Question

The composition of pennies has changed over the years, depending on a number of factors, including the availability of various metals. A penny minted in 1825 was pure copper; a penny minted in 1860 was 88% copper and 12% nickel; a penny minted in 1965 was 95% copper and 5% zinc; and a penny minted today is 97.5% zinc and 2.5% copper. Given that the densities of copper, nickel, and zinc are 8.92 g/cm^3 , 8.91 g/cm^3 , and 7.14 g/cm^3 , respectively, determine the density of each penny.

Answer 1

At 1825

The value is
`\rho_p =  8.9188 \ g/cm^3`

At 1965

The value is

The value is
`\rho_p =  8.831 \ g/cm^3`

At Today

The value is
`\rho_p = 8.8755 \ g/cm^3`

Step-by-step explanation:

From the question we are told that

The percentage of copper in 1825 penny is 100%

The percentage of copper in 1860 penny is 88%

The percentage of nickel is 1860 penny is 12%

The percentage of copper in 1965 penny is 95%

The percentage of zinc in 1965 penny is 5%

The percentage of copper in today's penny is 97.5%

The percentage of zinc in today's penny is 2.5%

The density of copper is
`\rho_c = 8.92 g/cm^3`

The density of zinc is
`\rho_z = 7.14 g/cm^3`

The density of nickel is
`\rho_n = 8.91 g/cm^3`

Considering 1825

The density of penny is
`\rho_p = 8.92 g/cm^3` because the penny was made up of 100% copper

Considering 1860

Generally the density of penny is mathematically evaluated as

`\rho_p = [(88)/(100) * \rho_c] +[(12)/(100) * \rho_z]`

=>
`\rho_p  =  [(88)/(100) *  8.92 ] +[(12)/(100) * 8.91 ]`

=>
`\rho_p =  8.9188 \ g/cm^3`

Considering 1965

Generally the density of penny is mathematically evaluated as

`\rho_p = [(95)/(100) * \rho_c] +[(5)/(100) * \rho_n]`

=>
`\rho_p  =  [(95)/(100) *  8.92 ] +[(5)/(100) * 7.14 ]`

=>
`\rho_p =  8.831 \ g/cm^3`

Considering today

Generally the density of penny is mathematically evaluated as

`\rho_p = [(97.5)/(100) * \rho_c] +[(2.5)/(100) * \rho_z]`

=>
`\rho_p  =  [(97.5)/(100) *  8.92 ] +[(2.5)/(100) * 7.14 ]`

=>
`\rho_p =  8.8755 \ g/cm^3`