Final answer:
A mountain climber's nylon rope with a force constant of 1.40 × 10⁴N/m would stretch under the climber's weight, and conservation of energy can be used to determine its stretch during a fall. The subject of the question is about the stretching of nylon climbing ropes, not the minimum breaking strength of manila ropes.
Step-by-step explanation:
When a 65.0-kg climber hangs from a nylon rope with a force constant of 1.40 × 104N/m, using Hooke's law and the concept of elasticity, it's possible to calculate the amount the rope would stretch. Although the information provided does not directly state the minimum breaking strength of manila rope used for lifelines, it closely relates to the tensile strength and stretching properties of nylon climbing ropes under similar conditions.
In the context of a climber who free-falls 2.00 m before the rope runs out of slack, conservation of energy principles can be applied to determine how much the rope stretches to break the fall.