Calculate the stretch of a nylon climbing rope
How much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping?
a) Can the rope's stretch be calculated accurately using Hooke's Law?
b) Does the stretch seem consistent with what you would typically observe for nylon climbing rope?
Answer:
a) The rope's stretch under a 65.0-kg climber's weight could be calculated using Hooke's Law, yet cannot be precise without the modulus of elasticity for nylon. However, a 9 cm stretch is reasonable for a nylon climbing rope.
b) Bungee cords, with high elasticity, would stretch much more under the same conditions.
When a 65.0-kg mountain climber hangs 35.0 m below a rock outcropping using a 0.800-cm diameter nylon rope, the stretch of the rope can be calculated. However, without the modulus of elasticity for nylon, the calculation won't be accurate.
Nylon ropes used for climbing are designed to have limited elasticity. A 9 cm stretch for a 65 kg climber seems reasonable based on the general properties of nylon ropes.
If the rope were a bungee cord instead, we would expect much greater stretching due to its high elasticity and energy absorption capabilities. Therefore, a 9 cm stretch would be inconsistent with a bungee cord's properties.