Final answer:
The work done to stretch a bungee cord with a nonlinear elastic force can be calculated by integrating the force function over the distance stretched, using the specific constants for the bungee cord in the question.
Step-by-step explanation:
The magnitude of the non-linear elastic force exerted by a bungee cord can be modeled with the provided function F(x) = k₁x + k₂x³ where x is the distance the cord is stretched, k₁ is the linear spring constant, and k₂ is the cubic spring constant. To find the work done to stretch the cord by a certain distance, one would calculate the integral of the force over the distance stretched. Using the constants k₁ = 204 N/m and k₂ = -0.233 N/m³, the work done to stretch a bungee cord 16.7 m can be found by evaluating the integral of F(x) from 0 to 16.7 meters.