Question

A cable pulled tightly and fixed at both ends is 4.0 m long and has a mass of 2.0 kg. A transverse pulse is produced by plucking one end. The pulse makes 4 trips down and back along the cable in 0.80 s. What is the tension in the cable?

Answer 1

Answer:

800 N

Explanation:

m = Mass of cable = 2 kg

L  = Length of cable = s = 4 m

t = Time taken = 0.8 seconds

Linear density is given by

$\mu=\dfrac{m}{L}\\\Rightarrow \mu=\dfrac{2}{4}\\\Rightarrow \mu=0.5\ kg/m$

Velocity is given by

$v=\dfrac{s}{t}\\\Rightarrow v=\dfrac{4\times 2\times 4}{0.8}$

Velocity is also given by

$v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow T=v^2\mu\\\Rightarrow T=(\dfrac{4\times 2\times 4}{0.8})^2\times \dfrac{2}{4}\\\Rightarrow T=800\ N$

The tension in the cable is 800 N