A 1.0 kg mass weighs 9.8 N on Earth's surface, and the radius of Earth is roughly 6.4 x 10^6 m. Calculate the average density of Earth
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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?
Physics - Damon, Monday, December 24, 2012 at 3:42pm
Mass over volume:
rho = 6.02 * 10^24 * 10^-18 / [(4/3) pi 6.4^3]
6*5e10
To calculate the average density of Earth, we can use the formula:
Density = Mass / Volume
Since we are given the weight of a 1.0 kg mass on Earth's surface, we can equate it to the gravitational force:
Weight = Mass * Gravitational Acceleration
On Earth's surface, the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the weight is:
Weight = 1.0 kg * 9.8 m/s^2 = 9.8 N
The weight can also be expressed as the gravitational force:
Weight = (G * Mass1 * Mass2) / Radius^2
Where G is the gravitational constant, Mass1 is the mass of the Earth, Mass2 is the mass of the object, and Radius is the radius of the Earth.
Since the object is on Earth's surface, we can assume the mass of Earth is much larger than the mass of the object. Therefore, we can consider Mass1 as the mass of the Earth.
Substituting the values, we can solve for the mass of the Earth:
9.8 N = (6.67 x 10^-11 N*m^2/kg^2) * Mass1 * 1.0 kg / (6.4 x 10^6 m)^2
Simplifying the equation:
9.8 N = 6.67 x 10^-11 N*m^2/kg^2 * Mass1 / (6.4 x 10^6 m)^2
Solving for Mass1, the mass of the Earth:
Mass1 = (9.8 N * (6.4 x 10^6 m)^2) / (6.67 x 10^-11 N*m^2/kg^2 * 1.0 kg)
Calculate the value:
Mass1 ≈ 5.98 x 10^24 kg
Now that we know the mass of the Earth, we can calculate its average density.
Density = Mass of Earth / Volume of Earth
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * Radius^3
Substitute the values and calculate:
Density = (5.98 x 10^24 kg) / [(4/3) * π * (6.4 x 10^6 m)^3]
Density ≈ 5.52 x 10^3 kg/m^3
Therefore, the average density of Earth is approximately 5.52 x 10^3 kg/m^3.
To calculate the average density of Earth, we need to use the formula:
Average Density = Mass / Volume
The mass of Earth is not given directly, but we can calculate it using the weight of a 1.0 kg mass on Earth's surface. We know that weight is the force experienced by an object due to gravity, and it is given by:
Weight = Mass × Acceleration Due to Gravity
In this case, the mass is 1.0 kg, and the weight is given as 9.8 N (Newtons). The acceleration due to gravity on Earth's surface is approximately 9.8 m/s^2.
Now, we can find the mass of Earth:
Mass of Earth = Weight of 1.0 kg mass / Acceleration Due to Gravity
Mass of Earth = 9.8 N / 9.8 m/s^2
Mass of Earth = 1.0 kg
So, the mass of Earth is 1.0 kg.
Next, we can find the volume of Earth using the formula for the volume of a sphere:
Volume = (4/3) × π × (radius)³
Plugging in the given radius of Earth (6.4 x 10^6 m) into the formula, we get:
Volume = (4/3) × π × (6.4 x 10^6 m)³
Next, calculate the volume using calculators or spreadsheet software.
Finally, we can calculate the average density of Earth:
Average Density = Mass of Earth / Volume of Earth
Plug in the value of the mass of Earth and the volume of Earth into the formula, and calculate the result to find the average density of Earth.