Chocolate milk mechanics question

[aspodkfpo]

Homework Statement

below

Relevant Equations

below

https://www.asi.edu.au/wp-content/uploads/2018/07/ASOE_2017-Physics-solutions.pdf

Question 11 b)
I don't see why they ignore the white milk in the middle in their model. Nor do I understand how they get that the white milk is also traveling at U. As for the rest of the algebra, there's no need to explain.

Do not understand 11c) statements:
- "Chocolate and plain milk might mix: any mixing will dissipate the kinetic energy of the wave at a microscopic level."
- "The chocolate milk and plain milk will also exert forces on each other. The wave is not made up of two blocks!" - Don't two blocks also exert forces on each other? What difference is the force exerted by these liquids on each other? What force is exerted by these liquids on each other?

Not to sure on the inner mechanics of how gravitational potential energy gets changed into a horizontal kinetic energy (normally its via a ramp). Someone explain please.

Please help.

 

[haruspex]

Question 11 b)
I don't see why they ignore the white milk in the middle in their model.

Me neither. If blocks 2 and 4 gain KE then all of the milk does. The only difference is that blocks moving vertically will move at a different speed from those going horizontally because they have a different distance to travel.
Arguably, the model should have a portion of the plain milk moving vertically up all the way along. The speeds of the vertical and horizontal movements would reduce as you go to the right along the tank. Similarly, the descending mix. Overall, it may look like an "irrotational flow".
Or, to keep it simple, make blocks 3 and 4 adjacent to 1 and 2, leaving the rest of the tank static. This would get close to their equation, but still needs terms for the KE of 1 and 3.

Chocolate and plain milk might mix: any mixing will dissipate the kinetic energy of the wave at a microscopic level.

Yes, the boundary would not be stable. Likely to be places where parts of block 2 go ahead, punching to the right, while at other parts of the boundary some plain milk backwashes into the chocolate. A bit like cells in convection.

The chocolate milk and plain milk will also exert forces on each other. The wave is not made up of two blocks!

Eh? No idea what they are getting at.