Finding density for identical spheres

In summary, the minimum density required for two identical spheres of diameter 8.55m on the surface of the earth to have a gravitational force between them equal to the weight of one of the spheres is approximately 3.3 * 10^10 kg/m^3. This is due to the small value of the gravitational constant, making it necessary for the spheres to have a large amount of mass in order to produce a comparable acceleration to the Earth.
  • #1
Tiven white
58
0

Homework Statement


Two identical spheres of diameter 8.55m are on the surface of the earth. The spheres are touching each other. What is the minimum density the spheres must have such that the gravitational force between them is at least equal to the weight of one of the spheres.


Homework Equations



F= m1*a = (G*m1*m2)/(r^2)
Newtons law of universal gravitation.

The Attempt at a Solution


I used the value for the acceleration of the Earth and multiplied it by the square of the radius between the spheres then divided the result by G to obtain m the mass m of one of the spheres was then divided by the volume of the sphere calculated from ((4/3)*Π*r^3) though this gave a value too high for the density of the sphere the value was like 3*10^10 kg/(m^3) higher than even the density of the planet is there any other insight to an attempt or solution to this problem it would be greatly appreciated.
 
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  • #2
Tiven white said:

Homework Statement


Two identical spheres of diameter 8.55m are on the surface of the earth. The spheres are touching each other. What is the minimum density the spheres must have such that the gravitational force between them is at least equal to the weight of one of the spheres.

Homework Equations



F= m1*a = (G*m1*m2)/(r^2)
Newtons law of universal gravitation.

The Attempt at a Solution


I used the value for the acceleration of the Earth and multiplied it by the square of the radius between the spheres then divided the result by G to obtain m the mass m of one of the spheres was then divided by the volume of the sphere calculated from ((4/3)*Π*r^3) though this gave a value too high for the density of the sphere the value was like 3*10^10 kg/(m^3) higher than even the density of the planet is there any other insight to an attempt or solution to this problem it would be greatly appreciated.

Your answer is in the right ballpark and I think you are doing the right thing, but I don't think it's quite right. Can you show your work. The density will have to be huge? Gravity is a very weak force.
 
Last edited:
  • #3
OK so where a= (G*m)/(r^2)
9.81 = ((6.67*10^-11)*(m)) / (8.55^2)
So (9.81)*( 8.55^2)/(6.67*10^-11) = m
So m = 1.08 * 10^13 kg


V =( 4/3)*(3.14)*(8.55/2)^3
V = 3.27 * 10^2 (m^3)
So density = (1.08* 10^13) ÷(3.27*10^2)
This implies the density =( 3.3 * 10^10 kg/m^3)
 
  • #4
Could u verify the working as u had asked.for.a sample of the calculations
 
  • #5
Tiven white said:
OK so where a= (G*m)/(r^2)
9.81 = ((6.67*10^-11)*(m)) / (8.55^2)
So (9.81)*( 8.55^2)/(6.67*10^-11) = m
So m = 1.08 * 10^13 kg


V =( 4/3)*(3.14)*(8.55/2)^3
V = 3.27 * 10^2 (m^3)
So density = (1.08* 10^13) ÷(3.27*10^2)
This implies the density =( 3.3 * 10^10 kg/m^3)
Looks right.
 
  • #6
haruspex said:
Looks right.

I agree. I was forgetting to divide the diameter by 2 to get the radius.
 
  • #7
So I was skeptical about why the spheres had to have such a huge density could I hear an explanation why
 
  • #8
Tiven white said:
So I was skeptical about why the spheres had to have such a huge density could I hear an explanation why

It's what I said in the first response. It's because G is so small. It's so small it's difficult to even measure using laboratory scale objects, http://en.wikipedia.org/wiki/Gravitational_constant#History_of_measurement It shouldn't be surprising that to get an amount of acceleration comparable to the acceleration produced by the whole Earth you'd need a lot of mass. Hence huge density.
 

1. What is the formula for finding the density of identical spheres?

The formula for finding density of identical spheres is: density = mass / (4/3 * pi * (radius)^3).

2. How do you measure the mass of identical spheres?

The mass of identical spheres can be measured using a scale or balance. The spheres should be weighed together to get an accurate measurement.

3. What is the unit of measurement for density?

The unit of measurement for density is typically grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3).

4. How do you measure the radius of identical spheres?

The radius of identical spheres can be measured using a ruler or caliper. The measurement should be taken from the center of the sphere to the edge.

5. Can the density of identical spheres vary?

No, the density of identical spheres should be the same as long as they have the same mass and radius. This is because density is an intrinsic property of a substance and is not affected by the amount of the substance present.

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