A research team is designing an experiment in which a short pulse must arrive at a sensor 25.0 m away along a taut synthetic fiber line no more than 0.180 s after emission. The fiber must be as light as possible while still meeting this timing requirement.
(a) If the maximum allowable tension that the apparatus can safely maintain is 350 N, determine the largest permissible value of the fiber’s mass per unit length.
(b) The available fiber has a density of 970 kg/m³ and a solid cylindrical cross-section. Using your result from part (a), calculate the maximum diameter the fiber may have.
(c) Suppose the team chooses a fiber whose actual diameter is 10 % smaller than the maximum calculated in part (b). Keeping the tension at 350 N, compute the pulse travel time along the 25.0 m length and evaluate whether the design meets the 0.180 s criterion.
(d) Discuss two practical factors—other than mass per unit length—that could influence the actual arrival time of the pulse in the real-world experiment, and describe how each factor might be mitigated.