Final answer:
The question is about calculating the stretch of a nylon climbing rope using Hooke's Law when a 65.0-kg climber is suspended from it. The calculated stretch, 9 cm, is reasonable for such material, which is not meant to stretch significantly.
Step-by-step explanation:
The question relates to the physical properties of a nylon climbing rope, specifically its minimum breaking strength when a climber is suspended from it. To determine the stretch of the rope when a 65.0-kg mountain climber hangs from it, we can use Hooke's Law, which states that the extension (Δx) is directly proportional to the force applied (F), which, for a climber's weight, would be their mass (m) times the acceleration due to gravity (g). The force constant (k) of the rope is given as 1.40 × 104N/m.
Using the formula F = k Δx, we rearrange to find Δx = F/k. Substituting the mass of the climber and acceleration due to gravity into the force value (F = mg), and knowing the force constant (k), we can calculate the stretch of the rope. The answer appears to be 9 cm, which is considered reasonable for a nylon climbing rope, as it's not designed to stretch excessively, unlike a bungee cord.