# Statics: Belt friction

1. Aug 11, 2013

### yaro99

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

2. Relevant equations
T1/T2=eμs
where T2 is the larger tension and β is the angle between the tensions.

3. 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 = e0.25*((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 = e0.25*(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.

2. Aug 11, 2013

### 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.