Final answer:
The potential energy of a spring can be calculated with the formula U = 1/2 k x^2, where k is the spring constant and x is the displacement from the equilibrium position. The potential energy change is found by calculating the energy at both displacements and finding the difference.
Step-by-step explanation:
To find the change in the potential energy of the spring, we can use the spring potential energy formula which is U = 1/2 k x^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position. The displacement should be calculated by subtracting the relaxed length of the spring from its current length.
The initial displacement is the initial length minus the relaxed length, which is 0.29m - 0.55m = -0.26m. The final displacement is 0.73m - 0.55m = 0.18m. Using the given spring constant of 810 N/m, we can calculate the initial and final potential energies: U_initial = 1/2 * (810 N/m) * (-0.26m)^2 and U_final = 1/2 * (810 N/m) * (0.18m)^2.
The change in potential energy (ΔU) is then U_final - U_initial. So, ΔU = (1/2 * 810 N/m * (0.18m)^2) - (1/2 * 810 N/m * (-0.26m)^2). This calculation will give you the change in potential energy between the two states of the spring.