# Percent copper in post-1982 pennies

kevinnn
% copper in post-1982 pennies

## Homework Statement

The total mass of each penny is 2.500g, the density of copper is 8.96g/ml, the density of zinc is 7.14g/ml and the mass of a penny if it was 100% copper would be 3.11g.

## The Attempt at a Solution

I am not too sure how to start this one. If someone could give me a boost I would appreciate it.

kevinnn
Sorry not the clearest. I want to know the percent composition by mass of zinc and copper.

Staff Emeritus
Homework Helper
You can figure the volume of the penny by using the figures for 100% copper. Once you do that, you can write an algebraic equation for the penny which is composed of a mixture of copper and zinc.

kevinnn
Ok well I got the volume of a penny to be 0.347ml. The only equation I can think to set up is

0.347ml=x(1ml/8.96)+y(1ml/7.14) From this I need a way to solve for x or y.?.?

Staff Emeritus
Homework Helper
You don't necessarily want to calculate the volume of the penny; that has already been done. You want to find out what the percentage of copper and zinc are in the new penny which has a mass of 2.500 g.

Whatever part of the new penny which isn't copper must be zinc. So, if x is the percentage of copper, what must the percentage of zinc be in the new penny?

Mentor
Ok well I got the volume of a penny to be 0.347ml. The only equation I can think to set up is

0.347ml=x(1ml/8.96)+y(1ml/7.14) From this I need a way to solve for x or y.?.?

There is another equation. x and y are fractions of zinc and copper - what is their sum?

SteamKing points you in the same direction, he just tries to use a single variable.

kevinnn
Well the answer I'm getting can't be right because it is more than 100%. The equations I set up though are

x+y=2.500g ==> x=2.500g-y

0.357ml=(2.500g-y)(1ml/8.96)+y(1ml/7.14)

x represents copper and y represents zinc.

Staff Emeritus
Homework Helper
Well the answer I'm getting can't be right because it is more than 100%. The equations I set up though are

x+y=2.500g ==> x=2.500g-y

0.357ml=(2.500g-y)(1ml/8.96)+y(1ml/7.14)

x represents copper and y represents zinc.

That's because you're not paying attention. If x = percentage of copper, what must be the percentage of zinc in the new penny?

kevinnn
The percentage of zinc would be (100-x). So I should eliminate the variable y and replace it with (100-x). So my equation would be 0.357ml=(x)(1ml/8.96)+(100-x)(1ml/7.14) Right?

Staff Emeritus
That's not right. You might find it easier to work with x as a fractional part (a number between 0 and 1) rather than a percentage. It's trivial to convert that fractional part to a percentage.

kevinnn
So your saying that I should use (1-x) instead of (100-x)? making my equation
0.375ml=(x)(1ml/8.96)+(1-x)(1ml/7.14)

kevinnn
This equation still does not work. I get a negative number and something greater than 100%. What am I doing wrong?

Staff Emeritus
So your saying that I should use (1-x) instead of (100-x)? making my equation
0.375ml=(x)(1ml/8.96)+(1-x)(1ml/7.14)

Don't drop units! If you had kept the units intact you would have seen that this is the wrong equation. That 8.96 and 7.14: Those are densities. Both terms on the right hand side have units of volume/density, or volume2/mass. The left hand side has units of volume. Your equation has inconsistent units.

Hint: You haven't used the fact that the penny's mass is 2.5 grams.

Staff Emeritus
Homework Helper
Been trying to tell OP that since Post #5.

kevinnn
The reason my units are just ml on the right hand side is because (x gCu)*(1ml/8.96 gCu) =x(1ml/8.96). The same is true for the other expression.

Staff Emeritus
x has to be unitless.

kevinnn
Well how do I get x unitless? I felt bad about not getting this problem but when I got to class turned out no one else I could find got it either. Are my equations even close to correct?

Staff Emeritus
Homework Helper
Are my equations even close to correct?

No. We've been trying to tell you that, but you haven't taken heed of our suggestions.

Forget the volume of the penny. That has already been calculated. It is the same for both the old penny and the new penny.

What you must find out is how much copper and how much zinc it takes to make a penny which has a mass of 2.500 grams.

You can use the mass of the new penny to figure out what the average density of the penny must be, given its mass of 2.500 grams. You also are given the densities of copper and zinc.

Once you know the average density of the new penny, you can write an algebraic equation using the densities of Cu and Zn to find out the proportions of the mixture which gives this average density.

kevinnn
What you must find out is how much copper and how much zinc it takes to make a penny which has a mass of 2.500 grams.
You can use the mass of the new penny to figure out what the average density of the penny must be, given its mass of 2.500 grams. You also are given the densities of copper and zinc.

I calculated the average density to be 2.80g/ml.

Once you know the average density of the new penny, you can write an algebraic equation using the densities of Cu and Zn to find out the proportions of the mixture which gives this average density.

An average density can be useful? That will not yield an inaccurate calculation?

Last edited:
kevinnn
1234 ignore this

Last edited:
Staff Emeritus
Homework Helper
What you must find out is how much copper and how much zinc it takes to make a penny which has a mass of 2.500 grams.
You can use the mass of the new penny to figure out what the average density of the penny must be, given its mass of 2.500 grams. You also are given the densities of copper and zinc.

I calculated the average density to be 2.80g/ml.

Once you know the average density of the new penny, you can write an algebraic equation using the densities of Cu and Zn to find out the proportions of the mixture which gives this average density.

An average density can be useful? That will not yield an inaccurate calculation?

The mass of the penny is 2.500 g. You already know the volume of the penny is 0.347 ml. How in the world does that make the average density of the coin 2.80 g/ml?

'That will not yield an inaccurate calculation?' = That will yield an accurate calculation.
Watch using double negatives in a sentence.

Clearly, you are having problems doing simple calculations and it doesn't seem that you understand the concept of density. Always check your work before presenting it, and study harder.

Staff Emeritus
Homework Helper
Look at it this way:
if the penny was 100% copper, its density would be 8.96 g/ml
if the penny was 100% zinc, its density would be 7.14 g/ml

Your average density for the new penny must lie between these two figures. It can't be less than 7.14 g/ml and it can't be greater than 8.96 g/ml.

This is the type of problem solved by Archimedes more than 2000 years ago.

kevinnn
That was a typo. I was looking at the wrong calculation in my calculator. I know how to find just and average density, it's 8.05g/ml.

Staff Emeritus