• Support PF! Buy your school textbooks, materials and every day products Here!

Fluids (Density)

  • #1
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)
 

Answers and Replies

  • #2
lightgrav
Homework Helper
1,248
30
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 Threads on Fluids (Density)

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
6K
Replies
4
Views
5K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
9K
  • Last Post
Replies
1
Views
1K
Top