---
title: "Glider 1 of mass \\(m\\) moves to the right with speed \\(v_0\\) along a horizontal frictionless track toward Glider 2 of mass \\(2m\\).  In Scenario 1, Glider 2 is initially at rest, and Glider 1 collides with and sticks to Glider 2, dissipating an amount of mechanical energy \\(\\Delta E_1\\).  In Scenario 2, Glider 2 is initially moving to the left with speed \\(v_0\\), and the two gliders collide head-on and stick together, dissipating an amount of mechanical energy \\(\\Delta E_2\\).  What is the ratio \\(\\dfrac{\\Delta E_2}{\\Delta E_1}\\)?"
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url: "https://nerd-notes.com/ubq/120729/"
date_modified: "2026-08-23T04:42:53+00:00"
---

# Glider 1 of mass \(m\) moves to the right with speed \(v_0\) along a horizontal frictionless track toward Glider 2 of mass \(2m\).

In Scenario 1, Glider 2 is initially at rest, and Glider 1 collides with and sticks to Glider 2, dissipating an amount of mechanical energy \(\Delta E_1\).

In Scenario 2, Glider 2 is initially moving to the left with speed \(v_0\), and the two gliders collide head-on and stick together, dissipating an amount of mechanical energy \(\Delta E_2\).

What is the ratio \(\dfrac{\Delta E_2}{\Delta E_1}\)?

Glider 1 of mass \(m\) moves to the right with speed \(v_0\) along a horizontal frictionless track toward Glider 2 of mass \(2m\).

In Scenario 1, Glider 2 is initially at rest, and Glider 1 collides with and sticks to Glider 2, dissipating an amount of mechanical energy \(\Delta E_1\).

In Scenario 2, Glider 2 is initially moving to the left with speed \(v_0\), and the two gliders collide head-on and stick together, dissipating an amount of mechanical energy \(\Delta E_2\).

What is the ratio \(\dfrac{\Delta E_2}{\Delta E_1}\)?

![A grayscale schematic showing two collision scenarios arranged vertically. The top half shows Scenario 1: a horizontal baseline represents the track. On the left sits a rectangular block labeled m with a horizontal arrow extending from its right side pointing right, labeled v_0. On the right sits a wider rectangular block labeled 2m with no velocity arrow. The bottom half shows Scenario 2: an identical horizontal baseline. On the left sits a rectangular block labeled m with a horizontal arrow pointing right labeled v_0. On the right sits a wider rectangular block labeled 2m with a horizontal arrow extending from its left side pointing left, labeled v_0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460173-GOy5H1.jpg)

- **A.** \(2\)
- **B.** \(3\)
- **C.** \(4\)
- **D.** \(\dfrac{9}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120729/*