A force of $55$ pounds stretches a spring $3$ inches. Use Hooke s Law to determine how far a force of $25$ pounds will stretch the spring. Round your answer to two decimal places.
A) $1.36$ inches
B) $2.68$ inches
C) $1.56$ inches
D) $1.68$ inches
E) $1.16$ inches

Question

Quizplus · Accepted Answer

Hooke's Law states that the force $F$ needed to extend or compress a spring by some distance $x$ is proportional to that distance. That is, $F = kx$, where $k$ is the spring constant. Given that a force of $55$ pounds stretches the spring $3$ inches, we can find $k = \frac{55}{3}$. To find how far a force of $25$ pounds will stretch the spring, we solve $25 = kx$ for $x$, giving $x = \frac{25}{k}$. Substituting the value of $k$ we found, $x = \frac{25}{\frac{55}{3}} = \frac{25 \cdot 3}{55} = \frac{75}{55} = 1.3636...$ inches, which rounds to $1.36$ inches.

A Force Of 555555 Pounds Stretches a Spring 333 Inches Use Hooke S Law to Determine How Far a Use

A Force Of $55$ Pounds Stretches a Spring $3$ Inches Use Hooke S Law to Determine How Far a Use