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A solid square table has an object on it, as shown below. There's an object at $M$ on one of its diagonals with $\dfrac{OM}{OC}=k$. Find the support force on table legs.

enter image description here

It is easy to see $N_B=N_D$. We do force analysis on the whole to get $$2N_B+N_A+N_C=G.$$ Then we do torque analysis on $AC$. In this case, $N_B,N_D$ doesn't contribute so $$kG=N_A+N_C.$$

I don't see anything else apart from these.

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  • $\begingroup$ With four legs the problem is indeterminate. You would need to know the elastic properties of the table. $\endgroup$
    – mike stone
    Sep 3, 2022 at 15:01
  • $\begingroup$ @mikestone The legs and table has no mass and never bends. $\endgroup$
    – youthdoo
    Sep 3, 2022 at 15:04
  • $\begingroup$ If it is compleletly rigid, then there is more than one answer. $\endgroup$
    – mike stone
    Sep 3, 2022 at 15:09
  • $\begingroup$ The problem is identical to finding the barycentric coordinates of point M given a polygon shape. $\endgroup$ Sep 3, 2022 at 15:36
  • $\begingroup$ @JohnAlexiou Why is that? $\endgroup$
    – youthdoo
    Sep 4, 2022 at 5:58

1 Answer 1

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Since, the table is in rotational equilibrium (as it does not topple), so torque about any point should be zero.

So, try to balance torque about points where torque due to either Na or Nc = 0 (i.e. - about points A and C) as an attempt to increase our equations with less number of variables in an attempt to simplify the math.

You could have also tried to balance torque about points B or D, but that will worsen the math out there for which you will require some geometry and cosine laws.

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