Question

An athlete of average size is hanging from the end of a 20 m long rope, which has a mass of 4 kg and is attached to a hook in the ceiling of a gym. If the athlete makes a sudden movement at the end of the rope, estimate how long it will take the disturbance to reach the hook.

Answer 1

The tension in the rope would be necessary. Supposing it is the weight of the athlete, we have:

\(\mathrm{T}=\mathrm{W}=\mathrm{m}_{\mathrm{a}} \mathrm{g}\) (consider a mass of \(70 \mathrm{~kg}\) )

The speed of the transversal wave has the formula:

\(v_{t}=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{m_{a} g l}{m_{r}}} \approx 58.6 \mathrm{~m} / \mathrm{s}\)

miu=mass of unit length of the rope

\(\mathrm{m}_{\mathrm{r}}=\) mass of the rope

The time to reach the hook: \(\mathrm{t}=\mathrm{l} / \mathrm{v}_{\mathrm{t}} \sim 0.34 \mathrm{~s}\).

The numerical result might be different, but the tension or the mass of the athlete is necessary.