- #1

guv

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- 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