Question

A certain uniform spring has spring constant. Now the spring is cut in half. What is the relationship between andthe spring constant of each resulting smaller spring? Explain your reasoning.

Short answer

When a spring of spring constant Kis cut in half the spring constant of each of the resulting smaller springs is 2K.

Step-by-step solution

Given data

A spring of spring constant K is cut in half.

Step 2:Variation of spring constant

Two springs of the same material but having different lengths l₁ and l₂have their spring constants K₁ and K₂related as

$l{}_1{k}_1=l_2{k}_2$

Determining the new spring constant when the length is halved

Let the initial length be L . Length of the new pieces when the spring is cut in half is L/2.

Thus from equation (I)

$$\begin{gathered} Lk=\frac{L}{2}k\text{'} \\ k\text{'}=2k \end{gathered}$$

Hence spring constant of each of the new pieces is2 K.