Chapter 1, Problem 1P

A constant force $F=2N$ is applied to a spring and the displacement x is measured as 0.2 m. If the spring force and displacement satisfy the linear relation $F=kx$, find the stiffness k of the spring.

To determine

The stiffness $k$ of the spring.

Answer to Problem 1P

The stiffness $k$ of the spring is $10\text{ N/m}$

Explanation of Solution

Given:

The constant force $F=2\text{ N}$ is applied to a spring, the displacement of the spring is $x=0.2\text{ m}$ and the linear relation of spring force and the displacement is $F=kx$.

Concept Used:

The relation of spring force and the displacement.

  $F=kx$ ...... (1)

Calculation:

Substitute $2\text{ N}$ for $F$ and $0.2\text{ m}$ for $x$ in equation (1)

  $2\text{ N}=k\left(0.2\text{ m}\right)$

Rearrange for $k$

  $\begin{array}{c}k=\frac{2\text{ N}}{\left(0.2\text{ m}\right)}\\ =10\text{ N/m}\end{array}$

Conclusion:

Thus, the stiffness $k$ of the spring is $10\text{ N/m}$