---
title: "Block 1 of mass \\(m_1\\) rests on a frictionless horizontal tabletop and is connected by a light, inextensible string passing over a frictionless, massless pulley to hanging block 2 of mass \\(m_2\\).  The system is released from rest, and block 2 accelerates downward through a vertical distance \\(d\\) while block 1 remains on the tabletop.  In terms of the magnitude of the string tension \\(T\\) and the distance \\(d\\), which of the following correctly gives the changes in mechanical energy \\(\\Delta E_1\\), \\(\\Delta E_2\\), and \\(\\Delta E_{\\text{sys}}\\) for the block 1–Earth system, the block 2–Earth system, and the two-block–Earth system, respectively?"
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url: "https://nerd-notes.com/ubq/120665/"
date_modified: "2026-08-23T04:42:32+00:00"
---

# Block 1 of mass \(m_1\) rests on a frictionless horizontal tabletop and is connected by a light, inextensible string passing over a frictionless, massless pulley to hanging block 2 of mass \(m_2\).

The system is released from rest, and block 2 accelerates downward through a vertical distance \(d\) while block 1 remains on the tabletop.

In terms of the magnitude of the string tension \(T\) and the distance \(d\), which of the following correctly gives the changes in mechanical energy \(\Delta E_1\), \(\Delta E_2\), and \(\Delta E_{\text{sys}}\) for the block 1–Earth system, the block 2–Earth system, and the two-block–Earth system, respectively?

Block 1 of mass \(m_1\) rests on a frictionless horizontal tabletop and is connected by a light, inextensible string passing over a frictionless, massless pulley to hanging block 2 of mass \(m_2\).

The system is released from rest, and block 2 accelerates downward through a vertical distance \(d\) while block 1 remains on the tabletop.

In terms of the magnitude of the string tension \(T\) and the distance \(d\), which of the following correctly gives the changes in mechanical energy \(\Delta E_1\), \(\Delta E_2\), and \(\Delta E_{\text{sys}}\) for the block 1–Earth system, the block 2–Earth system, and the two-block–Earth system, respectively?

![A schematic showing a horizontal tabletop supported on the left by a vertical leg. On the tabletop rests a rectangular block labeled \(m_1\). A horizontal line representing a string extends to the right from \(m_1\) to a circular pulley mounted at the right corner of the tabletop. The string passes over the pulley and extends vertically downward to a second rectangular block labeled \(m_2\), which hangs freely above a horizontal floor. An arrow pointing downward adjacent to \(m_2\) is labeled \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460152-k0uVaN.jpg)

- **A.** \(\Delta E_1 = +T d\), \(\Delta E_2 = 0\), and \(\Delta E_{\text{sys}} = +T d\)
- **B.** \(\Delta E_1 = 0\), \(\Delta E_2 = -T d\), and \(\Delta E_{\text{sys}} = -T d\)
- **C.** \(\Delta E_1 = +T d\), \(\Delta E_2 = +T d\), and \(\Delta E_{\text{sys}} = +2T d\)
- **D.** \(\Delta E_1 = +T d\), \(\Delta E_2 = -T d\), and \(\Delta E_{\text{sys}} = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120665/*