How Do You Calculate the Density of Earth's Core Given Its Mantle Density?

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In summary, using the given values and equations, the mean density of Earth's core is estimated to be 9222.22 kg/m^3, which may differ slightly from other calculations, but is of the same order of magnitude.
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mendem03
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Homework Statement


Assuming the Earth to be comprised of only a uniform density mantle and a uniform density
core and the mean density of the mantle to be 4700 kg=m3, determine the mean density of
the Earth's core. Take Earth's radius to be 6400 km and the radius of the core to be 3500 km.
Assume the Earth's mean density is 5520 kg=m3


Homework Equations


density = mass/volume


The Attempt at a Solution


V_c = 1.80 * 10^20 meter cubed
V_e = 1.10 * 10^21 meter cubed
V_m = V_e - V_c
= 9.20 * 10^20

M_e = M_c + M_m
M_e = D_c*V_c + D_m*V_m
D_c = (M_e - D_m*V_m)/V_c
D_c = 9222.22

I think I got the wrong answer so can someone help me with it.
 
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  • #2
From the givens, I got
D_c = (M_e - M_m) / V_c
= [ D_e*V_e - ((D_m (V_e - V_c)) ] / V_c

which is equivalent to yours and an answer, though slightly different, of the same order of magnitude.
 

1. What is density and why is it important?

Density is a measure of how much matter (mass) is packed into a certain volume. It is important because it can help identify and classify materials, and can also be used to determine the physical properties of a substance.

2. How do I calculate density?

Density is calculated by dividing the mass of an object by its volume. The formula is: Density = Mass ÷ Volume. The units for density are typically grams per cubic centimeter (g/cm3) for solids and liquids, and grams per liter (g/L) for gases.

3. What tools do I need to measure density?

To measure density, you will need a balance or scale to measure the mass of the object, and a ruler or measuring tape to determine its volume. You may also need a graduated cylinder or beaker to measure the volume of liquids.

4. Can density change?

Yes, density can change depending on the temperature and pressure of the substance. As temperature increases, the particles in a substance tend to expand and take up more space, resulting in a decrease in density. As pressure increases, the particles are compressed and take up less space, resulting in an increase in density.

5. How can I use density to identify unknown substances?

Density can be used as a characteristic property to identify unknown substances. By comparing the density of an unknown substance to the known densities of different materials, you can determine what the substance is made of. This can be especially useful in forensic science and environmental studies.

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