Contact forces

[Inertialforce]

1. The problem statement, all variables and given/known data
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.


2. Relevant equations
ΣFx and ΣFy


3. 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]

1. The problem statement, all variables and given/known data
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.


2. Relevant equations
ΣFx and ΣFy


3. 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?