A quick poll on a semantic matter

[nicksauce]

You are at the center of a sphere, and there is no net gravitational force on you. Which of the following do you most agree with?

**Assume you are a point particle**

 

[Dale]

Not only are there no net forces, there are also no tidal forces. That means that there are no internal stresses as you would get from being pulled equally in all directions.

 

[nicksauce]

For this case, you can assume "you" are a point particle :)

 

[Nugatory]

Not only are there no net forces, there are also no tidal forces. That means that there are no internal stresses as you would get from being pulled equally in all directions.

+1

Now, if I were a point particle, then the third "it's the same thing" choice would be defensible. Nicksauce, are you making a point about the difference between the idealized problems we see in physics classes and real-world problems?

 

[nicksauce]

Nicksauce, are you making a point about the difference between the idealized problems we see in physics classes and real-world problems?

My real reason for posting this is that I got in an argument about it with someone today and we spent a while on it. So I am now curious what other people think.

 

[Dale]

Classical point particles don't exist, but I would still say the same. The potential is uniform, so there is no force. It is easier to see using Poissons equation than Newtons equation.

 

[Mark M]

As DaleSpam said, there are not any forces. This result was proved by Newton, the shell theorem. And (as DaleSpam also said), there are no tidal forces, which makes the distinction between you standing inside the sphere and a point particle irrelevant to the result.

 

[Nugatory]

My real reason for posting this is that I got in an argument about it with someone today and we spent a while on it. So I am now curious what other people think.

So what were the various positions in the argument?

 

[nicksauce]

Yes of course there is no force. The real question is give that there is no force, what, semantically is a better description of that fact.

 

[Nugatory]

Yes of course there is no force. The real question is give that there is no force, what, semantically is a better description of that fact.

We're getting dangerously close to a discussion of whether a particular quantity might be better represented by "zero" (nothing there) or by "the sum of 3 and -3" (something there that happens to cancel).

 

[Vorde]

I think the most useful thing to say is that you are being pulled equally in all directions. Then you don't have to change anything about the way you are thinking if you want to talk about the gravitational potential somewhere else.

(Of course experimentally the two viewpoints are the same)

 

[Andrew Mason]

I think the most useful thing to say is that you are being pulled equally in all directions. Then you don't have to change anything about the way you are thinking if you want to talk about the gravitational potential somewhere else.

(Of course experimentally the two viewpoints are the same)

If this is a point particle, it is meaningless to talk about anything but a net force. A point particle does not have internal stress. Being pushed and pulled in different directions is something that can only be experienced by macroscopic bodies.

If this was a macroscopic body whose centre was at the centre of a sphere of uniform mass, the body would feel some internal stress due to 'tidal' forces (different parts of the body being situated in non-zero gravitational fields and having different directions).

AM

 

[Vorde]

I totally agree. All I was saying is that in my opinion (and as the OP said this is all semantics because we agree on the result) it's easier to say the forces cancel out than there is no force. This way if you suddenly start talking about a place not in the center of the sphere, you can just say that now some of the forces are greater and some lesser instead of introducing new forces that you weren't talking about before.

 

[mfig]

I vote for option 4:Option 4. Each and every "particle" of you is being pulled equally in all directions, resulting in no net pull.

 

[Dale]

I think the most useful thing to say is that you are being pulled equally in all directions. Then you don't have to change anything about the way you are thinking if you want to talk about the gravitational potential somewhere else.

(Of course experimentally the two viewpoints are the same)

Why would I have to change my way of thinking to talk about the gravitational potential somewhere else? Everywhere is the same rule, you are pulled in the direction of the gradient of the potential. So if the potential is constant you are not being pulled, if it is not then you are.

 

[Studiot]

I think Dale is correct on this one.

It is actualy easier with a point charge at the centre of an evenly charged sphere because you can envisage a point charge.

However if you map either the potential field or force field you can see that there is a zero at the centre, not a balancing act.

Steveb and some other physicists did a lot of work on this here

http://forum.allaboutcircuits.com/showthread.php?t=64107&highlight=charged+sphere&page=9

 

[Vorde]

I guess you're right, and when I tried to extend my line of reasoning to other scenarios I found that it failed. However I still think (after admitting defeat, as it were) that were I explaining gravitational potential to a student, if the student said that all forces were equal and opposite at the center and therefore cancel I would nod and move on, whereas if the student said that there is no force at the center I would pause to make sure he understood correctly.

 

[Andrew Mason]

I guess you're right, and when I tried to extend my line of reasoning to other scenarios I found that it failed. However I still think (after admitting defeat, as it were) that were I explaining gravitational potential to a student, if the student said that all forces were equal and opposite at the center and therefore cancel I would nod and move on, whereas if the student said that there is no force at the center I would pause to make sure he understood correctly.

If the student said that the forces on a body were equal and opposite, he/she should be asked to do a free-body diagram and try to explain why there are no tensions within the body to balance these opposing forces.

AM