How to find mass with gravitational attraction.

[ssjdbz101]

Hello, I'm trying to solve a problem, but I'm doing something wrong.

This is the problem out of my Physics book, but the problem I'm working on has different numbers, so any help will not be cheating, I just need to know the process.

Problem:
Two objects are attracted to each other gravitationally with a force of 2.5e-10 N when they are 0.25 meters apart. Their total mass is 4.0 kg. Find their individual masses.

Answer:
I know the answer is m1=3.9kg, and m2=0.1kg. But I don't know how they got this answer.

Help please.

 

[turdferguson]

You can calculate the product of the masses with the given force and distance. Then because you know the sum, you have a system of 2 equations with 2 unknowns

 

[ssjdbz101]

I know that, but I'm still confused.

Since the equation is: Fg = G m1m2/r^2

if I plug in the numbers I'm given:
Fg=2.5e-10
G=6.67e-11
r=0.25

I have: 2.5e-10 = 6.67e-11 m1m2 / 0.25^2.

I solve for m1m2, which is: m1m2 = (Fg*r^2)/G , right?

Doing that, I have m1m2 = (2.5e-10*0.0625)/6.67e-11 = 0.23426

Now what do I do?
I know m1=3.9, and m2=0.1, so shouldn't (m1m2=0.39) ?

The sum of the masses: (m1+m2=4), but how do I use this in the (m1m2=0.39) ?

I'm doing something wrong, but what?

 

[Anadyne]

I don't see anything wrong in your calculations but are you sure you copied the numbers right?

If you have two equations: m1 + m2 = 4 and m1*m2 = #

Solve for m1 in one equation like m1 = 4 - m2
And then plug that into the other equation m1*m2 = (4 - m2)*m2 = #
Once you have m2, go back to m1 + m2 = 4 to solve for m1.

The idea is to solve one equation for a variable. Then replace the same variable in the second equation so there's only one unknown.

 

[ssjdbz101]

Thanks, I figured it was that, but for some reason, I could not figure out (4-m2)*m2=#.
Major brain fart.

Thanks a lot!