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Water $(\backslash (\backslash$gamma$=62\mathrm{.}4\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{3\}\backslash ))$ is retained by a uniform thin semicircular dam having $1$ ft radius and $3$ ft depth into the plane of the figure. The dam weighs $70$ lb and is supported by a cable $\backslash ($ A C $\backslash )$ and by frictional contact with the bottom of the channel at $\backslash ($ B $\backslash ).$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Determine the minimum coefficient of friction required so that the dam does not slip at $\backslash ($ B $\backslash ).($Round the final answer to four decimal places.$)$

The minimum coefficient of friction is