Chapter 11, Problem 1PLA

To determine

The definition and equation of the spring constant and its unit.

Answer to Problem 1PLA

Spring constant is the force per unit elongation, $k=\frac{\left|F\right|}{\left|x-x_0\right|}$. And its unit is $\text{N}/\text{m}$.

Explanation of Solution

Spring constant is the force per unit elongation of the spring. The spring constant $k$ is different for different material of the spring.

Write the expression of Hooke’s law

    $F=-k\left(x-x_0\right)$

Here, $F$ is the force, $k$ is the spring constant, $x$ is the length of the spring after elongation and $x_0$ is the natural length of the spring.

Rearrange the above equation and solve for $k$

$k=\frac{\left|F\right|}{\left|x-x_0\right|}$

The unit of spring constant $k$ is $\text{N}/\text{m}$.

Conclusion:

Thus, spring constant is the force per unit elongation, $k=\frac{\left|F\right|}{\left|x-x_0\right|}$. And its unit is $\text{N}/\text{m}$.