pulley, and the introduction of height components is necessary for a complete analysis. The discussion highlights the complexity of the problem, particularly with the introduction of new variables and the challenge of solving equations involving higher powers of x.
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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