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

question 112

Multiple Choice

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, $F = k d$ 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.
$\begin{array}{|c|c|c|c|c|c|}\hline F & 20 & 40 & 60 & 80 & 100 \\\hline d & 1.9 & 3.8 & 5.7 & 7.6 & 9.5 \\\hline\end{array}$

• A) \(d = 0.675 F\)
• B) \(d = 0.118 \mathrm {~F}\)
• C) \(d = 0.112 F\)
• D) \(d = 0.095 F\)
• E) \(d = 0.905 F\)

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Definitions:

Summarizing Data

Summarizing data involves condensing large datasets into a simpler form, often through statistical analysis or visual representation.

Crosstab Query

A database query that aggregates information from one or more tables and displays it in a cross-tabulated format, often used for comparative analysis.

Calculates

The action of determining a numerical result based on given inputs or formulas, typically performed by software or a calculator.

Statistic

A numerical datum derived from a set of data, often used for analyzing and interpreting information.