Question

An ethernet cable is 4.15 m long and has a mass of 0.190 kg. A transverse pulse is produced by plucking one end of the taut cable. The pulse makes four trips down and back along the cable in 0.875 s. What is the tension in the cable?

Answer 1

Given

Length of the cable \(l=4.15 \mathrm{~m}\) Mass \(m=0.190 \mathrm{~kg}\)

Time \(t=0.875 \mathrm{~s}\)

The speed of the wave is

$$ \begin{aligned} v &=\frac{\text { Total distance }}{\text { time }} \\ &=\frac{4(8.3 \mathrm{~m})}{(0.875 \mathrm{~s})} \\ &=37.94 \mathrm{~m} / \mathrm{s} \end{aligned} $$

The tension in the cable is

$$ \begin{aligned} T &=v^{2} \mu \\ &=(37.94 \mathrm{~m} / \mathrm{s})^{2}\left(\frac{0.190 \mathrm{~kg}}{4.15 \mathrm{~m}}\right) \\ &=65.9 \mathrm{~N} \end{aligned} $$