Archimedes Principle and Specific Gravity Determination

[wildtron]

Homework Statement

a crown that is supposed to be pure gold has a mass of 850g. Its apparent mass when immersed in water is 798g. (a) what is the volume of the crown? (b)is it pure gold?If not, what is the percentage by volume of gold in the crown assuming that the crown is an alloy of lead and gold?

Homework Equations

density = m/v
specific gravity = weight of object in air /weight of object in air - weight of object immersed in water
density of gold = 19300kg/m^3
density of lead = 11300kg/m^3

The Attempt at a Solution

converted 850g to kg. 850g/1000g=.85kg
converted .85kg to weight. .85*9.8m/s^2=8.33 Newton
converted 798g to kg. 798g/1000g = .798kg
converter 798kg to weight. .798*9.8m/s^2=7.8204
used specific gravity
sp gr= 8.33N/8.33N - 7.8204N
cancel Newton
16.34615
since specific gravity is numerically equal to 1g/cm^3 in cgs system
16.34615*1g/cm^3 = 16.34615g/cm^3

converted 16.34615g/cm^3 to kg/m^3

16.34615g/cm^3 = 16346.15kg/m^3

density of crown = 16346.15kg/m^3

i don't know what's next...
i don't even know if I'm on the right track...

 

[mgb_phys]

I think you are making it a little unnecessarily complicated.

The difference in weight is equal to the mas sof water it displaces.
So it weighs the equivalent of 850-798g of water
And water has a density of 1g/cc, so it has a volume of how many cc ?

 

[kerimek]

As a scientist, the first thing I would do is to check my calculations and make sure they are correct. It seems like you have correctly converted the mass and weight of the crown, and calculated the specific gravity. However, there are a few things that could be improved in your solution.

First, the specific gravity should be calculated as the weight of the object in air divided by the difference between the weight of the object in air and the weight of the object immersed in water. So the correct calculation would be: sp gr = 8.33N / (8.33N - 7.8204N) = 16.34615.

Next, you have correctly converted the specific gravity to g/cm^3, but you do not need to convert it back to kg/m^3. The density of the crown is already in g/cm^3, so you can skip this step.

Now, to answer the questions:

(a) To find the volume of the crown, we can use the formula for density: density = mass/volume. Rearranging this equation, we get: volume = mass/density. So the volume of the crown would be: volume = 0.85kg / 16.34615 g/cm^3 = 0.052 cm^3.

(b) To determine if the crown is pure gold, we can compare the density of the crown (16.34615 g/cm^3) to the density of pure gold (19.3 g/cm^3). We can see that the density of the crown is lower than the density of pure gold, which means that the crown is not pure gold.

To calculate the percentage by volume of gold in the crown, we can use the formula: % gold = (density of gold / density of crown) * 100%. So the percentage by volume of gold in the crown would be: % gold = (19.3 g/cm^3 / 16.34615 g/cm^3) * 100% = 118.13%. This means that the crown is approximately 118% gold, which is not possible.

Therefore, we can conclude that the crown is not pure gold, and it is most likely an alloy of lead and gold. However, without knowing the exact composition of the alloy, we cannot determine the exact percentage by volume of gold in the crown.