Calculating the Radius of a Metallic Ball

[vinamas]

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)

 

[Simon Bridge]

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?

 

[vinamas]

density?

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?

 

[vinamas]

btw its not like am totally oblivious I have attempted to solve it many times but I don't even get close

 

[Simon Bridge]

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.

 

[vinamas]

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

 

[Simon Bridge]

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?

 

[vinamas]

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

 

[Simon Bridge]

Well done - what did you do in the end?