C. Spring Constants There are two key quantities in determining the potential energy stored in a spring the spring constant (a measure of stiffness), and how much the spring is stretched or compressed from equilibrium. Let's determine the spring constant from your experiment in part B. You're using two springs so it isn't completely straightforward. We need to determine how the force and potential energy from your two spring arrangement is related to the results for a single spring. 1. This analysis should be obvious to you now. When your cart is at the center, both springs are stretched by the same amount. Call that stretch s. Construct a qualitatively accurate free body diagram for this situation and determine the net force. a. Now suppose your cart is displaced a distance x away from the center. Construct a new free body diagram and determine the net force in terms of the spring constant k. b. Now assume your two spring arrangement is equivalent to a single spring of constant K. How must K be related to k in order to produce the same amount of force? 2. This sort of analysis - figuring out a single thing that is equivalent to an arrangement of multiple things - is quite common in physics. You'll do it a lot in Physics II. When you start designing your cart engines, you may want to attach springs in various ways to achieve your design goals. So lets do the same analysis as in part 1 for two other ways of attaching multiple springs. a. Suppose you have two springs attached to a single object side by side. Determine the equivalent spring constant K