Gravitational force and particles

[ace123]

3. In the figure below, two objects of mass m and 2m, are fixed in place on an axis.
(a) Now consider a third particle of mass 5m. Where must this object be placed so that there is zero net gravitational force on it from the first two objects: to the left of the first two objects, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? Explain fully.
(b) Repeat (a) for the case where the mass of the third object is 15m.
(c) Is there a point off the axis at which the net force on the third object would be zero? Explain fully.


a. I think it should be placed between them but closer to the less massive particle. Since we need a net force of zero the force by the mass m has to equal the force of mass 2m.

b. I think it's the same as a.

c. Don't fully understand what he means by this question but I'm guessing it would be a distance far away from the 2 masses so the r will be so big that any force will be neglegible.

Is this right? Can someone help me better understand this? Any help will be much appreciated

 

[ace123]

Sorry I forgot this picture. It's in the attachment and it's the third question. Thank you

 

[Dick]

Don't really need the picture. Your description is fine. You are, in spirit, right on all three. But for c) I think what you really want to say is that there is no such point. You can get far enough away that the force is in some sense, negligible, but it's still nonzero. The question does say, 'explain fully'. Why does it have to be closer to the smaller mass particle?

 

[ace123]

That's my problem I'm having difficulty explaining it. I think it's because the bigger distance between 2m and 5m will balance out with the larger numerator, 2m times 5m. And if it is closer to the m it will balance out with the smaller number, 1m times 5m. Does this make sense or is their some other way to explain this better and I'm just missing it?

Thanks for the help

 

[Dick]

That's my problem I'm having difficulty explaining it. I think it's because the bigger distance between 2m and 5m will balance out with the larger numerator, 2m times 5m. And if it is closer to the m it will balance out with the smaller number, 1m times 5m. Does this make sense or is their some other way to explain this better and I'm just missing it?

Thanks for the help

That's about it really. If it's at the midpoint, it will get pulled towards the larger mass. So you need to move towards the smaller mass to increase it's pull and decrease that of the larger mass. And, of course, outside of the interval between them they pull in the same direction. That's what I would say.

 

[ace123]

Thanks just wanted to be sure.