---
title: "A helium-filled balloon is attached by a string of negligible mass to a small \\(0.015 \\ \\text{kg}\\) object that is just heavy enough to keep the balloon from rising. The total mass of the balloon, including the helium, is \\(0.0050 \\ \\text{kg}\\). The density of air is \\(\\rho_{\\text{air}} = 1.29 \\ \\text{kg/m}^3\\), and the density of helium is \\(\\rho_{\\text{He}} = 0.179 \\ \\text{kg/m}^3\\). The buoyant force on the \\(0.015 \\ \\text{kg}\\) object is small enough to be negligible."
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url: "https://nerd-notes.com/ubq/81576/"
date_modified: "2025-03-13T06:22:56+00:00"
---

# A helium-filled balloon is attached by a string of negligible mass to a small \(0.015 \ \text{kg}\) object that is just heavy enough to keep the balloon from rising. The total mass of the balloon, including the helium, is \(0.0050 \ \text{kg}\). The density of air is \(\rho_{\text{air}} = 1.29 \ \text{kg/m}^3\), and the density of helium is \(\rho_{\text{He}} = 0.179 \ \text{kg/m}^3\). The buoyant force on the \(0.015 \ \text{kg}\) object is small enough to be negligible.

A helium-filled balloon is attached by a string of negligible mass to a small \(0.015 \ \text{kg}\) object that is just heavy enough to keep the balloon from rising. The total mass of the balloon, including the helium, is \(0.0050 \ \text{kg}\). The density of air is \(\rho_{\text{air}} = 1.29 \ \text{kg/m}^3\), and the density of helium is \(\rho_{\text{He}} = 0.179 \ \text{kg/m}^3\). The buoyant force on the \(0.015 \ \text{kg}\) object is small enough to be negligible.

![Diagram](https://nerd-notes.com/wp-content/uploads/2025/03/ballonattachedtoablockfrqfluids.png)

**Part a)** Draw and label the forces (not components) that act on the balloon. *(3 points)*

**Part b)** Calculate the buoyant force on the balloon. *(3 points)*

**Part c)** Calculate the volume of the balloon. *(3 points)*

**Part d)** A child holds the string midway between the balloon and the \(0.015 \ \text{kg}\) object. The child gets into a car, brings the balloon and the \(0.015 \ \text{kg}\) object into the car, and holds the string so that neither the balloon nor the \(0.015 \ \text{kg}\) object touches any surface. The car then begins to move forward, accelerating in a straight line. What behavior does the \(0.015 \ \text{kg}\) object exhibit when the car accelerates (i.e: it remains vertical, moves towards the front, moves to the right, etc)? Explain your reasoning. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/81576/*