Question

With what minimum acceleration can a fireman slide down a rope whose breaking strength is two-thirds of his weight?

Answer 1

Step 1: Assumption

Let the weight of the fireman be mg where g is the acceleration due to gravity and his downward acceleration be a.

The tension (T) will be, $T=\frac{2}{3}mg$

Step 2: Applying Newton's second Law

Applying Newton’s second law of motion on a foreman sliding downwards, The force will be the subtraction of weight and tension of the rope,

$$\begin{gathered} ma=mg-T=mg-\frac{2}{3}mg \\ a=\frac{g}{3} \end{gathered}$$

Hence, the minimum acceleration will be $\frac{g}{3}$.