Question

A certain spring has stiffness 190N/m. The spring is then cut into two equal lengths. What is the stiffness of one of these half-length springs?

Short answer

The value of stiffness is 380N/m.

Step-by-step solution

Identification of given data

The given data is listed below as,

The value of the spring stiffness is, $k_i=190\mathrm{N}/\mathrm{m}$.

Significance of the spring stiffness

The stiffness is described as the ratio of the applied load to the deflection of the spring. It is expressed as follows,

$\mathbf{k}\mathbf{=}\frac{\mathbf{F}}{\mathbf{x}}$

Here, F is the spring force and x is the deflection.

Calculation for the stiffness

As, the spring is cut into two equal parts so, the stiffness becomes double so, the equation of the final stiffness of the spring is expressed as:

$k_f=2k_j$

Here, $k_j$is the initial stiffness.

Substitute the values in the above equation.

$$\begin{gathered} K_f=2K_i \\ =2\times 190\mathrm{N}/\mathrm{m} \\ =380\mathrm{N}/\mathrm{m} \end{gathered}$$

Thus, the value of stiffness is 380N/m.