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In the static configuration of rectangular blocks shown below, we will assume that the gravitational force acting on each block is $1$. Each also has uniform density. We will also assume that:

  1. $(x_1,f_1)$ is the location and magnitude of the force that the ground exerts on block $1$.
  2. $(x_2,f_2)$ is the location and magnitude of the force that the ground exerts on block $2$.
  3. $(x_3,f_3)$ is the location and magnitude of the force that block $1$ exerts on block $3$.
  4. $(x_4,f_4)$ is the location and magnitude of the force that block $2$ exerts on block $3$.

3 blocks

By looking at the net force and net torque on each block it is easy to get six equations in eight unknowns. Am I correct in concluding that this system is statically indeterminate? Or am I missing something? If this this true then how would I solve for each of the $x_is$ and $f_is$?

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You are correct that is problem is statically indeterminate. Each contact has two unknowns (either two forces at the ends, a force and a moment at a fixed location, or a force and an arbitrary location). So you accounting for 4 contacts = 8 unknowns is correct, and each block has two equations of motion.

Having said that, there can be some reasonable assumptions that eliminate two unknowns. Those would be that the location $x_3$ and $x_4$ are known to be at the outside edges of block 3. The assumption is reasonable because the location of contact is very sensitive to any infinitesimal slope that blocks have (being a line-to-line contact). And parts being always elastic in real life, you can expect the inside edges of blocks 1 and 2 to deform downwards more than the outside edges.

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