Where does Gravitation equals zero?

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To find the point where gravitational forces cancel out between a 1kg and a 2kg mass placed 10m apart, the object must be positioned closer to the 1kg mass. The gravitational force equations indicate that the distance to the 1kg mass is denoted as "x," while the distance to the 2kg mass would be 10 - x. The net gravitational force can be set to zero by equating the forces from both masses, leading to the equation Fg=G*(m1*m)/r^2. The discussion emphasizes the importance of showing all calculations symbolically before substituting numerical values to ensure clarity in the solution process. The final goal is to solve for the exact distance "x" that results in zero net gravitational force.
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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
 
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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?
 
The 1 kg mass of course, but I don't know where to go from there :(
 
Sapphiretwirl said:
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.
 
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)
 
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.
 
I got 1.7 meters for x
 
I probably did something wrong
 
Sapphiretwirl said:
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.
 
  • #10
I really don't know what I did
 
  • #11
Sapphiretwirl said:
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?
 

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