# Statics Problem: hanging disk, tensions etc.

1. May 30, 2012

### jstone326

1. The problem statement, all variables and given/known data
The circular plate has a weight W and a center of gravity at its center. If it is supported vy three vertical cords tied to its edge, determine the largest distance d from the center to where any vertical force P can be applied so as not to cause the force in any one of the cables to become zero.
(see image)

2. Relevant equations
sum of Moments about somewhere are equal to 0

3. The attempt at a solution
I'm pretty lost as to how to start this problem. I think that I have to assume one of the tensions = 0, and that P would be located half way between C and A, thus making the angle between d and A/center = 60

Any help on how to approach this would be much appreciated.

Thanks

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2. May 31, 2012

### dikmikkel

You use newtons 1st law first:
$T_A+T_B+T_C - mg - P = 0$
Then the sum of Torques should also be zero at the limit:
$\vec{P}\times \vec{d} + \vec{T}_A\times \vec{r_A} +\vec{T}_B\times \vec{r_B} + \vec{T}_C\times \vec{r_C} = \vec{0}$
And use that the magnitude of the cross product of two vectors x,y is given by:
$\vec{x}\times \vec{y} = |x||y|\sin(\theta)$
So the point is, be careful with signs.