Final answer:
The potential energy stored in the ideal spring is calculated to be 110 Joules using the formula for elastic potential energy with the derived spring constant from the force and displacement provided.
Step-by-step explanation:
To calculate the potential energy stored in an ideal spring, we use the formula for elastic potential energy: PE = ½ kx², where k is the spring constant, and x is the displacement from the spring's rest position. In this case, the question directly provides the force (550 N) and the distance (0.400 m) but not the spring constant. However, we can derive the spring constant from Hooke's Law, which states that the force exerted by a spring is equal to the spring constant multiplied by the displacement: F = kx. Therefore, the spring constant k can be calculated as k = F / x. Once we find k, we insert it into the potential energy formula to get the answer.
The spring constant would be k = F / x = 550 N / 0.400 m = 1375 N/m. Now, the potential energy stored in the spring is PE = ½ (1375 N/m)(0.400 m)² = 110 J.