Buoyancy Equilibrium on a balance

Click For Summary

Discussion Overview

The discussion revolves around a physics problem involving buoyancy and equilibrium in a balance system. Participants explore the forces acting on a submerged cube in water and how these forces relate to the mass needed to restore equilibrium on the balance. The conversation includes theoretical considerations and mathematical reasoning related to buoyancy, tension, and the forces acting on the beaker and its contents.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the volume of the cube and begins to explore the buoyant force but expresses confusion about the next steps.
  • Another participant states that since the cube is submerged and not touching the bottom, the buoyant force cancels the gravitational force on the cube.
  • A later reply clarifies that while the cube has no net force, it experiences three forces: its weight, string tension, and buoyant force.
  • There is a discussion about whether the mass on the right pan of the balance equals the buoyant force acting on the cube, leading to a proposed mass of 0.064 kg based on the cube's volume and water density.
  • One participant expresses gratitude for the clarification and seeks to understand the principles that justify the relationship between buoyant force and the weight on the balance.
  • Another participant suggests analyzing the forces on the cube and the beaker system to understand the equilibrium condition better.
  • There is a discussion about the dependencies of the beaker's weight on the water and the cube's apparent weight, indicating the complexity of the forces involved.

Areas of Agreement / Disagreement

Participants generally agree on the role of buoyant force and its relationship to the mass needed for equilibrium, but there are nuances and conditions discussed that indicate some uncertainty and complexity in the problem. The discussion remains unresolved regarding the complete understanding of all forces acting on the system.

Contextual Notes

Participants mention various forces acting on the cube and the beaker system, but there are unresolved aspects regarding the dependencies of these forces and how they interact in the equilibrium condition.

Torquenstein101
Messages
10
Reaction score
0
A beaker filled with water is balanced on the left pan of a balance. A cube of 4 cm on an edge is attached to a string and lowered into the water so that it is completely submerged. The cube is not touching the bottom of the beaker. A weight of mass m is added to the right pan to restore equilibrium. What is m ?

Well i know that the volume of the cube is 64 cm^3 or 6.4x10^-5 m^3. And the buoyancy force would be the density of the water times the volume of the cube times g. But that's all I've gotten pretty much. I've tried using summation of torques about the pivot of the balance, but it just gets me more and more lost. All I need is a step in the right direction. Would i take into consideration the beaker's mass or density? It doesn't really specify it, but I would think it is made of glass and so the density of glass is 2.6 x 10^3 kg/m^3. The density of water is 1000kg/m^3 and i don't know if it is needed either but the density of air is 1.293 kg/m^3. Thanks.
 
Physics news on Phys.org
Since the cube is completely submerged and not touching the bottom, there is no net force acting on it. So the buoyancy cancels out the gravitational force on the cube.
 
Galileo said:
Since the cube is completely submerged and not touching the bottom, there is no net force acting on it. So the buoyancy cancels out the gravitational force on the cube.
True, the cube has no net force acting on it. But there are three forces acting on it: its weight, the string tension, and the buoyant force.

When the cube is lowered into the water, the left pan of the balance will experience an added force equal to the buoyant force on the cube. Choose the mass m accordingly.
 
When the cube is lowered into the water, the left pan of the balance will experience an added force equal to the buoyant force on the cube. Choose the mass m accordingly.

so are you saying the force mg on the right pan is equal to the buyoyant force on the cube in the beaker on the left pan? If this were true, then the density of the water times the volume of the cube would equal that mass m; which would turn out to be 0.064 kg. Is this correct? Or is there something I am missing?
 
Exactly correct.
 
ok i see. thank you, Doc Al, for helping me out. I spent hours on that problem and didnt realize that it would be like that. I know the problem is done and all, but how do you know that the buoyancy force is equal to the weight of the mass on the right pan? I mean to say, what principles or laws can be used to show this?
 
Excellent question. I'm glad to see you thinking.

There are several ways to understand what's going on.

Analyze the forces on the cube. Apply the equilibrium condition to figure out what the tension in the string must be.

Then analyze the forces on the beaker plus contents as a single system. What are all the forces acting on that system?
 
well the summation of forces on the cube shows the tension force is equal to the weight of the cube minus the Buoyant force. The new forces in the beaker system are the Normal force by the balance pan and the weight of the beaker. But isn't the weight of the beaker dependent on the weight of the water inside it as well as the apparent weight of the cube?
 
Torquenstein101 said:
well the summation of forces on the cube shows the tension force is equal to the weight of the cube minus the Buoyant force.
Right.
The new forces in the beaker system are the Normal force by the balance pan and the weight of the beaker.
Don't forget the string pulling up.
But isn't the weight of the beaker dependent on the weight of the water inside it as well as the apparent weight of the cube?
The weight of the beaker system just depends on the mass of its contents: beaker, water, and cube.
 

Similar threads

Undergrad What is the location of the center of buoyancy and how is it determined?
  • · Replies 14 ·
Replies
14
Views
11K
High School Archimedes principle and the density of a rock
  • · Replies 6 ·
Replies
6
Views
7K
Ice Core Density Problem (Inspired by NEEM)
  • · Replies 6 ·
Replies
6
Views
981
High School What factors affect the rate of sinking objects in water?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Moving object using buoyancy for project -- Help appreciated
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Solving a Buoyancy Question Involving Air & Water
  • · Replies 25 ·
Replies
25
Views
3K
How Does Buoyancy Affect Balance Scale Readings?
  • · Replies 4 ·
Replies
4
Views
4K
High School Actual value of normal reaction
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Buoyancy Force & Length of Submerged Cube
  • · Replies 11 ·
Replies
11
Views
3K
Buoyancy and the Archimedes Principle
  • · Replies 6 ·
Replies
6
Views
2K