 #1
guv
 77
 14
 Homework Statement:

Imagine a table shaped as a regular hexagon with length ##a## as shown in the attached figure. The table itself is massless. The table has 6 legs supporting it at each vertex on a leveled ground. Table itself is also horizontal.
Use the bottom left of the hexagon as the origin with side ##a## pointing to the right. Now suppose a force F is applied at a point ##(x,y)## on the table, what would be the force in each leg supporting the table?
The problem can be dimensionalized so the length ##a## is not really important, one can pretend ##a=1##
 Relevant Equations:

$$\vec F_{net} = 0$$
$$\vec \tau = 0$$
We know that the net force on the table must be zero
$$\sum F_i = F$$
We know that the components of the torque with respect to the origin is also 0.
$$\sum \tau_x = 0$$
$$\sum \tau_y = 0$$
$$\sum \tau_z = 0$$
But the problem becomes insufficiently constrained that there are only 4 equations while there are 6 potential unknowns other than the trivial symmetric cases. How to solve the 6 different tension force in each leg for arbitrary position ##(x,y)## where the force ##F## is applied?
Thanks
$$\sum F_i = F$$
We know that the components of the torque with respect to the origin is also 0.
$$\sum \tau_x = 0$$
$$\sum \tau_y = 0$$
$$\sum \tau_z = 0$$
But the problem becomes insufficiently constrained that there are only 4 equations while there are 6 potential unknowns other than the trivial symmetric cases. How to solve the 6 different tension force in each leg for arbitrary position ##(x,y)## where the force ##F## is applied?
Thanks