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Two springs of force constants $k_1$ and $k_2$ are connected in series. What is the effective force constant $k_{\text{eff}}$ of the combination?
- A.$k_1 + k_2$
- B.$\frac{k_1 k_2}{k_1 + k_2}$
- C.$\frac{k_1 + k_2}{k_1 k_2}$
- D.$\sqrt{k_1 k_2}$
Show correct answer & step-by-step solution
Correct answer: B — $\frac{k_1 k_2}{k_1 + k_2}$
Solution
For springs in series, the total extension is the sum of individual extensions, leading to the relation . Solving this for gives .
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