In 1983 the United States began coining the cent piece out...

In 1983 the United States began coining the cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper cent is $3.083 \mathrm{~g}$, whereas that of the new cent is $2.517 \mathrm{~g} .$ Calculate the percent of zinc (by volume) in the new cent. The density of copper is $8.960 \mathrm{~g} / \mathrm{cm}^{3}$, and that of zinc is $7.133 \mathrm{~g} / \mathrm{cm}^{3} .$ The new and old coins have the same volume.

Key Concepts

Density

Density is defined as mass per unit volume and is a fundamental physical property that characterizes materials. It allows us to relate the mass of a substance to the volume it occupies. This concept is crucial when comparing different materials, as the same mass of two substances can occupy different volumes if their densities differ.

Volume Fraction

The volume fraction represents the proportion of the total volume that a particular component in a mixture occupies. In problems involving composite materials, like coins made of different metals, determining the volume fraction of each component helps in understanding the material's overall composition even when the components have varying densities.

Mass-to-Volume Conversion

Mass-to-volume conversion is the process of using the density of a material to convert between its mass and the volume it occupies. This conversion is essential when dealing with composite systems, enabling the calculation of individual volumes from known masses and densities of the components.

Composite Material Analysis

Composite material analysis involves studying mixtures that are made up of two or more distinct materials. In such analyses, the conservation of total volume or mass is used to set up equations relating the components’ masses and volumes. This approach is necessary when determining the proportion of each component in the overall mixture, such as calculating the percent by volume of one material in an alloy.

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