A carefully designed experiment can measure the gravitational force between masses of 8 kg. Given that the density of iron is 7860 kg/m3, what is the gravitational force between two 8.00-kg iron spheres that are touching?

To calculate the gravitational force between two objects, you can use Newton's law of universal gravitation, which states that the gravitational force (F) between two masses (m1 and m2) is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers.

The equation for Newton's law of universal gravitation is:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (6.67 x 10^-11 N(m^2/kg^2))
m1 and m2 are the masses of the objects
r is the distance between their centers

In this case, you have two iron spheres with a mass of 8.00 kg each. Since they are touching, the distance between their centers is equal to the sum of their radii.

To find the radius of the iron spheres, we can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

Since the density of iron is given as 7860 kg/m^3, we can equate the volume of the sphere to the mass of the sphere divided by the density of iron:

(4/3) * π * r^3 = m / ρ

Solving for r:

r^3 = (3m) / (4πρ)

Now we can substitute the values into the formula to calculate the gravitational force:

F = (G * m1 * m2) / r^2

Remember to convert the mass of the spheres to kilograms before substituting into the equation.

Calculations:
1. Calculate the radius of the sphere:
- Convert the density to kilograms per cubic meter: 7860 kg/m^3
- Use the given mass to calculate the volume:
(4/3) * π * r^3 = (2 * 8.00 kg) / 7860 kg/m^3
- Solve for r by taking the cube root of both sides
- Calculate the radius r.

2. Substitute the values into the formula for Newton's law of universal gravitation:
- F = (6.67 x 10^-11 N(m^2/kg^2) * (8.00 kg) * (8.00 kg)) / (2r)^2

3. Calculate the gravitational force F.

Following these steps, you can calculate the gravitational force between the two 8.00 kg iron spheres that are touching.