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Answer :
Final answer:
To calculate the stretch of the nylon rope when a 65.0-kg climber hangs from it, Hooke's Law would be applied using the rope's elastic properties. However, a numeric answer cannot be provided without the rope's specific spring constant or modulus of elasticity. Nylon ropes typically stretch less than bungee cords, which are designed for significant elongation.
Explanation:
To determine the amount of stretch in the nylon rope used by a 65.0-kg mountain climber, we will apply principles of physics to calculate the elongation caused by the force exerted by the climber on the rope. This force is due to the weight of the climber (mass multiplied by gravitational acceleration).
The calculation would require the use of Hooke's Law, which relates the force exerted on a spring-like object to its elongation (F = kx), where F is the force, k is the spring constant, and x is the elongation. Nylon rope has certain elastic properties, but it is not as elastic as a bungee cord, so it would not stretch as much under the same force.
The elongation of the nylon rope can be estimtated using material properties such as its modulus of elasticity and cross-sectional area, but without these specific values or the actual spring constant for the rope, we cannot provide a numerical answer. As per common observation, nylon ropes do have some stretch under load, but not to the extent of a bungee cord, which is specifically designed to stretch substantially to absorb energy safely.
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