# Find the position of equlibrium

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1. Jan 23, 2017

### doktorwho

1. The problem statement, all variables and given/known data
From the diagram below find the position of the man ($x$) if the system is in balance. Total length is $L$ and the man is distance $x$ from one end.
2. Relevant equations
3. The attempt at a solution

I know that the system must be in balance if all the torque and all the forces equate to zero. That said i tried this:
The left tension force i name $T_1$ and the right $T_2$. And i take the right point as reference point.
$\sum M=T*L-mg\frac{L}{2}-Mg(L-x)=0$
$\sum F=T+F-(m+M)g=0$
These equation i know but still cnat express $x$ as i have too many unknowns. Could i eliminate something here?

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2. Jan 23, 2017

### Orodruin

Staff Emeritus
Hint: Look at the force equation for the lower pulley and pick a smart reference point for your torque computation.

3. Jan 23, 2017

### doktorwho

That force should equal the tension on the right, right? I picked a reference point to the right so it an be lost. Can you provide another hunt so i can see what you mean?

4. Jan 23, 2017

### TomHart

I think there is something wrong with your sum of forces equation.

5. Jan 23, 2017

### Orodruin

Staff Emeritus
Which force? There are three forces acting on that pulley.