Final answer:
The work done to stretch a bungee cord can be found by integrating the force function over the distance the cord is stretched. For the provided force function F(x) = k1x + k2x^3 with given constants, integration from 0 to 16.7 m will yield the required work.
Step-by-step explanation:
Calculating Work Done on a Bungee Cord
The work done to stretch a bungee cord can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. However, in the case of a bungee cord being stretched, we are looking at the work done against the elastic potential energy stored in the cord.
To find the work done on a bungee cord with a nonlinear elastic force, one must integrate the force function over the distance it is stretched. Given the force function F(x) = k₁x + k₂x³, where k₁ is the linear spring constant and k₂ is the nonlinear coefficient, and x is the distance stretched from equilibrium, the work W is given by:
W = ∫ F(x) dx = ∫ (k₁x + k₂x³) dx
For the specified force function with constants k₁ = 204 N/m and k₂ = -0.233 N/m³, one would need to integrate this function from 0 to 16.7 m to calculate the total work done to stretch the cord by 16.7 m.