A high wire artist is going to walk across a steel wire that has a diameter of 1

Question

A high wire artist is going to walk across a steel wire that has a diameter of 1.3 cm and a length of 33 m. Before stepping on the wire, the person touches it and notices that it takes 1.4 s for a pulse to travel the length of the wire and return.
(a) What is the speed of the pulse?
m/s
(b) What is the mass of the wire?
kg
(c) What is the tension in the cable?
N
(d) If the tension in the cable were to increase by a factor of 2.00 and no other changes were made, by what factor will the speed of the pulse change?

Explanation / Answer

a)
distanec travelled d = 66 m time taken t = 1.4 sec v = 66 / 1.4    = 47.14 m/s

(b) The wire is in cylindrical so volume of wire v = r2l                                                                    = (3.14)(0.0065 m)2(33m)                                                                    = 0.0043 m3 density of steel = 7900 kg / m3

Mass of wire = density * volume                      = (7900 kg / m3)(0.0043 m3)

                     =  34.58 kg

c) v2 = T / (m/L)

     T = v2 . (m / L)              = ( 47.14 m/s)2(34.58 kg / 33m)          = 2328 N
(d) The speed increased in factor = sqrt (2)                                               = 1.414

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