Penny for your thoughts?

Question

Had a quick question for a physics density problem.

Pure copper penny mass = 3.083 g
Copper-clad Zinc penny mass= 2.517g
Total Volume of each penny is the same.
Density of copper is 8.960 g/cm^3
Density of zinc is 7.133 g/cm^3

What fraction of the volume of the new penny is occupied by zinc?

I'm a bit lost on this problem...could you possibly show your work. Thanks much!

Answer 1

First you need to find the volume of the penny. To do so you have to take the mass of the pure copper penny and divide by the density of copper. This will leave you with units of cm
^3 so you know you have a volume. The volume of the penny is about .344 cm^3. This will also be the volume of the other penny.

To find the portion of the penny that is zinc you will need to set up an equation. You know that mass / density will give you volume so you have to do this for zinc and copper in the second penny. Then you take that number and multiply it by whatever fraction of the penny it makes up.

x will be used to denote the fraction of the penny made up of zinc

x (2.517/7.133) + (2.517/8.96)(1-x) = .344


.35286x + .280915 - .280915x = .344


.071945 x = .063085

x = .876

If you want to make that into a nicer fraction you'll have to round it a little. 9/10 comes out fairly close to the mass given in the problem so I would go with that.

Answer 2

The additional penny is curiosity. You would additionally seem at it as cost. "A penny stored is a penny earned." Of the 2 cents, just a penny is wanted for the concept. So, each contributors generate profits.

Answer 3

The 1st answer appears to have given the mass fraction of zinc; the question asks for volume fraction.
x = vol. fraction that is Zn
1-x = vol. fraction that is Cu
v = vol. of penny = 3.083/8.960 = 0.3441
new penny mass = v*x*7.133 + v*(1-x)*8.960 = 2.517
7.133x + 8.960(1-x) = 2.517/v
(7.133-8.960)x = 2.517/v - 8.960
x = (2.517/v - 8.960)/(7.133-8.960) = 0.900