# Acceleration due to buoyancy and mass renormalization

## TL;DR

This paper investigates the acceleration of buoyant objects in fluids, clarifies misconceptions, and demonstrates how added mass leads to mass renormalization, supported by theoretical calculations and experimental validation.

## Contribution

It provides a detailed analysis of added mass for various shapes, introduces a simple approximation for slender bodies, and experimentally confirms the theoretical predictions.

## Key findings

- Theoretical added mass calculations match experimental results.
- Slender-body limit exhibits non-analytic, singular behavior.
- Added mass concept effectively illustrates mass renormalization.

## Abstract

The acceleration of a light buoyant object in a fluid is analyzed. Misconceptions about the magnitude of that acceleration are briefly described and refuted. The notion of the added mass is explained and the added mass is computed for an ellipsoid of revolution. A simple approximation scheme is employed to derive the added mass of a slender body. The slender-body limit is non-analytic, indicating a singular character of the perturbation due to the thickness of the body. An experimental determination of the acceleration is presented and found to agree well with the theoretical prediction. The added mass illustrates the concept of mass renormalization in an accessible manner.