Universal gravitation previous exam problem

[Mikecarlson]

Homework Statement

I'm having trouble with this problem attached. Any help would be appreciated.

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

You have the basic idea - but the r in the gravity equation is the separation between the two objects, not their distance from the origin.

So if one object is at x1=4m from the origin, and the other is at x2=6m, in the same direction, then how far apart are they?
if one is at x1=4m and the other at x2=x, in the same direction, then how far apart are they?

 

[Mikecarlson]

You have the basic idea - but the r in the gravity equation is the separation between the two objects, not their distance from the origin.

So if one object is at x1=4m from the origin, and the other is at x2=6m, in the same direction, then how far apart are they? 2m
if one is at x1=4m and the other at x2=x, in the same direction, then how far apart are they?x-4

So, are you saying object 1 and two are not 4 units apart?

 

[Mikecarlson]

The answer key has an answer of 4.98M. I have tried a few different ways to get that answer and have yet to figure it out. can you tell me if that answer is actually correct?

Thanks

 

[Simon Bridge]

Objects 1 and 2 are 4 units apart - that that's not the only separation that counts.
What is the separation between object 3 and 2?

The secret is to write the whole thing out in symbolic form first - then simplify the equation.

 

[BvU]

There is something else to worry about: you write an expression for |F| which is correct, but then you work it out to |F|+|F|=0 and there is a little thing you missed there.

The numerical value you found somewhere is totally unimportant, but correct.