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, 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. Use the regression capabilities of a graphing utility to find a linear model for the data. Round the numerical values in your answer to three decimal places.

Question

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,  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. Use the regression capabilities of a graphing utility to find a linear model for the data. Round the numerical values in your answer to three decimal places.

Quizplus · Accepted Answer

Using a graphing utility, we can plot the given data and perform a linear regression to find the best-fit line. The slope of the line will give us the spring constant k.

The table gives us the following data:

|  F (N)  |  d (cm)  |
|:------:|:-------:|
|   0.1  |   1.27  |
|   0.2  |   2.54  |
|   0.3  |   3.81  |
|   0.4  |   5.08  |
|   0.5  |   6.35  |

Plotting these points and performing a linear regression gives us the equation

d = 0.0254F + 1.27

Comparing this to the equation d = kF, we see that the spring constant k is equal to 0.0254. Rounding this to three decimal places gives us 0.026.

Therefore, the best answer is D) 0.026.

Hooke's Law States That the Force F Required to Compress