A bag contains a mixture of copper and lead BBs. The average density of the BBs is 9.80 {\rm g/cm^3}. Assuming that the copper and lead are pure, determine the relative amounts of each kind of BB.
You can do this more easily with a sheet of graph paper but this will have to do since we can't draw pictures.
11.34...............9.80.........8.93
d Pb...............d mixture.....d Cu
|....................|............|
100%Pb...............?..........0%Pb
0%Cu.................?........100% Cu
Look at the above as a graph.
The total span of density is from 11.34 to 8.93 = 2.41 units.
From Pb to mixture is 11.34-9.80 = 1.54
From mixture to Cu is 9.80-8.93 = 0.87
So % Cu = (1.54/2.41)*100 = ??
%Pb = (0.87-2.41)*100 = ??
Check my thinking.
I'm not sure you got the lead part right, whats simpler is once you get the copper do 1-copper answer to find the lead as the bb's are mixed together (must add up to 100%)
To determine the relative amounts of copper and lead BBs in the bag, we can set up a system of equations based on the average density and the densities of copper and lead.
Let's assume the bag contains x copper BBs and y lead BBs.
The density of copper is 8.96 g/cm^3, and the density of lead is 11.34 g/cm^3.
The average density of the BBs is given as 9.80 g/cm^3.
The total volume of the BBs can be calculated by dividing the total mass by the average density.
The total mass can be calculated by multiplying the mass of each type of BB by its respective number:
Total mass = mass of copper BBs + mass of lead BBs
Total mass = (mass of 1 copper BB)(number of copper BBs) + (mass of 1 lead BB)(number of lead BBs)
Total mass = (8.96 g/cm^3)(x) + (11.34 g/cm^3)(y)
The total volume can be calculated by dividing the total mass by the average density:
Total volume = Total mass / Average density
Total volume = [(8.96 g/cm^3)(x) + (11.34 g/cm^3)(y)] / 9.80 g/cm^3
Since volume is equal to the sum of the volumes of each type of BB, we can write:
Total volume = (Volume of x copper BBs) + (Volume of y lead BBs)
Total volume = (volume of 1 copper BB)(number of copper BBs) + (volume of 1 lead BB)(number of lead BBs)
The volume of each type of BB can be calculated using their respective densities:
Total volume = [(8.96 g/cm^3)(x) / density of copper] + [(11.34 g/cm^3)(y) / density of lead]
Equating the two expressions for total volume:
[(8.96 g/cm^3)(x) + (11.34 g/cm^3)(y)] / 9.80 g/cm^3 = [(8.96 g/cm^3)(x) / density of copper] + [(11.34 g/cm^3)(y) / density of lead]
Now we can solve this equation for x and y to determine the relative amounts of each kind of BB.
To determine the relative amounts of copper and lead BBs in the mixture, we can use their densities and the average density of the BBs.
Let's assume the mass of the copper BBs is m1 and the mass of the lead BBs is m2.
The average density of the BBs, which is 9.80 g/cm^3, can be calculated using the formula:
Average Density = (Density of Copper BBs * Mass of Copper BBs + Density of Lead BBs * Mass of Lead BBs) / Total Mass of BBs
Substituting the given density values, we have:
9.80 g/cm^3 = (Density of Copper BBs * m1 + Density of Lead BBs * m2) / (m1 + m2)
Since copper is denser than lead, we have the following values:
Density of Copper BBs = 8.96 g/cm^3
Density of Lead BBs = 11.34 g/cm^3
Substituting these values, we get:
9.80 g/cm^3 = (8.96 g/cm^3 * m1 + 11.34 g/cm^3 * m2) / (m1 + m2)
Now, we have one equation with two variables. To solve for these variables, we need another equation.
Let's use the fact that the total mass of the BBs is equal to the sum of the masses of copper and lead BBs:
Total Mass of BBs = m1 + m2
Unfortunately, we don't have the total mass information.
Therefore, we cannot determine the exact relative amounts of copper and lead BBs without additional information.
To obtain the relative amounts, we need to know either the total mass of the BBs or the mass of one type of BB (either copper or lead). With this information, we could solve the system of equations to find m1 and m2, giving us the relative amounts.