Calculating Thickness of Copper Cladding on Zinc Pennies | US Mint 1983-Present

In summary, the US Mint has been producing pennies made of zinc with a copper cladding since 1983. These pennies have a mass of 2.50 g and can be modeled as a uniform cylinder with a height of 1.23 mm and a radius of 9.50 mm. To find the thickness of the copper cladding, we can use the formula m = (ρ Cu)Vcu + (ρ Zn) Vzn, where ρ is the density of copper and zinc, and Vcu and Vzn are the volumes of copper and zinc respectively. By solving the equation, the thickness of the copper cladding is found to be approximately 0.32 mm.
  • #1
knowNothing23
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26 ••• Since 1983, the US Mint has coined pennies that are made out of zinc
with a copper cladding. The mass of this type of penny is 2.50 g. Model the penny
as a uniform cylinder of height 1.23 mm and radius 9.50 mm. Assume the copper
cladding is uniformly thick on all surfaces. If the density of zinc is 7140 kg/m3
and that of copper is 8930 kg/m3, what is the thickness of the copper cladding?

The problem is similar to a coin inside a coin. We need to find the outer coin's height- the inner coin's height or thickness of the outer coin.

The inner coin is made of Zinc.

m = (ρ Cu)Vcu + (ρ Zn) Vzn, where p is rho of Cu and Zn respectively and Vcu and Vzn are volumes of copper and zinc respectively.

m = ρ Cu[ 2π(r)square d + 2πr (h − 2d )d ] + ρ Zn π (r − d )(square) (h − 2d ), where d is the thickness sought.

Could someone help? I don't undestand why the V covering the zinc coin is, what's in bold.
The volume I get is total volume- volume of zinc coin: πr(square)h-π(r-d)(square)(h-2d)
 
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  • #2
one of the Cu π(r)square d is the top disk , the other π(r)square d is the bottom disk.
2πr (h − 2d) d is the edge band , in between the top and bottom disks "approximately".
Your way is exact , so it's better ... if you can solve it.
 

Related to Calculating Thickness of Copper Cladding on Zinc Pennies | US Mint 1983-Present

1. How is the thickness of copper cladding on zinc pennies calculated?

The thickness of copper cladding on zinc pennies is calculated by using a specialized instrument called a micrometer. This instrument measures the thickness of a material by applying pressure on it and then measuring the distance between the two points of contact. The thickness of the copper cladding is then calculated by subtracting the thickness of the zinc core from the total thickness of the penny.

2. Why is the thickness of copper cladding important in pennies?

The thickness of copper cladding is important in pennies because it contributes to the overall weight and durability of the coin. It also affects the appearance and design of the penny. A thicker copper cladding can make the penny more resistant to wear and tear, while a thinner cladding may result in a more lightweight and potentially weaker coin.

3. What is the purpose of copper cladding on zinc pennies?

The purpose of copper cladding on zinc pennies is to protect the zinc core from corrosion. Copper is a more corrosion-resistant metal compared to zinc, and by coating the zinc core with a layer of copper, the penny is able to withstand the elements for a longer period of time.

4. Has the thickness of copper cladding on pennies changed over time?

Yes, the thickness of copper cladding on pennies has changed over time. In 1982, the US Mint changed the composition of pennies from 95% copper and 5% zinc to 97.5% zinc and 2.5% copper. This resulted in a thinner copper cladding on pennies minted after 1982. In 2019, the US Mint announced that they would be changing the composition of pennies again, this time to a zinc core coated with a copper-plated zinc layer.

5. How accurate are the measurements of copper cladding thickness on pennies?

The measurements of copper cladding thickness on pennies are very accurate. The micrometer used by the US Mint is a highly precise instrument, and the thickness of the copper cladding is measured in microns (millionths of a meter). This level of accuracy ensures that the pennies minted meet the standard specifications set by the US Mint.

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