A chain lies on a rough horizontal table. It starts sliding...

A chain lies on a rough horizontal table. It starts sliding when one-fourth of its length hangs over the edge of the table. The coefficient of static friction between the chain and the surface of the table is
(a) $\frac{1}{2}$
(b) $\frac{1}{3}$
(c) $\frac{1}{4}$
(d) $\frac{1}{5}$

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Key Concepts

Static Friction

Static friction is the force that resists the initiation of motion between two surfaces in contact. It acts up to a maximum threshold determined by the coefficient of static friction multiplied by the normal force. This concept is crucial in understanding when an object, like a chain on a table, will begin to move as the gravitational force overcomes the resisting static friction force.

Equilibrium Analysis

Equilibrium analysis involves evaluating the balance of forces acting on a body. In the context of this problem, it is used to determine the point at which the gravitational force pulling the chain off the table exceeds the maximum static frictional resistance. Establishing this balance is key to predicting the onset of motion.

Distributed Mass Systems

A distributed mass system refers to objects whose mass is spread continuously over a length or area rather than concentrated at a point. When analyzing such systems, it is important to consider the contribution of each part of the object to overall forces and torques, as seen with a chain where the weight of the overhanging portion creates a net force that can initiate movement.

Transcript

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