# Two toy models for the motion of a leaky tank car

## TL;DR

This paper introduces two simplified models for a leaky tank car's motion, demonstrating how fluid drainage affects its movement through analytical and numerical approaches, illustrating conservation of momentum.

## Contribution

The paper presents two novel toy models that simulate the leaky tank car problem using basic Lagrangian mechanics, one analytically solvable and the other numerically adaptable.

## Key findings

- Both models show the tank car turns around once, consistent with conservation of momentum.
- The models can handle various initial conditions and mass ratios.
- The approach requires only basic mechanics, making it accessible for educational purposes.

## Abstract

I present two toy models for the motion of a tank car as fluid drains out of an off-center opening, based on replacing the fluid with particles. No knowledge beyond simple Lagrangian mechanics is required. The first toy model is solved analytically and the second can be simulated numerically for a variety of initial conditions and mass ratios. Both toy models show the car turning around once as is required by conservation of momentum.