Hooke's Law states that the force F required to compress or stretch a spring (within its elastic limits) is proportional to the distance d that the spring is compressed or stretched from its original length. That is, F = kd, where k is a measure of the stiffness of the spring and is called the spring constant. The table shows the elongation d in centimeters of a spring when a force of F newtons is applied.

(a) Use the regression capabilities of a graphing utility to find a linear model for the data. 

(b) Use a graphing utility to plot the data and graph the model. How well does the model fit the data? Explain.

(c) Use the model to estimate the elongation of the spring when a force of 55 newtons is applied.

Transcribed Image Text:

F 20 d 1.4 2.5 40 60 4.0 80 5.3 100 6.6