What are the tension forces and angles in this stationary equilibrium setup?

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The discussion focuses on calculating the tension forces and angles in a stationary equilibrium setup involving two crayon boxes and three cords. Box A, with a mass of 11.0 kg, is positioned on a frictionless ramp at an angle of θ = 30.0 degrees, while Box B, with a mass of 7.0 kg, hangs vertically. The tension forces are defined as TA for Box A, TB for Box B, and TC for the cord attached to the ceiling. The equations governing the system include TA = mA * g * sin(θ) and TB = mB * g * sin(θ), with the need to determine the angles for equilibrium.

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A stationary arrangement of two crayon boxes and three cords. Box A has a mass of 11.0kg and is on a ramp at angle θ=30.0 degrees; box B has a mass of 7.00 kg and hangs on a cord. The cord connected to Box A is parallel to the ramp which is frictionless (a) What is the tension in the upper cord, and (b) what angle does that cord make with the horizontal?



Let TA = tension force in the cord attached to block A.
TB = tension force in the cord attached to block B.
TC = tension force in the cord attached to ceiling.
φ = angle of cord attached to ceiling with the horizontal
θ = angle of ramp = 30 degrees

1.Ta-magsin
2.Tb-mbgsin=0
3.Tcsin=magsin+mbg
4.Tccos=magsin
5=T^2c(cos^2+sin^2)

that's what I know so far (on what equations to use for each step)
 

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I think you need to modify your diagram. The cord connected to A should be parallel to the ramp. The cord connected to B is vertical, but far enough to the right so that B is not in contact with the ramp (you're OK with this one) and the cord supporting the whole thing is NOT vertical. It makes whatever angle is needed to produce equilibrium. You need to have angles after your cos and sin in your equations so you know which angle you are talking about.
 

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