Question

A certain spring has stiffness$\mathbf{140}\mathbf{N}\mathbf{/}\mathbf{m}$. 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$280\mathrm{N}/\mathrm{m}$.

Step-by-step solution

Identification of given data

The given data can be listed below as:

The value of the spring stiffness is${\mathrm{K}}_{\mathrm{i}}=140\mathrm{N}/\mathrm{m}$

Significance of the spring stiffness

The stiffness is referred to as the property of a particular object that resists deformation under the action of an external force.

Calculation for the stiffness

The equation of the final stiffness of the spring is expressed as:

${\mathrm{K}}_{\mathrm{f}}=2{\mathrm{K}}_{\mathrm{i}}$

Here,${\mathrm{K}}_{\mathrm{f}}$is the final stiffness and ${\mathrm{K}}_{\mathrm{i}}$is the initial stiffness.

Substitute the values in the above equation.

$$\begin{gathered} {\mathrm{K}}_{\mathrm{f}}=2{\mathrm{K}}_{\mathrm{i}} \\ =2\times 140\mathrm{N}/\mathrm{m} \\ =280\mathrm{N}/\mathrm{m} \end{gathered}$$

Thus, the value of stiffness is$280\mathrm{N}/\mathrm{m}$