Where does Gravitation equals zero?

[Sapphiretwirl]

Homework Statement

So a 1kg mass and a 2kg mass are placed 10m away from each other, somewhere in between them the force of gravity cancles out. Where would am object with a mass of m be placed so that it is not affected by either of the 1kg and 2kg masses?

Homework Equations

Not sure, something with gravitation,rotational motion, angular velocity Ect.

The Attempt at a Solution

F=G*m1(m)/r

 

[Doc Al]

Your formula is not quite right; see: Gravity

All you need to worry about is the force of gravity. Hint: Will the ƩF = 0 point will be closer to the 1 kg mass or the 2 kg mass?

 

[Sapphiretwirl]

The 1 kg mass of course, but I don't know where to go from there :(

 

[Doc Al]

The 1 kg mass of course, but I don't know where to go from there :(

Good!

Call the distance to the 1 kg mass "x". What is the force of gravity from the 1 kg mass at that point?

If the distance to the 1 kg mass is x, what would be the distance to the 2 kg mass? What is the gravitational force from the 2 kg mass at that point?

Solve for the distance that makes the net force zero.

 

[Sapphiretwirl]

I've tried but I can't solve for the distance, the furthest I've gotten is this

Fg=G*(m1(m2))/r^2

0=6.67*10^-11(2/x^2)

 

[Office_Shredder]

Isn't it a bit weird that your formula for the force of gravity doesn't involve the mass m of the object we are looking at?

There are two sources of gravity, each of them acts on the object in a different direction.

 

[Sapphiretwirl]

I got 1.7 meters for x

 

[Sapphiretwirl]

I probably did something wrong

 

[haruspex]

I got 1.7 meters for x

Pls post your working, not just the numeric answer. Preferably, do all the working in symbols, only plugging in numbers at the end. Follow Doc Al's recipe.

 

[Sapphiretwirl]

I really don't know what I did

 

[haruspex]

I really don't know what I did

Then start again, following Doc Al's recipe. Answer each question in turn, as far as you can:

Call the distance to the 1 kg mass "x". What is the force of gravity from the 1 kg mass at that point?

If the distance to the 1 kg mass is x, what would be the distance to the 2 kg mass?

What is the gravitational force from the 2 kg mass at that point?