Final answer:
The energy stored per unit extension of a spring is not E - k. Instead, it is derived from the potential energy stored in the spring, calculated with the formula PEs = ½kx², where k is the spring constant and x is the extension. The energy per unit extension simplifies to ½kx.
Step-by-step explanation:
When considering the potential energy of a spring, we often refer to the expression for calculating the energy stored as a result of stretching or compressing a spring. According to Hooke's Law, the force F required to do so is proportional to the displacement x from its undeformed state, with a proportionality constant k, known as the spring constant. The formula PEs = ½kx² defines the potential energy stored in the spring, where PEs is the spring's potential energy, k is the spring's force constant, and x is the displacement from its original, undeformed position.
The energy stored per unit extension, if we consider stretch x as the 'unit' extension, would be ½kx² divided by x, which simplifies to ½kx. However, the question as phrased suggests to subtract the spring constant from the energy, which seems to be a misunderstanding. The correct concept is that energy per unit extension is not simply E minus k but rather derived from the potential energy equation by dividing the total energy by the extension x.