15. On October 21, 1982, the Bureau if
the Mint changed the composition of
pennies. Instead of an alloy of 95% Cu
and 5% Zn by mass, a core of 99.2 Zn
and 0.8% Cu with a thin shell of copper
was adopted. The overall composition of
the new penny was 97.6% Zn and 2.4%
Cu by mass. Assume the volume of the
individual metals that make up each
penny can be added together to give the
overall volume of the penny, and assume
each penny is the same size. (Density of
Cu = 8.96 g/cm3; density of Zn = 7.14
g/cm3) Does this account for the
difference in mass among the pennies?
To determine whether the difference in mass among the pennies can be accounted for by the change in composition, we need to compare the expected mass of the new penny to the actual mass of the new penny.
First, let's calculate the expected mass of the new penny using the given composition. We know that the overall composition of the new penny is 97.6% Zn and 2.4% Cu by mass.
Assuming each penny is the same size, we can calculate the expected mass by considering the mass of the core (99.2% Zn and 0.8% Cu) and the mass of the shell (copper).
To calculate the mass of the core:
- Mass of Zn in the core = 99.2% × mass of the core
- Mass of Cu in the core = 0.8% × mass of the core
To calculate the mass of the shell (copper):
- Mass of Cu in the shell = 97.6% × mass of the shell
Now, let's calculate the expected mass of the new penny by adding the masses of the core and the shell.
Expected mass of the new penny = mass of the core + mass of the shell
To compare this with the actual mass of the new penny, we need to know the actual mass of the new penny.
Once we have the expected and actual mass values, we can compare them to determine if the difference in mass among the pennies can be accounted for by the change in composition.
To find the expected mass of the new penny, you need to know the mass of the core and the shell, along with the mass of Zn and Cu in each.
To find the actual mass of the new penny, you will need a sample penny or the exact mass of a new penny.
Once you have these values, you can compare the expected and actual mass of the new penny to determine if they match and thus account for the difference in mass among the pennies.