Topic: Machine Design
A closed-coil helical compression spring with 20 active coils has a spring stiffness of K. It is cut into two parts having 8 and 12 active coils respectively. What is the stiffness of the spring with 8 active coils?
- A. 1.5 K
- B. 2.0 K
- C. 2.5 K
- D. 3.0 K
Answer: C. 2.5 K
Explanation: The stiffness of a helical spring ($k$) is inversely proportional to the number of active coils ($n$), i.e., $k \propto \frac{1}{n}$. Thus, $k_1 n_1 = k_2 n_2$.
$K \times 20 = k_{new} \times 8 \implies k_{new} = K \times \frac{20}{8} = 2.5 K$.