Search: a 1.0 kg mass weighs 9.8 n on earths surface and the radius of the earth is roughly 6.4x10 to the 6 m. what is the mass of the earth and the average density of Earth
use the formula F=(G(m1)(m2))/r^2
G=universal gravitational constant=
6.67x10^-11 N m^2/kg^2
F=9.8 N (given)
m1=1.0 kg (given)
m2=mass of earth (variable)
r=6.4x10^6 m (given)
9.8 N=((6.67x10^-11 N m^2/kg^2)(1.0 kg)(m2))/(6.4x10^6 m)
x=6.02x10^24 kg
Why did the mass go on a diet? Because it wanted to weigh less on Earth! But enough weight loss jokes, let's calculate the mass of the Earth and its average density.
To find the mass of the Earth, we can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force (in this case, the weight of the 1.0 kg mass, which is 9.8 N),
G is the gravitational constant,
m1 is the mass of the Earth, and
r is the radius of the Earth.
Rearranging the equation to solve for the mass of the Earth (m1), we have:
m1 = (F * r^2) / (G * m2)
Substituting the given values:
F = 9.8 N
r = 6.4 x 10^6 m
m2 = 1.0 kg
G = 6.67430 x 10^-11 N·(m/kg)^2 (the gravitational constant)
Let me do the maths... and... drumroll please...
The mass of the Earth is approximately 5.98 x 10^24 kg! Wow, that's a lot of weight to carry around.
Now, to find the average density of the Earth, we know that:
Density = Mass / Volume
But we don't have the volume of the Earth. Don't worry, we can use the formula for the volume of a sphere:
Volume = (4/3) * π * r^3
Substituting the given radius:
r = 6.4 x 10^6 m
Let me grab my calculator and... viola!
The calculated average density of the Earth is around 5.52 x 10^3 kg/m^3.
So there you have it: the mass of the Earth and its average density. But remember, these are just approximate values, because Earth likes to keep a little mystery about itself!
To find the mass of the Earth, we can use the formula for gravitational force:
F = G * ((m1 * m2) / r^2)
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2)
m1 is the mass of the Earth
m2 is the mass of the 1.0 kg object
r is the radius of the Earth
We know that the weight of the 1.0 kg mass is 9.8 N on Earth's surface, which is equal to the force of gravity acting on it. Therefore,
F = 9.8 N
Plugging in the known values and solving for the mass of the Earth (m1):
9.8 N = (6.67 × 10^-11 N(m/kg)^2) * ((m1 * 1.0 kg) / (6.4 × 10^6 m)^2)
Simplifying further:
9.8 N = (6.67 × 10^-11 N(m/kg)^2) * (m1 / (6.4 × 10^6)^2 kg)
Rearranging the equation to solve for m1:
m1 = (9.8 N * (6.4 × 10^6)^2 kg) / (6.67 × 10^-11 N(m/kg)^2)
Calculating m1:
m1 = 5.972 × 10^24 kg
Therefore, the mass of the Earth is approximately 5.972 × 10^24 kg.
To find the average density of the Earth, we can use the formula:
Density = Mass / Volume
We already know the mass of the Earth, which is approximately 5.972 × 10^24 kg. The volume of a sphere (the Earth) is given by:
Volume = (4/3) * π * r^3
Plugging in the known values and solving for the average density:
Density = (5.972 × 10^24 kg) / ((4/3) * π * (6.4 × 10^6 m)^3)
Calculating the average density:
Density = 5515.3 kg/m^3
Therefore, the average density of the Earth is approximately 5515.3 kg/m^3.
To find the mass of the Earth, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2),
m1 is the mass of the first object,
m2 is the mass of the second object, and
r is the distance between the centers of the objects.
In this case, we know the mass of the smaller object (1.0 kg) and the weight (9.8 N) which is the force due to gravity acting on it. Since weight is the force of gravity on an object, we can set F = 9.8 N and m1 = 1.0 kg. Also, we know the radius of the Earth (6.4 x 10^6 m), which represents the distance from the center of the Earth to the surface.
Using these values, we can rearrange the formula to solve for the mass of the Earth (m2) as follows:
m2 = (F * r^2) / (G * m1)
m2 = (9.8 N * (6.4 x 10^6 m)^2) / (6.67 x 10^-11 Nm^2/kg^2 * 1.0 kg)
Calculating this equation will give us the mass of the Earth.
Now, to find the average density of the Earth, we can use the formula:
Density = mass / volume,
where the volume of a sphere is given by:
Volume = (4/3) * pi * r^3
Using the known mass of the Earth and its radius, we can calculate the average density using these formulas.
Let's now calculate the mass of the Earth and average density:
First, we calculate the mass of the Earth:
m2 = (9.8 N * (6.4 x 10^6 m)^2) / (6.67 x 10^-11 Nm^2/kg^2 * 1.0 kg)
m2 ≈ 5.972 × 10^24 kg
So, the mass of the Earth is approximately 5.972 × 10^24 kg.
Next, we calculate the average density of the Earth:
Volume = (4/3) * pi * r^3,
where r = 6.4 x 10^6 m.
Volume = (4/3) * 3.14 * (6.4 x 10^6 m)^3
Average Density = mass of Earth / volume
Average Density ≈ (5.972 × 10^24 kg) / [(4/3) * 3.14 * (6.4 x 10^6 m)^3]
The calculation will give us the average density of the Earth.