Maximum hanging length of a chain on a table – Rankers Physics

Friction: Practice Problem & Solution

A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is: (1991)
(20%)
(25%)
(35%)
(15%)

Solution Explained:

To solve this problem, we apply the core principles of Friction. Understanding the underlying formula is key to arriving at the correct answer below:

For equilibrium, the weight of the hanging part must equal the maximum static friction on the table. If (x) is the fraction hanging, then \(xMg = mu(1-x)Mg\). So, \(x = \mu(1-x)\). This gives \(x = \frac{\mu}{1+\mu}\). With \(\mu = 0.25\), \(x = \frac{0.25}{1+0.25} = \frac{0.25}{1.25} = 0.20\) or (20%).

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