How does friction affect tension in a statics problem involving belt friction?

[yaro99]

Homework Statement

Homework Equations

T₁/T₂=e^μ_s*β
where T₂ is the larger tension and β is the angle between the tensions.

The Attempt at a Solution

Isolating each pipe:

W₁ = 50*9.81 = 490.5N
For pipe B, β = (2π)/3
For pipe C, β = π/3

For pipe B, T₂ = 490.5N, so I have:
490.5/T = e^{0.25*((2π)/3)}
T = 290.6N

Now here is where I made the wrong choice. On pipe C, I chose W₂ to be T₂ because if equilibrium is maintained, it would make sense for W₂ to be going down, not up. This got me the wrong answer.

Then I tried making T₂ = T instead:
290.6/W₂ = e^0.25*(π/3)
W₂ = 233.7N
m = 233.7/9.81 = 22.8kg

22.8kg is the right answer. I am just not understanding why T is the stronger tension on pipe C. It seems to me that it would cause the 50kg weight to start falling.

 

[Delphi51]

You mean as in the 290.6 N outbalancing the 233.7 N?
The friction force helps the weaker force to hold the balance.