Chapter 20, Problem 49P

Hooke's law, which holds when a spring is not stretched too far, signifies that the extension of the spring and the applied force are linear ly related. The proportionality is parameterized by the spring constantk. A value for this parameter can be established

TABLE P20.49

Experimental values for elongation x and force F for the spring on an automobile suspension system.

Displacement, m	0.10	0.17	0.27	0.35	0.39	0.42	0.43	0.44
Force, ${10}^4\text{N}$	10	20	30	40	50	60	70	80

FIGURE P20.49

Plot of force $\left({\text{in 10}}^4\text{newtons}\right)$ versus displacement (in meters) for the spring from the automobile suspension system.

experimentally by placing known weight son to the spring and measuring the resulting compression. Such data were contained inTable P20.49 and plotted in Fig. P20.49. Notice that above a weight of $40\times {10}^4$ N, the linear relationship be tween 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.