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

question 7

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.
$\begin{array}{|c|c|}\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \\\hline 20 & 2.8 \\\hline 40 & 5.0 \\\hline 60 & 8.0 \\\hline 80 & 10.6 \\\hline 100 & 13.2 \\\hline\end{array}$

Find the equation of the line that seems to best fit the data. Use the model to estimate the elongation of the spring when a force of 50 kilograms is applied. Round your answer to one decimal place.

• A) \(13.2\) centimeters
• B) \(9.9\) centimeters
• C) \(3.3\) centimeters
• D) \(6.6\) centimeters
• E) \(5.0\) centimeters

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Definitions:

Substitutability

The degree to which one good can be replaced by another in consumption or production without affecting consumer satisfaction or output.

Price Elasticity of Demand

A gauge of demand elasticity in reaction to price adjustments for a particular commodity.

Unity

In economic terms, unity can refer to a sense of agreement or cohesion among members of a market or organization, striving towards common goals or values.