Final answer:
Cutting a spring into two halves doubles the spring constant of each half. As the potential energy stored in a spring is directly proportional to the spring constant, the potential energy in each half would also be doubled, assuming the same amount of compression.
Step-by-step explanation:
When a spring is cut into two equal parts, its spring constant k is doubled. Considering the formula for the potential energy (PEs) stored in a spring is PEs = 1/2kx², where k is the spring constant and x is the compression or elongation from its rest length, if each new spring is compressed the same amount as the original, the potential energy stored in each half would be doubled.
This is because the potential energy is directly proportional to the spring constant. If you originally had a spring with a constant of 120 N/m and you compress it by 3 cm, the potential energy stored is 1/2 × 120 N/m × (0.03 m)². If the spring were cut in half, the new spring constant would be 240 N/m, and the potential energy stored on compressing the cut spring by 3 cm would now be 1/2 × 240 N/m × (0.03 m)², which results in a doubling of the stored energy.