Final answer:
Without additional data pertaining to the spring constant (k) or the work done for a specific displacement, it is not possible to solve for the natural (unstretched) length of the spring based on the information provided about the energy required for its stretching.
Step-by-step explanation:
To determine the natural length of the spring, we need to understand the relationship between the energy stored in the spring and its extension from the natural length. The work done to stretch or compress a spring can be calculated using the following formula for elastic potential energy: W = 1/2 k x^2, where W is the work done on the spring, k is the spring constant, and x is the displacement from its natural length.
In the given scenario, we know the work done but not the spring constant or the natural length. However, we can form a set of two equations based on the work done for two different extensions. For the first extension from 1m to 6m, the work done is 2 J and for the second extension from 6m to 8m, it is an additional 4 J.
Before proceeding, we must recognize that there isn't enough information to solve for the natural length of the spring directly from the given numbers; more information about the spring constant or the actual work involved for a specific displacement is necessary.