Serway & Jewett — Energy of a System: Problem 17.

When different loads hang on a spring, the spring stretches to different lengths as shown in the following table. (a) Make a graph of the applied force versus the extension of the spring. (b) By least-squares fitting, determine the straight line that best fits the data. (c) To complete part (b), do you want to use all the data points, or should you ignore some of them? Explain. (d) From the slope of the best-fit line, find the spring constant \(k\). (e) If the spring is extended to \(105\text{ mm}\), what force does it exert on the suspended object? | \(F\text{ (N)}\) | 2.0 | 4.0 | 6.0 | 8.0 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | \(L\text{ (mm)}\) | 15 | 32 | 49 | 64 | 79 | 98 | 112 | 126 | 149 | 175 | 190 |