Weight of a Box between two fluids of different densities

Click For Summary

Homework Help Overview

The problem involves a box floating between two fluids of different densities, where participants are tasked with determining the mass of the box using various parameters related to fluid dynamics and buoyancy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of free body diagrams and the forces acting on the box, including buoyancy and pressure from both fluids. There is an exploration of the relationship between the pressures at different depths and how they affect the box's equilibrium.

Discussion Status

Some participants have provided insights into the pressures exerted by the fluids and how they interact, while others are questioning their understanding of the buoyancy forces involved. There appears to be productive dialogue regarding the conceptual underpinnings of the problem.

Contextual Notes

Participants are navigating assumptions about the pressures and buoyancy forces acting on the box, as well as the implications of the box's position between the two fluids. There is mention of a free body diagram and an attached file that may contain additional context.

viciousp
Messages
49
Reaction score
0

Homework Statement


A box with a height L, and a cross sectional Area A is floating between two fluids of densities p1 and p2. Determine the mass of the box using ho, h1, h2, p1, p2, and A.


Homework Equations


F= pVg


The Attempt at a Solution



In the file attached I drew my free body diagram and the image of the box. Solving my FBD I get:

mg+p1(A)(ho)g=p2(A)(h2)g

Solving for m:

p2(A)(h2)-p1(A)(ho)

but with Archimedes principal the answer should be p2(A)(h2)+p1(A)(h1), so what did I do wrong/forget?

Thanks
 

Attachments

  • Drawing_FBD.jpg
    Drawing_FBD.jpg
    6.2 KB · Views: 409
Physics news on Phys.org
The bottom liquid is under the top liquid (obviously), but this has consequences for the pressures that are felt by the box in the bottom liquid.
 
So the only thing I can think of is the pressure of the top liquid acting on the bottom liquid, as well as the buoyancy of the bottom liquid with respect to the top liquid.

Im assuming these two forces are equal to each other Fb= (h1+h0)A*p1. If I include the buoyancy of liquid 2 on liquid 1 on the box diagram it does give me the answer I want, but I don't conceptually understand why.
 
Write the expressions for the pressures at the bottom of the box and the top of the box (at depths h0 and h0+h1+h2).
 
Ahh, I see thanks now it makes sense.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
9
Views
8K
  • · Replies 15 ·
Replies
15
Views
10K
Replies
1
Views
1K
Replies
4
Views
4K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 13 ·
Replies
13
Views
20K