Hooke’s 1aw, which holds when a spring is not stretched too far, signifies that the extension of the spring and the applied force are linearly related. The proportionality is parameterized by the spring constant k. A value for this parameter can be established experimentally by placing known weights onto the spring and measuring the resulting compression. Such data is contained in Table P20.45 and plotted in Figure. Notice that above a weight of 40 x 10⁴ N, the linear relationship between the force and displacement breaks down. This sort of behavior is typical of what is termed a “hardening spring.” Employ linear regression to determine a value of k for the linear portion of this system. In addition, fit a nonlinear relationship to the nonlinear portion.

Caclooet, 0.10 0.17 0.27 0.35 0.39 042 0.43 044 Foce, 10 N 10 20 30 40 50 60 70 80 INooldeal behavoor spring is ardening Hooke's law 0.4: 0.2 Displacement, m Foree. 10* N