On October 21, 1982, the Bureau of the Mint changed the...

On October 21, 1982, the Bureau of the Mint changed the composition of pennies (see Exercise 120). 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. Does this account for the difference in mass among the pennies in Exercise 120? 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 $\mathrm{Cu}=8.96 \mathrm{g} / \mathrm{cm}^{3} ;$ density of $\mathrm{Zn}=7.14 \mathrm{g} / \mathrm{cm}^{3} . )$

Key Concepts

Core-Shell Structure

A core-shell structure is a type of composite material where one material forms the core and another forms an outer layer or shell. In the case of the coin, the core-shell design involves a predominantly zinc core with a pure copper plating. This structural design influences the coin’s mass distribution and overall density, leading to differences compared to a homogeneous alloy.

Volume Additivity

Volume additivity is the assumption that the total volume of a composite object is equal to the sum of the volumes of its constituent materials. This concept is used to analyze the coins by assuming that the individual metals’ volumes directly add up to the coin’s total volume, thereby linking composition, density, and overall mass.

Alloy Composition

Alloy composition refers to the percentage by mass of each metal present in a metal mixture. In this context, it is important to understand how the switch from a copper-zinc alloy with one set of percentage compositions to a core and shell design with different percentages affects the overall distribution of metals within the coin.

Density

Density is the mass per unit volume of a substance and plays a crucial role in determining how different metals contribute to the overall mass of an object. Since copper and zinc have different densities, altering the proportion of each metal in the coin leads to changes in the coin's mass even if the volume remains the same.

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