Solving for Tension in Two Block System

[Inertialforce]

Homework Statement

Two blocks of equal mass hang vertically from a ceiling as shown in the diagram. A horizontal string connects the two vertical strings. Determine the tension T1 in the horizontal string. All strings are considered to be massless.

Homework Equations

ΣFx and ΣFy

The Attempt at a Solution

m1 = m2 (therefore I referred to the masses as just "m")
angle = 90(degrees)

ΣFy = may
Ta + Tb -mg -mg = 0
Ta + Tb - 2mg = 0
Ta + Tb = 2mg
Ta = 2mg - Tb


ΣFx = max
TaT1 - TbT1 = 0
TaT1 = TbT1
(2mg - Tb)T1 = TbT1
T1 = TbT1 / (2mg-Tb)

I got this question wrong and since there are no numerical values given I am unsure as to where I am going wrong.

 

[alphysicist]

Homework Statement

Two blocks of equal mass hang vertically from a ceiling as shown in the diagram. A horizontal string connects the two vertical strings. Determine the tension T1 in the horizontal string. All strings are considered to be massless.

Homework Equations

ΣFx and ΣFy

The Attempt at a Solution

m1 = m2 (therefore I referred to the masses as just "m")
angle = 90(degrees)

ΣFy = may
Ta + Tb -mg -mg = 0
Ta + Tb - 2mg = 0
Ta + Tb = 2mg
Ta = 2mg - Tb

I would suggest you also draw the freebody diagram for just one mass; then you can find the tension in each string Ta and Tb (though I don't think you need them for this problem).

ΣFx = max
TaT1 - TbT1 = 0
TaT1 = TbT1
(2mg - Tb)T1 = TbT1
T1 = TbT1 / (2mg-Tb)

This expression for the x direction does not look right. For example, you can see that you can just cancel out the T1 completely from any of these equations. Also, the expression TaT1 - TbT1 = 0 does not have the right units to be a force equation, and Ta and Tb do not have any components in the horizontal direction.

Instead, when you are writing the horizontal equation, pick a specific point (for example, one knot where strings come together) and write the horizontal equation for that. What do you get?