# Torque on a suspended plank

1. Nov 24, 2014

### tzar1990

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

The object is balance. Calculate T1 and T2. (yes, this plus the diagram is really the entirety of the question)

2. Relevant equations

Στ = 0
τ = F⋅r
F = mg

3. The attempt at a solution

First, we treat the left side as a fixed point and solve for the vertical component of T2

Στ = 0
20⋅9.8⋅1 + 10⋅9.8⋅1.5 - 2T2y = 0
343 = 2T2y
T2y = 171.5

Next, we treat the right side as fixed and solve for the vertical component of of T1
Στ = 0
0.5⋅10⋅9.8 + 1⋅20⋅9.8 - 2⋅T1Y = 0
245 = 2T1Y
T1Y = 122.5

To verify, we check that the sum of the forces up should equal the sum of the forces down
T1Y + T2Y = 20*9.8 + 10 * 9.8
171.5 + 122.5 = 196 + 98
294 = 294

And this is the point where I get stuck. As far as I can tell, the situation is balanced for all cases where the force left due to T1 is equal to the force right due to T2, meaning you have everything from the case where both wires are vertical (and thus the x-components of their tension is zero) to the case where both are nearly horizontal (and the x-components of both approach infinity) being true.

What am I missing?

2. Nov 24, 2014

### SteamKing

Staff Emeritus
Unless you know the angles which T1 and T2 make with the horizontal, you can't work out the horizontal components of the tension.
Writing the moment equation can only give you the vertical component of the tensions.

3. Nov 24, 2014

### tzar1990

Thank you! That's what I told my student, but she seemed doubtful that an official question would have a misprint like that. Nice to hear that I'm not just missing something obvious.

4. Nov 24, 2014

### haruspex

... except that, knowing one angle would do.

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