Final answer:
The potential energy stored in the ideal spring, when a force of 13.4 N compresses it, can be calculated using the formula U = 1/2 kx², resulting in 4.33 J of potential energy, which does not match the provided options.
Step-by-step explanation:
The question involves calculating the potential energy stored in an ideal spring when a force is applied to it. The formula to calculate the potential energy (U) stored in a spring is given by U = 1/2 kx², where k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this scenario, we are told that a force of 13.4 N holds the spring in compression, and the spring constant (k) is 20.8 N/m. To find the displacement (x), we can use the formula F = kx, which gives us x = F/k. Substituting the given values, we get x = 13.4 N / 20.8 N/m = 0.644 m (or 64.4 cm). Next, using the potential energy formula, U = 1/2 (20.8 N/m)(0.644 m)², we can calculate the potential energy stored in the spring.
Therefore, the potential energy stored in the spring equals 1/2 * 20.8 * (0.644)² = 4.33 J. Among the given options, none directly match this calculated value, so it would seem there's a mistake in the provided options or the values given in the question.