Converting from mass/volume to length

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Discussion Overview

The discussion revolves around a homework problem involving the conversion of mass and volume to thickness in angstroms for a piece of gold leaf. Participants explore the relationship between volume, area, and thickness, while addressing potential errors in the problem statement.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that the volume of 1.93 mg of gold is calculated as 10^(-4) cm^3, but express uncertainty about how to convert this to thickness.
  • One participant suggests that the area measurement of 14.5 cm^3 is likely a typo, as it should represent area in cm^2 rather than volume.
  • Another participant proposes that the thickness can be derived from the equation relating volume to area and thickness, suggesting that the formula should be volume = area × thickness.
  • Some participants challenge the clarity of the problem statement, questioning the units used and the implications of the given values.
  • One participant calculates thickness as 6.9 x 10^(-6) cm^3 but acknowledges that this is not a valid thickness measurement.
  • There is a discussion about converting the final thickness from cm to angstroms, with some participants providing insights on the necessary conversions.

Areas of Agreement / Disagreement

Participants generally agree that there is a typo in the problem statement regarding the area measurement. However, there is no consensus on the correct interpretation or resolution of the problem, as multiple viewpoints and calculations are presented.

Contextual Notes

Limitations include the unclear definition of the area measurement and the potential for misinterpretation of units. The discussion reflects various assumptions about the relationships between volume, area, and thickness.

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Homework Statement


A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.


Homework Equations


Angstrom=10^(-10) meters
d=mass over volume


The Attempt at a Solution


I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how
 
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dchau503 said:

Homework Statement


A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.


Homework Equations


Angstrom=10^(-10) meters
d=mass over volume


The Attempt at a Solution


I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how

There is at least one typo in the problem statement. What are the units of area?

Once you fix that, the volume of the leaf is just the area multiplied by the thickness, right?
 
dchau503 said:

Homework Statement


A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.

Homework Equations


Angstrom=10^(-10) meters
d=mass over volume

The Attempt at a Solution


I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how

One problem may be the area of 14.5... cm^3 is not area.
If I assume that to be cm^2 the problem works out fine.
I think of it as a very shallow box of gold with a volume of LxWxH where you know L and W and just need H so that the volume becomes what it's supposed to be. LxW is area, so AxH should = Volume.

Good?
 


berkeman said:
There is at least one typo in the problem statement. What are the units of area?

Once you fix that, the volume of the leaf is just the area multiplied by the thickness, right?

There's no area measurement listed in the original question. But that would make it a lot easier, if the problem did list it.

Edit: actually, the problem did say the "area of 14.5 cm^3"...but that's weird because a cubed unit signifies volume, not area.
 


dchau503 said:
There's no area measurement listed in the original question. But that would make it a lot easier, if the problem did list it.

Edit: actually, the problem did say the "area of 14.5 cm^3"...but that's weird because a cubed unit signifies volume, not area.

So the units must be wrong...
 


Jakeus314 said:
One problem may be the area of 14.5... cm^3 is not area.
If I assume that to be cm^2 the problem works out fine.
I think of it as a very shallow box of gold with a volume of LxWxH where you know L and W and just need H so that the volume becomes what it's supposed to be. LxW is area, so AxH should = Volume.

Good?

Your advice put me on the right track, but I still don't have the complete answer:

I did 14.5 cm^3 x (thickness) = 1X10^(-4) cm^3

From the equation, I solved that thickness is 6.9 x 10^(-6) cm^3. I got the right significant figures, but not the right units. How do I convert that answer into angstroms?
 
dchau503 said:
Your advice put me on the right track, but I still don't have the complete answer:

I did 14.5 cm^3 x (thickness) = 1X10^(-4) cm^3

From the equation, I solved that thickness is 6.9 x 10^(-6) cm^3. I got the right significant figures, but not the right units. How do I convert that answer into angstroms?

14.5 cm^3 is an error on someones part.
6.9 x 10^(-6) cm^3 is not a thickness.

Solving for thickness,
14.5 cm^2 x (thickness in cm) = 1*10^(-4) cm^3
Gives a thickness in cm.
Convert that to angstroms since those are the requested units.

cm^3 / cm^2. Yields cm
 
Jakeus314 said:
14.5 cm^3 is an error on someones part.
6.9 x 10^(-6) cm^3 is not a thickness.

Solving for thickness,
14.5 cm^2 x (thickness in cm) = 1*10^(-4) cm^3
Gives a thickness in cm.
Convert that to angstroms since those are the requested units.

cm^3 / cm^2. Yields cm

Thanks for the answer. I finally understand the problem and it's solution, even with the typo in the problem. :(

Crash-course study books frequently have mistakes in them, lol.
 

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