Max Liquid-1 Amount for Cube to Slide Across Room w/Liquid-2 & Friction

[MisterMumbleX]

This is a question I made up for a math research paper. Please tell me what you think about it, I'm not asking anyone to do any math or physics, just comment.

A waterproof cube with edges of length d is completely submerged in liquid-2 of density ρ2 in a cube-shaped room with lengths of k ∙ d (where k is a positive constant) that is filled with liquid-2. The cube lies on the bottom surface of the room, which has a coefficient of kinetic friction of uk with the cube. The cube is sent sliding across the room in linear motion by unidentified means with a momentum p while carrying an unknown amount of liquid-1, which has density ρ1. If liquid-2 flows in the direction opposite the cube’s motion, what is the maximum amount of liquid-1 that the cube can carry and still travel the distance kd to the other side of the room? The gravitational acceleration constant is g. Ignore any effects of viscosity.

 

[Valerie Park]

This is an interesting question that combines concepts from physics and mathematics, such as momentum, density, friction, and acceleration. It would be fascinating to explore the various factors that influence the cube's movement and how they interact with each other. It could lead to some intriguing new insights into the behavior of liquids in motion.