A 1.0kg mass weighs 9.8 Newton on earth's surface, and the radius of Earth is roughly 6.4 x 10 to the power of 6. The mass of the earth is 6.02 x 10 to the power of 24. Calculate the average density of Earth?
Mass over volume:
rho = 6.02 * 10^24 * 10^-18 / [(4/3) pi 6.4^3]
To calculate the average density of Earth, we need to use the formula:
Density = Mass / Volume
1. First, let's find the volume of Earth. The volume of a sphere is given by the formula:
Volume = (4/3) * π * (radius^3)
2. In this case, the radius of Earth is given as 6.4 x 10^6 meters. So we substitute this value into the formula:
Volume = (4/3) * π * (6.4 x 10^6 meters)^3
3. Calculate the volume:
Volume = (4/3) * π * (262,144 x 10^18 meters^3)
= 1.09 x 10^21 meters^3
4. Now, we have the volume of Earth. Next, we calculate the mass of Earth. The mass of Earth is given as 6.02 x 10^24 kilograms.
5. Finally, we substitute the mass and volume values into the density formula:
Density = Mass / Volume
Density = (6.02 x 10^24 kilograms) / (1.09 x 10^21 meters^3)
6. Calculate the density:
Density = 5.51 x 10^3 kilograms/meter^3
Therefore, the average density of Earth is 5.51 x 10^3 kilograms/meter^3.
To calculate the average density of Earth, we can use the formula:
Density = Mass / Volume
The mass of Earth is given as 6.02 x 10^24 kg. To find the volume of Earth, we can use the formula for the volume of a sphere:
Volume = (4/3) * π * radius^3
The radius of Earth is approximately 6.4 x 10^6 meters.
Let's calculate the volume first:
Volume = (4/3) * 3.14 * (6.4 x 10^6)^3
Volume = 4/3 * 3.14 * (4.096 x 10^18)
Volume = 1.737 x 10^19
Now, using the mass of Earth and the calculated volume, we can find the average density:
Density = 6.02 x 10^24 kg / 1.737 x 10^19 m^3
Now, let's divide the numbers:
Density ≈ 3.466 x 10^5 kg/m^3
Therefore, the average density of Earth is approximately 3.466 x 10^5 kg/m^3.