According to a high wire artist he will do a trick where he is going to walk acr

Question

According to a high wire artist he will do a trick where he is going to walk across a steel wire which has a diameter of 1.6 cm and a length of 36 m. however before stepping foot on the wire, the artist touches it and notices that it takes 1.9 s for a pulse to travel the length of the wire and back.
(a) What would be the speed of the pulse?
1 m/s
(b) What would be the mass of the wire?
2 kg
(c) What would be the tension in the cable?
3 N
(d) suppose the tension in the cable were to increase by a factor of 1.60 and there were no other changes made, by what factor will the speed of the pulse change?
4

Explanation / Answer

Given Diameter of the wire , d = 1.6 cm Length of the wire , l = 36 m Radius of the wire, r = 0.8 cm Time taken for the pulse twice the length , t = 1.9 s a) Speed of the pulse, v = 2 l / t = 2 *36 m / 1.9 s                                   v = 37.9 m/s b) The mass of the wire , m = steel * V                                           = (7860 kg /m^3) *( r^2 l )                                       m =  (7860 kg /m^3) * 3.14 *(0.008 m)^2 *36 m                                       m = 56.86 kg ˜ 56.9 kg c) Tension in the cable by using the relation     v = T /     ---1 Here is the mass per unit length , = m / l = 56.9 kg / 36 m                                                       = 1.58 kg / m Now, 37.9 m/s = T / 1.58 kg/m               T = (37.9 m/s)^2 *1.58 kg / m               T = 2269.5 N d) If the tension is increased by a factor of 1.60, then from     eq 1 v T     v1 / v2 = T1 / T2     v1 / v2 = T1 / 1.6 T1       v2 = 1.6 v1       v2 = 1.26 v1 The speed will increase by a factor 1.26

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