Question

A telephone lineman is told to stretch the wire between two poles so the poles exert an 800N force on the wire. As the lineman does not have a scale to measure forces, he decides to measure the speed of a pulse created in the wire when he hits it with a wrench. The pulse travels 60m from one pole to the other and back again in 2.6s. The 60m wire has a mass of 15kg.

Should the wire be tightened or loosened?

A. Loosened
B. Tightened

Answer 1

Answer: f = 532.46 N

Explanation:

V = √(f / u) is the formula that describe the relationship between the speed of a pulse moving on a rope, and the force being exerted on the rope.

u = m / L, such that

u = 15 / 60

u = 0.25 kg/m

We calculate the speed of the pulse

v = distance / time

v = (2 * 60) / 2.6

v = 46.15 m/s

v = √(f / u)

F = uv²,

F = 0.25 * 46.15 * 46.15

F = 532.56 N

The rope should be tightened because the force in the wire is less than the required force.

Answer 2

The wire in the given case should be tightened.

Based on the given information,

• The mass (M) of the wire is 15 kg.  

• The length (L) of the wire is 60 m.  

• The time (t) of travel is 2.6 s and the distance (d) travelled is 2×60 m = 120 m.  

Now the relationship between the velocity and tension can be determined by,

$v = \frac{d}{t}$

$=\sqrt{\frac{T}{M/L}$

$T = \frac{M}{L} ({d/t)^{2} }$

$T = \frac{15}{60} *(120/2.6)^{2} \\T = 532.455 N$

As it can be seen that the tension is small, thus, there is a need to tighten the wire.

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