# Three-log problem [closed]

Three uniform round rigid cylindrical logs of the same size and weight are placed on a horizontal plane. The two at the bottom are touching each other, the third one is placed on the top as shown in the picture. The coefficient of friction between any two logs is $\mu_1$, the coefficient of friction between any log and the floor is $\mu_2$. For some asymptotic values of $\mu_{1}$ and $\mu_{2}$ one can immediately conclude about existence or non-existence of equilibrium. For example if both $\mu_{1}$ and $\mu_{2}$ are zero then obviously there is no equilibrium. Further, one can argue that if either $\mu_1$ or $\mu_2$ is zero than there is no equilibrium no matter what the other coefficient is. In general, for what values of $\mu_1$ and $\mu_2$ would this system be in equilibrium?

## closed as off-topic by user10851, ACuriousMind♦, CuriousOne, Emilio Pisanty, John RennieMar 2 '16 at 6:52

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• What picture? Is this a homework question? – naught101 Mar 1 '16 at 23:22
• @naught101: no, this is not a homework, just what I think is a fun physics question – Maxim Umansky Mar 1 '16 at 23:37
• @MaximUmansky: I kind of like it too but it looks like it's going to be closed any time now. – Gert Mar 2 '16 at 0:19
• Might help if the image was cropped properly. – naught101 Mar 2 '16 at 0:51
• @Gert: Glad to hear you like it, then go ahead and solve it before it is closed by all those people who don't! – Maxim Umansky Mar 2 '16 at 1:36