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, Fk= 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) F =12.098d
B) Fd= 3.024
C) F = 6.049d
D) Fd= 4.537
E) F = 7.561d

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, Fk= 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) F =12.098d
B) Fd= 3.024
C) F = 6.049d
D) Fd= 4.537
E) F = 7.561d

Quizplus · Accepted Answer

The equation of the line that best fits the data should reflect Hooke's Law, F = kd. By examining the given data, we can see that as the force increases, the elongation also increases in a manner that suggests a linear relationship. Option C, F = 6.049d, is the correct choice because it represents a direct proportionality between force and elongation, consistent with Hooke's Law.

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