Question

A uniform spring of force k is connected into two pieces of length in ratio 1:2 .What is the force constant of each piece in terms of k?

Answer 1

A uniform spring of force $k$ is connected into two pieces of length in ratio 1:2. What is the force constant of each piece in terms of $k$?

**Solution:**

Force constant is inversely proportional to the length of the spring ($L_1$ - length of the smaller part of the spring, $L_1$ - length of the bigger part of the spring):

$$k_1 = k \frac{L}{L_1} = k \frac{L}{\frac{1}{3}L} = 3k$$ $$k_2 = k \frac{L}{L_2} = k \frac{L}{\frac{2}{3}L} = 1.5k$$

**Answer:** Force constant of the part $\frac{1}{3}L$ (smaller part) is $3k$, force constant of the part $\frac{2}{3}L$ (bigger part) is $1.5k$