Two men each have a mass of 90 kg. If the gravitational force between them is 8.64 x 10^-8 N, how far apart are they? G = 6.67 * 10^-11 N(m/kg)^2

I have been trying to figure it out and i can't. I have no one to show me how either

Question

Two men each have a mass of 90 kg. If the gravitational force between them is 8.64 x 10^-8 N, how far apart are they? G = 6.67 * 10^-11 N(m/kg)^2

I have been trying to figure it out and i can't. I have no one to show me how either

matt101 · Answer

Just plug these numbers into Newton's law of universal gravitation:

$$F={Gm_1m_2 \over r^2}$$

anonymous · Answer

I don't know how to do that. I am using APEX and it doesn't give a good description on how to plug them it :(

matt101 · Answer

In that equation, F is the force, G is the gravitational constant, m(1) and m(2) are the masses of the two objects, and r is the distance between the objects.

You have all the information given except for r, which you need to solve for. Let me know what you get!

anonymous · Answer

still nothing besides a ridiculous number. I've reread the material from APEX over and over and i still don't understand.

matt101 · Answer

What number did you get?

anonymous · Answer

I don't know how to use the formula. I got 116581.709...

anonymous · Answer

I did everything wrong with the formula.

matt101 · Answer

Hey! Let's back up for one second.

The equation we're using is:

$$F={Gm_1m_2 \over r^2}$$
We want to solve for r, so it might make it easier to isolate r on one side. To do that, multiply both sides by r^2, then divide both sides by F. This will give you:

$$r^2={Gm_1m_2 \over F}$$
But this is solving for r^2, and we only want r! So the last thing to do is take the square root of both sides, leaving:

$$r=\sqrt{Gm_1m_2 \over F}$$
From the question we have the following information:
F = 8.64 x 10^(-8) N
G = 6.67 * 10^(-11) N(m/kg)^2
m(1) = 90 kg
m(2) = 90 kg

Does that help?

anonymous · Answer

Yes a lot more. Can i just plug that into my scientific calculator and solve?

matt101 · Answer

You absolutely can! Do you understand the steps I followed?

anonymous · Answer

a little bit. I still can't figure it out! I got 79.07

matt101 · Answer

Maybe you just made a mistake typing the numbers into your calc!

You should have:

$$r=\sqrt{6.67 \times 10^{-11} \times 90 \times 90 \over 8.64 \times 10^{-8}}$$
Try it one more time!

anonymous · Answer

is it 2.5?

matt101 · Answer

It sure is!

anonymous · Answer

Thank you!

matt101 · Answer

Meaning the people are 2.5 m apart, which is a reasonable answer!