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## Homework Statement

The object is balance. Calculate T

_{1}and T

_{2}. (yes, this plus the diagram is really the entirety of the question)

## Homework Equations

Στ = 0

τ = F⋅r

F = mg

## The Attempt at a Solution

First, we treat the left side as a fixed point and solve for the vertical component of T

_{2}

Στ = 0

20⋅9.8⋅1 + 10⋅9.8⋅1.5 - 2T

_{2y}= 0

343 = 2T

_{2y}

T

_{2y}= 171.5

Next, we treat the right side as fixed and solve for the vertical component of of T

_{1}

Στ = 0

0.5⋅10⋅9.8 + 1⋅20⋅9.8 - 2⋅T

_{1Y}= 0

245 = 2T

_{1Y}

T

_{1Y}= 122.5

To verify, we check that the sum of the forces up should equal the sum of the forces down

T

_{1Y}+ T

_{2Y}= 20*9.8 + 10 * 9.8

171.5 + 122.5 = 196 + 98

294 = 294

And this is the point where I get stuck. As far as I can tell, the situation is balanced for all cases where the force left due to T

_{1}is equal to the force right due to T

_{2}, meaning you have everything from the case where both wires are vertical (and thus the x-components of their tension is zero) to the case where both are nearly horizontal (and the x-components of both approach infinity) being true.

What am I missing?