---
title: "A particle of mass \\(m\\) is constrained to move along the \\(x\\)-axis in a region where its potential energy \\(U(x)\\) varies with position as shown in the graph. Four locations along the \\(x\\)-axis are labeled \\(x_1\\), \\(x_2\\), \\(x_3\\), and \\(x_4\\), where \\(x_2\\) corresponds to a local minimum of \\(U(x)\\). Which of the following correctly ranks the \\(x\\)-component of the net conservative force \\(F_x\\) exerted on the particle at these four positions from greatest to least?"
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url: "https://nerd-notes.com/ubq/120652/"
date_modified: "2026-08-23T04:42:30+00:00"
---

# A particle of mass \(m\) is constrained to move along the \(x\)-axis in a region where its potential energy \(U(x)\) varies with position as shown in the graph. Four locations along the \(x\)-axis are labeled \(x_1\), \(x_2\), \(x_3\), and \(x_4\), where \(x_2\) corresponds to a local minimum of \(U(x)\). Which of the following correctly ranks the \(x\)-component of the net conservative force \(F_x\) exerted on the particle at these four positions from greatest to least?

A particle of mass \(m\) is constrained to move along the \(x\)-axis in a region where its potential energy \(U(x)\) varies with position as shown in the graph. Four locations along the \(x\)-axis are labeled \(x_1\), \(x_2\), \(x_3\), and \(x_4\), where \(x_2\) corresponds to a local minimum of \(U(x)\). Which of the following correctly ranks the \(x\)-component of the net conservative force \(F_x\) exerted on the particle at these four positions from greatest to least?

![A 2D Cartesian graph with a horizontal axis labeled x and a vertical axis labeled U(x), with no gridlines. A single continuous smooth solid curve represents potential energy. Starting at the top left with high potential energy, the curve slopes steeply downward to the right through a solid dot labeled x_1, reaches a smooth rounded local minimum with a horizontal tangent at a solid dot labeled x_2, ascends with a moderate positive slope through a solid dot labeled x_3, and curves upward more steeply through a solid dot labeled x_4. From each of the four dots, a vertical dashed line extends straight down to the horizontal axis where the corresponding position labels x_1, x_2, x_3, and x_4 appear along the axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460150-PVdDJB.jpg)

- **A.** \((F_x)_4 > (F_x)_3 > (F_x)_2 > (F_x)_1\)
- **B.** \((F_x)_1 > (F_x)_2 > (F_x)_3 > (F_x)_4\)
- **C.** \((F_x)_4 > (F_x)_1 > (F_x)_3 > (F_x)_2\)
- **D.** \((F_x)_1 > (F_x)_2 > (F_x)_4 > (F_x)_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120652/*