This is actually for a computer science homework problem, but I haven't studied any physics in five years so I'm having a bit of trouble. I'm given a table of three legs with their coordinates and I am told that a weight is placed at some coordinate $(x_0, y_0)$ on the table. (We are told to disregard the weight of the table itself in our calculations)
We have to first balance the forces; since this is a static system I would assume that, for $F_1, F_2, F_3, W$ the forces exerted by each leg and the weight, we have $F_1 + F_2 + F_3 + W = 0$. On the other hand, intuition is telling me that the forces exerted opposing the weight on the table would be related to the position of the weight, since it is not necessarily centered. I would think that they would be inversely proportional to the distance between the weight and each leg.
We need to solve a system of linear equations for the three forces after being given the value of W and its position. I have the two other linear equations which are calculating torque of the three forces over x and y axes. I am just unsure of how to represent the position of the weight in my system.
Torque equations as requested: $\frac{\cos(7\pi/6)}{\sqrt{3}}F_2 + \frac{\cos(11\pi/6)}{\sqrt{3}}F_3 = 0$ and $\frac{1}{\sqrt{3}}F_1 + \frac{\sin(7\pi/6)}{\sqrt{3}}F_2 + \frac{\sin(11\pi/6)}{\sqrt{3}}F_3 = 0$ for table-leg vertices at $(0,\frac{1}{\sqrt{3}}), (\frac{1}{2},\frac{-1}{2\sqrt{3}}), (\frac{-1}{2}, \frac{-1}{2\sqrt{3}})$.
The equations may be wrong, I'm pretty rusty with this stuff. Tips would be appreciated.
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