A man wants to slide down a rope. The breaking load for the rope (2)/(3) rd of the weight of the

step 1 In this question we have given a fireman which wants to slide down on a rope and without breakin

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

A man wants to slide down a rope. The breaking load for the rope $\frac{2}{3}$ rd of the weight of the man. With what minimum acceleration should fireman slide down?
(a) $\frac{g}{4}$
(b) $\frac{g}{3}$
(c) $\frac{2 g}{3}$
(d) $\frac{g}{6}$

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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 product of its mass and acceleration. This principle is key in analyzing situations where an object is accelerating, as it allows us to form equations that balance the forces, such as gravitational force and tension, to determine how acceleration affects the net force on the object.

Rope Tension Under Acceleration

When an individual accelerates downward while hanging from a rope, the effective tension in the rope is reduced by the product of the mass and the acceleration in addition to the gravitational force. Understanding this relationship is crucial for calculating the tension in the rope and ensuring that it stays within safe limits, especially when there is a maximum allowable load.

Breaking Load Considerations

The breaking load is the maximum force a rope can endure before it fails. In problems where safety is a factor, comparing the calculated tension in the rope during acceleration with the rope's breaking load ensures that the system operates within safe limits. This concept is essential in engineering and physics to design systems that avoid structural failure.

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