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title: "Two ideal, massless springs have spring constants \\(k_1 = k\\) and \\(k_2 = 2k\\). In Scenario 1, the two springs are connected in series end-to-end to support a hanging block of weight \\(W\\) in static equilibrium. In Scenario 2, the same two springs are connected in parallel side-by-side to support the same hanging block of weight \\(W\\) in static equilibrium with equal stretch in both springs. What is the ratio \\(\\dfrac{\\Delta x_{\\text{series}}}{\\Delta x_{\\text{parallel}}}\\) of the total extension of the springs in Scenario 1 to the total extension in Scenario 2?"
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url: "https://nerd-notes.com/ubq/120568/"
date_modified: "2026-08-23T04:41:39+00:00"
---

# Two ideal, massless springs have spring constants \(k_1 = k\) and \(k_2 = 2k\). In Scenario 1, the two springs are connected in series end-to-end to support a hanging block of weight \(W\) in static equilibrium. In Scenario 2, the same two springs are connected in parallel side-by-side to support the same hanging block of weight \(W\) in static equilibrium with equal stretch in both springs. What is the ratio \(\dfrac{\Delta x_{\text{series}}}{\Delta x_{\text{parallel}}}\) of the total extension of the springs in Scenario 1 to the total extension in Scenario 2?

Two ideal, massless springs have spring constants \(k_1 = k\) and \(k_2 = 2k\). In Scenario 1, the two springs are connected in series end-to-end to support a hanging block of weight \(W\) in static equilibrium. In Scenario 2, the same two springs are connected in parallel side-by-side to support the same hanging block of weight \(W\) in static equilibrium with equal stretch in both springs. What is the ratio \(\dfrac{\Delta x_{\text{series}}}{\Delta x_{\text{parallel}}}\) of the total extension of the springs in Scenario 1 to the total extension in Scenario 2?

![A grayscale schematic diagram showing two spring configurations suspended from a horizontal ceiling line. On the left, labeled 'Scenario 1', two vertical coil springs are connected end-to-end in series from the ceiling down to a square mass labeled W; the upper spring is labeled k and the lower spring is labeled 2k. On the right, labeled 'Scenario 2', the two springs are suspended side-by-side in parallel from the ceiling down to a light horizontal bar that supports the same square mass labeled W; the left spring is labeled k and the right spring is labeled 2k. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460099-jfVfaD.jpg)

- **A.** \(\dfrac{9}{4}\)
- **B.** \(\dfrac{9}{2}\)
- **C.** \(6\)
- **D.** \(9\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120568/*