Estimating the Mass of an 18 Carat Gold Ring Using Basic Geometry

[Jimmy87]

Homework Statement

An 18 carat gold ring is made from an alloy containing 75% gold with small amounts of other metals including copper and silver. By considering the ring to be a cylinder, find an order of magnitude estimate for the mass of the ring.

Homework Equations

density of gold - 19.32g per cubic cm
Density = Mass/Volume

The Attempt at a Solution

I am not quite sure about what it means by treating it as a cylinder. Does it mean to imagine cutting the ring and flattening it out to form a straight line which resemble a cylinder? I really have no idea how to go about this. I guess you would then use mass = density x volume where you use the volume of a cylinder. What is the best way to go about finding approximate dimensions of a ring without having one?

 

[Chestermiller]

Is this all the information they gave? Is this the exact problem statement?

Chet

 

[Jimmy87]

Is this all the information they gave? Is this the exact problem statement?

Chet

Yes, this all the information given and it is written word for word from my textbook.

 

[Chestermiller]

I guess they want you to solve the problem in a general way by specifying the dimensions of the ring algebraically, without assigning any numerical values for them. Inner radius r_i cm, outer radius r_o cm, and height h cm. I would also look up the densities of silver and copper just to see how they compare with gold.

Chet

 

[Jimmy87]

I guess they want you to solve the problem in a general way by specifying the dimensions of the ring algebraically, without assigning any numerical values for them. Inner radius r_i cm, outer radius r_o cm, and height h cm. I would also look up the densities of silver and copper just to see how they compare with gold.

Chet

Why would you need an inner and outer radius?

 

[Chestermiller]

Why would you need an inner and outer radius?

Because you need an opening to put your finger through.

Chet

 

[Jimmy87]

Because you need an opening to put your finger through.

Chet

Could you not just treat the ring as a cylinder by imagining snapping it and form a straight line instead of a ring and treating that as the cylinder? So kind of like bending the ring into a straight line and standing it upright?

 

[Chestermiller]

Could you not just treat the ring as a cylinder by imagining snapping it and form a straight line instead of a ring and treating that as the cylinder? So kind of like bending the ring into a straight line and standing it upright?

I guess you could do that, but it wouldn't be as good an approximation to an actual ring shape. Still, I guess the focus of this exercise is not so much the geometry of the ring as it is applying knowledge of how to work with density.

Chet

 

[Jimmy87]

I guess you could do that, but it wouldn't be as good an approximation to an actual ring shape. Still, I guess the focus of this exercise is not so much the geometry of the ring as it is applying knowledge of how to work with density.

Chet

Thanks. So how do you do it your way because you just have air in the middle? Or would you factor that in and subtract that? How would you go about showing this with algebra as you said before?

 

[Chestermiller]

Thanks. So how do you do it your way because you just have air in the middle? Or would you factor that in and subtract that? How would you go about showing this with algebra as you said before?

This is a typical SAT problem. I don't want to give an answer before you have had a chance to think about it a little more. What are your thoughts on how to approach this?

Chet

 

[Herman Trivilino]

Could you not just treat the ring as a cylinder by imagining snapping it and form a straight line instead of a ring and treating that as the cylinder? So kind of like bending the ring into a straight line and standing it upright?

I believe that is what's intended by the direction given in the statement of the problem. Since they ask for an order of magnitude estimate, they are looking for a numerical answer. I believe they want you to make reasonable assumptions about the dimensions of the cylinder.