Final answer:
The potential energy of a spring, calculated as PEs = ½kx², represents the energy stored when a spring is displaced by x from its undeformed position. Potential energy in a spring is part of the total mechanical energy of a system involving conservative forces.
Step-by-step explanation:
The difference of potential energy in a spring is determined by the spring's force constant (k) and the displacement (x) from its undeformed position. According to Hooke's law, the potential energy of a spring (PEs) is given by the formula PEs = ½kx². This equation represents the energy stored within the spring when it is either stretched or compressed by the distance x. The potential energy is a form of mechanical energy, which for a conservative force, is the sum of kinetic energy (KE) and potential energy (PE).
When discussing the potential energy stored in the spring during an experiment with two carts connected by a spring with a spring constant of 120 N/m, where the spring compresses from 5.0 cm to 2.0 cm, the potential energy (U) at the point of maximum compression can be calculated using the formula U = ½kx², where x is the change in length from the original uncompressed length.