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A cubic block with uniform density $\rho$ and side length $a$ rests on a slope, with one of its face facing directly downwards. The slop is inclined at an angle $\theta$ with the horizontal. Assume that the coefficient of friction is infinite.

The block will topple if $\theta>\pi/4$. When $\theta=\pi/4$, all reaction force of the slope concentrates at the lowest edge in contact with the slope.

Now, my question is, for a given value of $\theta$, what is the pressure at a point at the bottom of the block with a distance $x$ from the lowest edge? For $0\leq x\leq a$, the pressure $p(x)$ decreases, since a moment need to be generated by the reaction force to balance out the moment of gravity.

How can I find a formula for $p(x)$?

Ma Joad
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  • https://physics.stackexchange.com/q/95234/37364 – mmesser314 Oct 18 '19 at 03:54
  • Why do you think the pressure (normal stress) will vary over the surface in contact with the cube? – Bob D Oct 18 '19 at 06:02
  • This would have a (probably complicated) solution for a block of rubber. Then you could take the limit as the block becomes inelastic. However, the elastic properties have multiple parameters, so there might be different results depending on how you take the limit in the parameter space. – Keith McClary Oct 25 '19 at 05:11

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