Question

A fireman wants to slide down a rope. The breaking lead for the rope is $\frac{3}{4}$ of the weight of the man. With what minimum acceleration should the fireman slide down? (Acceleration due to gravity is g)

Answer 1

Step1: Given data

The breaking lead for the rope is $\frac{3}{4}$ of the weight of the man

Step2: Formula used

$F=ma[F=force,m=mass,a=acceleration]$

Step3: Calculating the minimum acceleration

Newton's second law states that the force required to accelerate a body is equal to the product of its mass and acceleration. The acceleration will be smaller for a large mass. As a result, more force is required to accelerate the body.

The force is imparted through the rope as the firefighter slides down it. Tension is the force exerted on the rope.
The minimum tension at the rope when the fireman slide down is given as, $mg-\frac{3}{4}mg$

This force equating with the minimum tension at the rope, we get

$$\begin{gathered} ma=mg-\frac{3}{4}mg \\ a=g-\frac{3}{4}g \\ a=g\left(1-\frac{3}{4}\right) \\ a=\frac{g}{4} \end{gathered}$$

The fireman should slide down with a minimum acceleration of $\frac{1}{4}$ of the acceleration due to gravity.