Four springs are stretched to the same distance from the equilibrium position. the spring constants are listed in the table. which lists the springs based on the amount of elastic potential energy, from greatest to least? x, y, w, z x, w, y, z z, w, y, x z, y, w, x

The correct answer is: X, W, Y, Z

In fact, the elastic potential energy of a spring is given by

where k is the spring constant and x is the stretching of the spring with respect to its rest position.

In this problem, all the four springs are stretched by the same distance x. This means that their difference in potential energy is due only to the difference between their spring constant: the larger the spring constant, the greater the energy. Therefore we can list the springs from the one with largest spring constant to the one with smallest constant, and this list corresponds to listing the springs from the one with largest energy to the one with smallest energy:
X, W, Y, Z