Final answer:
A mountain climber stretching a nylon rope, according to Hooke's Law
Step-by-step explanation:
To determine how much a 65.0-kg mountain climber stretches a 0.800-cm diameter nylon rope when hanging 35.0 m below a rock outcropping, we can use Hooke's Law. Hooke's Law states that the elongation of a material is directly proportional to the force applied to it.
- First, we need to find the force applied to the rope. The weight of the climber can be calculated using the formula: weight = mass * gravitational acceleration. Substituting the given values, we get weight = 65.0 kg * 9.8 m/s² = 637 N.
- The force applied to the rope is equal to the weight, so it is also 637 N.
- Using Hooke's Law, F = k * Δx, where F is the force, k is the force constant (also known as Young's modulus), and Δx is the elongation or stretch in meters.
- We can rearrange the equation to solve for Δx: Δx = F / k.
- Substituting the values, Δx = 637 N / (1.35 × 10^10 N/m²) = 4.72 × 10^(-8) m or 4.72 nm.
(b) The answer seems consistent with what we have observed for nylon ropes. Nylon ropes are known for their low stretchability, so a stretch of 4.72 nm for a nylon rope is plausible.
If the rope were actually a bungee cord, it would stretch much more than nylon. Bungee cords are designed to have a higher stretchability, enabling them to absorb and dissipate the energy when a person jumps off a platform.