---
title: "An explosive mechanism of negligible mass is placed between two movable blocks of masses \\(m_1\\) and \\(m_2\\) on a horizontal, frictionless track. The blocks are initially held together at rest, and when the mechanism detonates, it releases a constant, unknown mechanical energy \\(E_0\\) entirely into the kinetic energies of the separating blocks. Block 1 is equipped with a sensor that measures its post-explosion kinetic energy \\(K_1\\), while block 2 has no sensor. In order to determine \\(E_0\\) from multiple trials using different values of the mass ratio \\(\\dfrac{m_1}{m_2}\\), which of the following correctly identifies the quantity that should be plotted on the vertical axis versus \\(\\dfrac{m_1}{m_2}\\) on the horizontal axis to produce a linear graph, along with the slope and vertical intercept of that graph?"
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url: "https://nerd-notes.com/ubq/124427/"
date_modified: "2026-09-28T14:05:20+00:00"
---

# An explosive mechanism of negligible mass is placed between two movable blocks of masses \(m_1\) and \(m_2\) on a horizontal, frictionless track. The blocks are initially held together at rest, and when the mechanism detonates, it releases a constant, unknown mechanical energy \(E_0\) entirely into the kinetic energies of the separating blocks. Block 1 is equipped with a sensor that measures its post-explosion kinetic energy \(K_1\), while block 2 has no sensor. In order to determine \(E_0\) from multiple trials using different values of the mass ratio \(\dfrac{m_1}{m_2}\), which of the following correctly identifies the quantity that should be plotted on the vertical axis versus \(\dfrac{m_1}{m_2}\) on the horizontal axis to produce a linear graph, along with the slope and vertical intercept of that graph?

An explosive mechanism of negligible mass is placed between two movable blocks of masses \(m_1\) and \(m_2\) on a horizontal, frictionless track. The blocks are initially held together at rest, and when the mechanism detonates, it releases a constant, unknown mechanical energy \(E_0\) entirely into the kinetic energies of the separating blocks. Block 1 is equipped with a sensor that measures its post-explosion kinetic energy \(K_1\), while block 2 has no sensor. In order to determine \(E_0\) from multiple trials using different values of the mass ratio \(\dfrac{m_1}{m_2}\), which of the following correctly identifies the quantity that should be plotted on the vertical axis versus \(\dfrac{m_1}{m_2}\) on the horizontal axis to produce a linear graph, along with the slope and vertical intercept of that graph?

![A schematic diagram showing two rectangular blocks on a horizontal surface representing a frictionless track. The left block is labeled m_1 and the right block is labeled m_2. Between the two blocks is a small rectangular mechanism labeled bolt with two small outward-pointing horizontal arrows on either side indicating separation. A horizontal dashed line below the blocks represents the track surface. Above block 1, a small sensor icon is depicted. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604320-hUG60G.jpg)

- **A.** Vertical axis: \(K_1\); Slope: \(-E_0\); Vertical intercept: \(E_0\)
- **B.** Vertical axis: \(\dfrac{1}{K_1}\); Slope: \(\dfrac{1}{E_0}\); Vertical intercept: \(-\dfrac{1}{E_0}\)
- **C.** Vertical axis: \(\dfrac{1}{K_1}\); Slope: \(\dfrac{1}{E_0}\); Vertical intercept: \(\dfrac{1}{E_0}\)
- **D.** Vertical axis: \(\dfrac{1}{K_1}\); Slope: \(\dfrac{1}{E_0}\); Vertical intercept: \(0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124427/*