---
title: "A composite foam sample consists of a solid material of uniform density \\(\\rho_s\\) interspersed with air-filled voids of negligible density. The void fraction \\(\\phi\\) is defined as the ratio of the volume of the voids to the total outer volume of the foam block. The block is placed in a liquid of density \\(\\rho_f\\), where \\(\\rho_s > \\rho_f\\). In terms of \\(\\rho_s\\) and \\(\\rho_f\\), what is the minimum void fraction \\(\\phi_{\\text{min}}\\) required for the foam block to float in the liquid?"
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url: "https://nerd-notes.com/ubq/119084/"
date_modified: "2026-08-18T04:48:43+00:00"
---

# A composite foam sample consists of a solid material of uniform density \(\rho_s\) interspersed with air-filled voids of negligible density. The void fraction \(\phi\) is defined as the ratio of the volume of the voids to the total outer volume of the foam block. The block is placed in a liquid of density \(\rho_f\), where \(\rho_s > \rho_f\). In terms of \(\rho_s\) and \(\rho_f\), what is the minimum void fraction \(\phi_{\text{min}}\) required for the foam block to float in the liquid?

A composite foam sample consists of a solid material of uniform density \(\rho_s\) interspersed with air-filled voids of negligible density. The void fraction \(\phi\) is defined as the ratio of the volume of the voids to the total outer volume of the foam block. The block is placed in a liquid of density \(\rho_f\), where \(\rho_s > \rho_f\). In terms of \(\rho_s\) and \(\rho_f\), what is the minimum void fraction \(\phi_{\text{min}}\) required for the foam block to float in the liquid?

![A rectangular cross-section of a foam block labeled with total outer volume V. Inside the outer boundary, the block consists of a shaded solid matrix labeled with density \rho_s and several unshaded white circular regions representing internal air voids of total volume V_{\text{void}}. Below the block, a liquid container is shown with liquid labeled with density \rho_f. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787028523-zi524B.jpg)

- **A.** \(\phi_{\text{min}} = \dfrac{\rho_f}{\rho_s}\)
- **B.** \(\phi_{\text{min}} = \dfrac{\rho_s - \rho_f}{\rho_f}\)
- **C.** \(\phi_{\text{min}} = \dfrac{\rho_f}{\rho_s - \rho_f}\)
- **D.** \(\phi_{\text{min}} = \dfrac{\rho_s - \rho_f}{\rho_s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119084/*