A fireman wants to slide down a rope. The breaking load for...

A fireman wants to slide down a rope. The breaking load for the rope is $\frac{3}{4}$ th of the weight of the fireman. The acceleration of the fireman to prevent the rope from breaking will be (Acceleration due to gravity is $g$ )
(A) $g / 4$
(B) $g / 2$
(C) $3 g / 4$
(D) Zero

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Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In the context of sliding down a rope, this law is used to relate the gravitational force, tension, and acceleration to ensure that the forces do not exceed the safety limits of the rope.

Tension in a Rope

Tension is the force exerted along a rope when it is pulled tight by forces acting from opposite ends. In problems like this, understanding how tension changes with acceleration is crucial since the rope's tension must not exceed its breaking load when supporting the weight of the fireman.

Breaking Load

The breaking load is the maximum force a rope can withstand before it fails. Here, it is specified as a fraction of the fireman’s weight, serving as a critical safety limit that dictates the maximum tension the rope can handle during the descent.

Force Analysis in Dynamic Systems

Analyzing the forces acting on the fireman by constructing a free-body diagram—including gravitational force and rope tension—allows one to apply Newton's Second Law effectively. This analysis is essential for determining the required acceleration that keeps the tension within the safe, predetermined limits.

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