Gravitational force between two golf balls of nuclear matter?

Question

What would be the gravitational force between two golf balls (each with a 4.28 cm diameter), 1.15 meter apart, if they were made of nuclear matter?

This is the question I need to solve

I figure I need to use F = G * [(m*m)/r^2]

I know G is 6.67e-11
I figure r is 0.575m

but I'm having trouble finding the masses of the golf balls because I dont really understand nuclear matter

they say density of nuclear matter is 2.31e17kg/m^3

Answer 1

Yah, good thing too! Cuz if you understood nuclear matter the way I do, you'd go what the heck (or sumthin').

Let me tell you what nuclear matter is -- or at least the way you're supposed to understand it for this question.

You know that golf balls and all other stuff are made of atoms, right?

And atoms are made of protons and neutrons and these make up the nucleus (positive charge). And electrons (negative charge) move around the nucleus.

The amount of space taken up by the electrons is very very much (more than 99% of the volume of the atom). Yet they contribute very very little to the mass of the atom.

To get nuclear matter, you just get rid of the electrons. And you're left with just the nuclei (protons & neutrons) all packed together. When they had the electrons, they were far apart. But now without the electrons,... OK, you get the picture.

So that's why nuclear matter is so very dense.

But it's also positively charged because the electrons are no longer there to neutralize the charge of the protons. HOw the heck do you hold all those nuclei together when they are all positive charged and pushing each other away?

Well, to do this question you'll have to ignore that little detail.

So now, to the question.

First off, why do you say you figure r to be 0.575m? r is already given to you as 1.15m.

To calculate the mass of each golf ball, use the density given (2.31E17kg/m^3) and multiply that by the volume of the golf ball. I got 4.11E-5m^3 for the volume and 9.48E12kg for the mass. (Be careful to convert the cm to m and the diameter to radius.)

Plug in the values and get F = 4.54E15N.

Now, this is by using r = 1.15m. r could actually be more because when they say that the golf balls are 1.15m apart, they could mean from surface to surface and not from centre to centre. If they mean the distance from the surface of one golf ball to the surface of the other golf ball is 1.15m, then you'll have to take into account the radius of the golf balls: just add 4.28cm to 1.15m and use that value for r in the equation.

Answer 2

You have the right equation you'll need to solve it, and to find the mass of the two golf balls you will need to use the density of nuclear matter and multiply it by the volume of the ball.

Remember, D = m/V so since we know density, and the diameter of the ball we can figure out the volume of the two balls and from there get the mass.

Vsphere = (4/3) * pi * r^3

Vsphere = ((4/3) * 3.14) * ((2.14)^3)

Vsphere = 4.186 * 9.80cm^3

Vsphere = 41.023 cm^3 for the golf ball volume

D = m/V

m = D * V

m = 2.31 x 10^17kg/m^3 * .41023 m^3

m = 9.476 x 10^16 kg for each golf ball of nuclear matter.

Now to use your correct equation, however the r in your equation will be a bit different than what you've calculated. The r in the equation is the distance between the center of the masses to each other. So in this case r would be 1.578m (radius of golf ball 1 + radius of golf ball 2 + distance between them) converted to meters.

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

F = 6.67 x 10^-11 * [(9.476 x 10^16 * 9.476 x 10^16) / 1.578]

F = 6.67 x 10^-11 * (8.979 x 10^33 / 1.578)

F = 6.67 x 10^-11 * 5.690 x 10^33

F = 3.795 x 10^23 Final answer.

I hope this helps you out.

Answer 3

Using your notation, m = rho V = rho 4/3 pi R^3; where rho = the density you gave, R = d/2 = .0428/2 meter the radii of each golfball. Thus F = G m^2/r^2 = G (rho V)^2/r^2 = G (rho V/r)^2; where r = 1.15 meter apart from center to center (assumed). If you meant 1.15 m from surface to surface, you need to add .0428 meter for 1.1928 meter (do you see why?).

Not clear what you mean by "I figure r is 0.575m' You already gave r = 1.15 meters apart. r is the full distance between centers of mass, not half distance.

Anyway, F = G (rho 4/3 pi R^3)^2/r^2 and you have all the numbers; so you can do the math. If you do everything in kg, m, and sec, F will be in kg-m/sec^2 units, which is known as Newtons.

Answer 4

Use the density figure that you showed in the additional remarks. Calculate the volume of the golf balls using the radii that you have, the mass of each using the density, then the force equation you have to get the gravitational attraction.

Answer 5

C. Will increase if the objects are moved closer together. The gravitational force varies by the inverse of the distance squared, so it's not always the same. Also it is proportional to mass, meaning that it will increase if either object gains mass, not decrease. Finally, if the objects are moved closer together, the force increases because the distance is in the denominator of the equation.