A high wire artist is going to walk across a steel wire that has a diameter of 2

Question

A high wire artist is going to walk across a steel wire that has a diameter of 2.0 cm and a length of 32 m. Before stepping on the wire, the person touches it and notices that it takes 1.7 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) Time (t) taken to travel along the length of the wire = (1.7 s)/2                                                                                  = 0.85 s Distance (S) traveled by the pulse = 32 m Then speed (v) of the pulse is                  v = S / t                    = (32 m) / (0.85 s)                    = 37.65 m/s (b) Mass (m) of the wire is calculated as                  m = (density)(volume)                     = V                     = (7850 kg/m3)()(0.01 m)2(32 m)                     = 78.9 kg (c) Linear mass density () of steel wire is                   = m / L                      = (78.9 kg) / (32 m)                      = 2.47 kg/m Then tension (T) in the string is              T = v2                 = (37.65 m/s)2(2.47 kg/m)                 = 3495.8 N (d) If tension (T) is increased by 2 times, then speed (v) is increased by 2 times. (d) If tension (T) is increased by 2 times, then speed (v) is increased by 2 times.

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