This paper investigates the added-mass effect in the design of partitioned algorithms for fluid-structure interaction (FSI) problems, particularly focusing on numerical instabilities that arise under certain combinations of physical parameters. The authors consider a simplified model of a potential fluid interacting with a linear elastic thin tube to analyze the added-mass effect, which is known to cause numerical difficulties. They derive stability and convergence conditions for both explicit and implicit schemes, showing that explicit schemes can be unconditionally unstable if the density ratio of the structure and fluid is below a critical threshold, while implicit schemes require careful relaxation parameters to ensure convergence. Numerical results validate these theoretical findings, confirming the influence of geometry and density ratio on the stability of the schemes. The paper also discusses the behavior of iterative methods such as Dirichlet/Neumann and Neumann/Dirichlet subiterations, providing insights into their convergence properties. Finally, dimensional analysis is used to characterize the numerical properties of partitioned schemes, offering a more general perspective on the stability of FSI simulations.This paper investigates the added-mass effect in the design of partitioned algorithms for fluid-structure interaction (FSI) problems, particularly focusing on numerical instabilities that arise under certain combinations of physical parameters. The authors consider a simplified model of a potential fluid interacting with a linear elastic thin tube to analyze the added-mass effect, which is known to cause numerical difficulties. They derive stability and convergence conditions for both explicit and implicit schemes, showing that explicit schemes can be unconditionally unstable if the density ratio of the structure and fluid is below a critical threshold, while implicit schemes require careful relaxation parameters to ensure convergence. Numerical results validate these theoretical findings, confirming the influence of geometry and density ratio on the stability of the schemes. The paper also discusses the behavior of iterative methods such as Dirichlet/Neumann and Neumann/Dirichlet subiterations, providing insights into their convergence properties. Finally, dimensional analysis is used to characterize the numerical properties of partitioned schemes, offering a more general perspective on the stability of FSI simulations.