A carefully designed experiment can measure the gravitational force between masses of 9 kg. Given that the density of iron is 7860 kg/m3, what is the gravitational force between two 9.00-kg iron spheres that are touching in N?
V=4πR³/3
Density ρ=m/V = 3•m/4•π•R³ = >
R=cuberoot(3•m/4•π• ρ) = cuberoot(3•9•9/4•π•7860) =0.065 m.
the gravitational constant
G =6.67•10^-11 N•m²/kg²,
F =G•m1•m2/R² = =6.67•10^-11•9²/0.065²=1.28•10^-6 N
The third line
R=cuberoot(3•m/4•π• ρ) = cuberoot(3•9/4•π•7860) =0.065 m.
I'm supposed to get 3.21e-07 N.
F =G•m1•m2/(2R)² = 6.67•10^-11•9²/(2•0.065)²=1.28•10^-6/4 =0.32•10^-6 N
To calculate the gravitational force between two iron spheres, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant (approximately 6.67430 x 10^-11 N*m^2/kg^2)
m1 = mass of the first sphere
m2 = mass of the second sphere
r = distance between the centers of the spheres
In this case, we are given the mass of each sphere as 9.00 kg. Since the spheres are touching, the distance, r, between their centers can be assumed to be the sum of their radii.
To find the radius of the sphere, we need to use the density information. The formula for the volume of a sphere is:
V = (4/3) * π * r^3
We can rearrange this formula to solve for the radius:
r = (3 * V / (4 * π))^(1/3)
Given that the density of iron is 7860 kg/m^3, the mass of each sphere can be used to find its volume:
V = m / density
Once we have the radius, we can substitute the values in the gravitational force formula to calculate the result. Let's do the calculations step by step:
Step 1: Calculate the volume:
V = 9.00 kg / 7860 kg/m^3
V ≈ 0.001145512 m^3
Step 2: Calculate the radius:
r = (3 * 0.001145512 m^3 / (4 * π))^(1/3)
r ≈ 0.063048 m
Step 3: Calculate the gravitational force:
F = (6.67430 x 10^-11 N*m^2/kg^2) * (9.00 kg) * (9.00 kg) / (2 * 0.063048 m)^2
F ≈ 2.1202986 x 10^-8 N
Therefore, the gravitational force between the two 9.00-kg iron spheres that are touching is approximately 2.12 x 10^-8 N.