Final answer:
The potential energy of a compressed spring with an initial energy of 13.5 J remains 13.5 J, as the potential energy in a perfect spring depends on the displacement, not on the direction of that displacement (compression or stretch).
Step-by-step explanation:
The subject of this question is Physics, specifically it pertains to the concept of elastic potential energy in springs as described by Hooke's law. According to the provided information, the spring in discussion has an initial elastic potential energy of 13.5 J. When a spring is compressed or stretched, its potential energy changes in accordance with the amount of displacement and the spring constant (k). The formula to calculate this energy is given by U = 1/2kx², where x is the displacement from the rest position. For a perfect spring, the potential energy will be the same whether the spring is compressed or stretched, if the displacement is the same.
Therefore, when the spring is compressed the potential energy remains 13.5 J assuming the displacement from the equilibrium position while compressed is the same as when it was stretched. No information provided in the question suggests a change in the displacement, and therefore the potential energy of the spring when compressed would also be 13.5 J.