A bag contains a mixture of copper and lead BBs. the Average density of the BBs is 9.50g/cm^3. Assuming that the copper and lead are pure determine the relative amounts of each kind of BB
Look up the densities of lead and copper. Lead: 11.34 g/cm^3. Copper: 8.93 g/cm^3
If f is the fraction of the BBs that are copper (which would be a volume fraction), then 1-f is the fraction that are lead, then
8.93 f + 11.34(1-f) = 9.50
Solve for f
To determine the relative amounts of copper and lead BBs in the bag, we can use the concept of density. Since we are given the average density of the BBs, we can start by comparing it to the densities of pure copper and lead.
The density of pure copper is approximately 8.96 g/cm^3, and the density of pure lead is approximately 11.34 g/cm^3.
Since the average density of the BBs is 9.50 g/cm^3, which is closer to the density of copper, we can conclude that the mixture contains a higher proportion of copper BBs.
To calculate the relative amounts, we need to find the ratio of the densities. Let's call the relative amount of copper BBs "x" and the relative amount of lead BBs "y".
Density of mixture = (Density of copper * x) + (Density of lead * y)
9.50 = (8.96 * x) + (11.34 * y)
We also know that the relative amounts of copper and lead BBs should add up to 100%, so:
x + y = 1
Now we have a system of two equations to solve simultaneously:
8.96x + 11.34y = 9.50
x + y = 1
We can solve this system of equations to find the relative amounts of copper and lead BBs in the bag.
To determine the relative amounts of copper and lead BBs in the bag, we need to use the average density and the densities of copper and lead.
The density of an object can be calculated using the formula: density = mass/volume.
Since the average density of the BBs is given as 9.50 g/cm^3, we can set up the following equation:
9.50 g/cm^3 = (mcopper * ρcopper + mlead * ρlead) / (mcopper + mlead)
where:
- mcopper is the mass of the copper BBs
- mlead is the mass of the lead BBs
- ρcopper is the density of copper (8.96 g/cm^3)
- ρlead is the density of lead (11.34 g/cm^3)
We can simplify this equation by multiplying both sides by (mcopper + mlead):
9.50 g/cm^3 * (mcopper + mlead) = mcopper * ρcopper + mlead * ρlead
We can rearrange this equation to solve for mcopper:
9.50 g/cm^3 * mcopper + 9.50 g/cm^3 * mlead = mcopper * ρcopper + mlead * ρlead
9.50 g/cm^3 * mcopper - mcopper * ρcopper = mlead * ρlead - 9.50 g/cm^3 * mlead
Now, we can factor out mcopper and mlead:
mcopper * (9.50 g/cm^3 - ρcopper) = mlead * (ρlead - 9.50 g/cm^3)
Finally, we solve for mcopper/mlead:
mcopper / mlead = (ρlead - 9.50 g/cm^3) / (9.50 g/cm^3 - ρcopper)
By substituting the known values of ρcopper and ρlead into the equation, you can determine the relative amounts of copper and lead BBs in the bag.