Final answer:
None of the answer options provided match the calculation for the spring constant and work based on Hooke's Law. The correct spring constant is approximately 40.875 N/m, and the work required to stretch the cord is approximately 2943 J.
Step-by-step explanation:
When a 50 kg person hangs from a 20 m bungee cord, and it stretches to a length of 32 m, we can find the spring constant by using Hooke's Law, which states that F = kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, the force applied equals the weight of the person (F = mg), which is 50 kg × 9.81 m/s² = 490.5 N. The displacement x is the amount the cord has stretched, which is 32 m - 20 m = 12 m.
Using Hooke's Law, we solve for k:
k = F/x = 490.5 N / 12 m = 40.875 N/m (approximately).
Since none of the provided options has this spring constant, we cannot choose any of them.
To calculate the work required to stretch the cord, we use the formula for the work done on a spring: W = ½ kx², where W is the work, k is the spring constant, and x is the displacement.
W = ½ × 40.875 N/m × (12 m)² = 2943 J (approximately)
Again, none of the options matches this value. Therefore, the correct answer is not listed among the given options A, B, C, or D.