Hooke's Law States That the Force $F$ Required to Compress or Stretch a Spring (Within Its Elastic

question 54

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 the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied.
$\begin{array}{|c|c|}\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \\\hline 20 & 3.5 \\\hline 40 & 6.3 \\\hline 60 & 10.0 \\\hline 80 & 13.3 \\\hline 100 & 16.5 \\\hline\end{array}$

Find the equation of the line that seems to best fit the data.

• A) \(\quad F = 12.098 d\)
• B) \(F = 3.024 d\)
• C) \(\quad F = 6.049 d\)
• D) \(\quad F = 4.537 d\)
• E) \(\quad F = 7.561 d\)

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Definitions:

Capacity Constraint

A limitation on the resources available for production, such as time, labor, or materials, which can affect the maximum output levels.

Double-subscripted Variables

Variables in mathematical modeling that are indexed by two sets, often used to represent the elements in a matrix or a two-dimensional array.

Capacity Constraint

A limitation or restriction on the maximum level of output that a system or process can handle.

Double-subscripted Variables

Variables that are identified by two subscripts, often used in mathematical and statistical models to represent two-dimensional data.