202211031053 Statics Figures (Elementary) Q2

87. A homogeneous chain (i.e., \rho =\textrm{Const.}) with a length l lies on a table. What is the maximum length l_1 of the part of the chain hanging over the table if the coefficient of friction between the chain and the table is k?

Extracted from B. Bukhovtsev et al. (1978). Problems in Elementary Physics.


Roughwork.

\begin{aligned} f = kN & = W_1 \\ k\rho (l-l_1)g & = \rho l_1g \\ \end{aligned}

Answer. \displaystyle{l_1=l\frac{k}{k+1}}.