# Statics (smooth pin + tension)

• Feb 10th 2010, 04:53 PM
jegues
Statics (smooth pin + tension)
1. The problem statement, all variables and given/known data
See figure.

2. Relevant equations
sum Fx = 0
sum Fy = 0
sum M = 0

3. The attempt at a solution
See figure (written in my writing).

Are the tensions A and B suppose to be the same? I imagine not because they are at different angles so they have different magnitudes but at the same time tension should be constant over the smooth pulley.

I'm having trouble solving the tension in ADB.

Any ideas?
• Feb 11th 2010, 04:58 AM
Hello jegues
Quote:

Originally Posted by jegues
...Are the tensions A and B suppose to be the same?

Yes. You have given the correct reason why:
Quote:

tension should be constant over the smooth pulley.
...and the additional clue is in the question, which you quote:
Quote:

There's only one tension asked for, so it must be the same in both parts of the cable.

• You have the angle at $\displaystyle A$ wrong. $\displaystyle \tan A = \tfrac25$, not $\displaystyle \tfrac 23$.

• Your $\displaystyle \Sigma f_x$ and $\displaystyle \Sigma f_y$ equations are OK apart from this (and, of course, you need to put the same tension in both parts of the cable). Then:

• You need to take moments to solve this problem. If you take moments about $\displaystyle C$, you'll get the tension immediately. Then use the $\displaystyle \Sigma f_x$ and $\displaystyle \Sigma f_y$ equations to find the reaction at $\displaystyle C$.

Here's the $\displaystyle \Sigma M$ equation:
$\displaystyle T\times AC\sin\angle A+T\times BC\sin\angle B - 40\times 5.5=0$
Can you complete it now?