Calculating the Radius of a Metallic Ball

  • Thread starter Thread starter vinamas
  • Start date Start date
  • Tags Tags
    Ball Radius
Click For Summary

Homework Help Overview

The discussion revolves around calculating the radius of a metallic ball that is part of a floating object in water. The problem involves understanding the principles of buoyancy and density, specifically applying Archimedes' principle to a composite object scenario.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the mass of the fluid displaced and the mass of the object to determine floating behavior. Questions arise regarding the calculations of volume and mass for both the object and the ball, as well as the implications of density on buoyancy.

Discussion Status

Some participants have offered insights into the principles of buoyancy and the equations related to volume and density. There is a recognition of the need to clarify assumptions about the floating state of the object and how it relates to the submerged portion. Multiple interpretations of the problem are being explored, with some participants expressing uncertainty about their understanding.

Contextual Notes

Participants mention constraints such as the specific measurements provided for the object and the ball, as well as the requirement to apply known equations for volumes and densities. There is an acknowledgment of the original poster's struggle with the problem, indicating a need for further review of foundational concepts.

vinamas
Messages
43
Reaction score
1

Homework Statement


A mettalic ball is dangling from a light thread connected to an object that is floating on water the objects length is 6 cm and its area is 12 cm^2 and its density is 0.30g/cm^3 if the floating part of the object is 4 cm what's the radius of the ball (the balls density is 19.3g/cm^3

Homework Equations


Fb=9.81*V*density
V=4/3*r^3*pi
Fg=mg

The Attempt at a Solution


honestly no I idea how (the answer is 3.1 mm)
 
Physics news on Phys.org
If you really have no idea at all, then you need to review your course notes, a text, and maybe googling the subject you just covered in class.
So what determines how much of an object floats above the water?
 
density?
Simon Bridge said:
If you really have no idea at all, then you need to review your course notes, a text, and maybe googling the subject you just covered in class.
So what determines how much of an object floats above the water?
 
btw its not like am totally oblivious I have attempted to solve it many times but I don't even get close
 
An object will float if the mass of fluid displaced is equal to the mass of the object. This is called "the principle of Archimedes" and you should memorize it.

... in this case you have a composite object.
The mass of an object is it's volume times it's density.
You know an equations for the volumes of various geometric objects.
 
Simon Bridge said:
An object will float if the mass of fluid displaced is equal to the mass of the object. This is called "the principle of Archimedes" and you should memorize it.

... in this case you have a composite object.
The mass of an object is it's volume times it's density.
You know an equations for the volumes of various geometric objects.
The object is not completely floating 2 cm of it is submerged in water and that submerged part has the thread that connects the ball to the object
now I can calculate the volume of the object overall floating or the submerged part each with its mass I just don't know how to calculate the mass or volume of the ball
 
An object is either floating or it isn't. There is no "completely".
All floating objects are at least partly submerged - it is also possible to float when completely submerged.
The principle of Archimedes works for anything that floats ... everything else sinks.
So you also need to realize that a sunk object, that is not being supported, displaces it's own volume of water. All this should be in your class notes.

You know equations for the volumes of objects ... i.e an object with cross-section area A and height H has volume AH if that object has density p, then it's mass is pAH ... see how I did that?

Do you know the formula for the volume of a ball with radius r?
 
Simon Bridge said:
An object is either floating or it isn't. There is no "completely".
All floating objects are at least partly submerged - it is also possible to float when completely submerged.
The principle of Archimedes works for anything that floats ... everything else sinks.
So you also need to realize that a sunk object, that is not being supported, displaces it's own volume of water. All this should be in your class notes.

You know equations for the volumes of objects ... i.e an object with cross-section area A and height H has volume AH if that object has density p, then it's mass is pAH ... see how I did that?

Do you know the formula for the volume of a ball with radius r?
I have solved it thank you I just re arranged some formulas and it worked like magic this is physics I guess
 
Well done - what did you do in the end?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
Replies
3
Views
3K
  • · Replies 13 ·
Replies
13
Views
8K
Replies
2
Views
2K
Replies
3
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K