---
title: "A ball of mass \\(m\\) is thrown vertically upward. The ball moves from an initial height \\(y_i\\) to a higher final height \\(y_f\\) while in free fall. Consider two different system definitions:  System 1: The ball only System 2: The ball and Earth  Which of the following correctly describes the work done or the energy of the specified system as the ball rises?"
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url: "https://nerd-notes.com/ubq/109309/"
date_modified: "2026-03-21T23:23:48+00:00"
---

# A ball of mass \(m\) is thrown vertically upward. The ball moves from an initial height \(y_i\) to a higher final height \(y_f\) while in free fall. Consider two different system definitions:

System 1: The ball only
System 2: The ball and Earth

Which of the following correctly describes the work done or the energy of the specified system as the ball rises?

A ball of mass \(m\) is thrown vertically upward. The ball moves from an initial height \(y_i\) to a higher final height \(y_f\) while in free fall. Consider two different system definitions:

System 1: The ball only
System 2: The ball and Earth

Which of the following correctly describes the work done or the energy of the specified system as the ball rises?

![A side-by-side comparison of two scenarios. On the left, labeled System 1, a small ball is shown moving upward from y_i to y_f with a velocity vector pointing up. A dashed box tightly encloses only the ball. On the right, labeled System 2, the same ball is shown rising, but the dashed box encloses both the ball and a segment of the Earth's surface below it. Arrows labeled F_g point downward on the ball in both scenarios.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774135428-7XDIrI.jpg)

- **A.** In System 1, the gravitational potential energy of the ball increases because the ball is moving farther from the Earth.
- **B.** In System 1, the total mechanical energy of the system is conserved because gravity is a conservative force.
- **C.** In System 2, the Earth exerts an external force on the ball, doing negative work that decreases the total mechanical energy of the system.
- **D.** In System 2, the gravitational potential energy of the system increases because the internal gravitational force does negative work on the ball.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109309/*