Question

An old rope can now only safely suspended 120 kg. When the rope is tied to a beam, it hangs down with a vertical length of 12.0 m. Calculate the minimum time required for an 85kg person starting from rest to climb the entire length of the rope without breaking it

Answer 1

Explanations & Calculations

• The person can clime at some acceleration that would cause tension on the rope which is the maximum bearable.
• If that acceleration is taken as $\small a$ then by applying F = ma for the man's climb upwards

$\qquad\qquad \begin{aligned} \small T-mg&=\small ma\\ \small a&=\small \frac{120\times9.8\,ms^{-2}-85\,kg\times9.8\,ms^{-2}}{85\,kg}\\ &=\small 4.0\,ms^{-2} \end{aligned}$

• Then at this acceleration, he could climb the rope at a time of (using s = ut+1/2at^2)

$\qquad\qquad \begin{aligned} \small 12.0\,m&=\small 0+\frac{1}{2}\times4.0\,ms^{-2}\times t^2\\ \small t &=\small 2.4\,s \end{aligned}$