What Is the Gravity Force Between Two 1 kg Weights at Zero Distance?

In summary, the conversation discusses the concept of gravity force between two weights at zero distance. While Newton would say the force is infinite, Archimedes believes it is extreme but not necessarily infinite. This is because Archimedes views force as a geometrical potential that is dependent on the distance from the center. The conversation also touches on the idea of infinity and zero in calculations, concluding that their product is undefined. The concept of zero distance is deemed unphysical, and it is acknowledged that physical laws do not have to produce sensible answers in such situations. The conversation ultimately suggests seeking the help of a mathematician to define the product of infinity and zero.
  • #1
deda
185
0
How much will be the gravity force between two weights each of which with 1 kg at zero distance? If you ask Newton the answer will unconditionally be infinity but Archimedes would say extreme for sure but not necessary infinite.

Here is why: The force in Archimedes’s physics is more like geometrical potential the body has. Geometrical potential is sort of storage for the geometrical distance form the center yet to be achieved. Now let's begin from the end i.e. let the weights be on zero distance (in the center of the lever). Now if you arm each weight with 1 N in opposite direction the weights won't end in infinity but their extreme distance i.e. the distance when all the force is exhausted will be finite. Now arm them with 2 N per each. When they combust that force they’ll achieve twice longer distance than before. So, the only case of having infinite force at zero distance is when they were released from infinite distance with zero force.
 
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  • #2
The combination of infinity and zero pop-up frequently in calculations. It is agreed that

infinity over zero is infinity.

zero over infinity is zero.

infinity is the inverse of zero and vice versa.

But the is the product of infinity and zero a finite quantity?
 
  • #3
To completely satisfy the Newton paradox, the weights would both have to have zero volume and thus be of infinite density. It won't happen!
 
  • #4
[tex] F = Gm_1 m_2/r^2 = G m_1 m_2/0^2[/tex]

This equation makes no sense. The answer is not zero. The answer is not infinity. It is undefined, there is no answer, because it is not a legitimate situation.
 
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  • #5
Zero distance is unphysical. No one ever said physical laws should have to produce sensible answers in unphysical situations.

- Warren
 
  • #6
chroot said:
Zero distance is unphysical. No one ever said physical laws should have to produce sensible answers in unphysical situations.

- Warren
It is again the traditional way of doing physics that cosider the basic matter quanta solid so at it's center there are two sequences of that basic quanta that can be considered at zero distance.

I don't believe anybody understood what my original post is all about.
 
  • #7
deda,

Aren't you trying to define or "finitize" the product of infinity and zero? Maybe a mathematician can help you? There seem to be a lot of knowledgeable math experts in this forum.
 
  • #8
Antonio Lao said:
There seem to be a lot of knowledgeable math experts in this forum...

...Who know when to smile and click the left button on their mouse...
 

FAQ: What Is the Gravity Force Between Two 1 kg Weights at Zero Distance?

1. What is meant by "zero distance" in terms of gravity force?

Zero distance refers to a theoretical point at which two objects are considered to be touching or in direct contact with each other. In terms of gravity force, this means that the distance between the two objects is extremely small, approaching a distance of zero.

2. How does gravity force change at zero distance?

At zero distance, the force of gravity between two objects is at its maximum strength. This is because the force of gravity is inversely proportional to the distance between two objects, meaning that as the distance decreases, the force increases.

3. Can gravity force exist at zero distance?

In theory, yes, gravity force can exist at zero distance between two objects. However, in reality, it is impossible for two objects to be at an exact distance of zero from each other, as they would need to occupy the same point in space.

4. What is the significance of studying gravity force at zero distance?

Studying gravity force at zero distance can help us better understand the fundamental laws of physics, specifically the relationship between distance and force. It can also provide insights into the behavior of objects in extreme gravitational conditions, such as black holes.

5. Is zero distance the same as zero gravity?

No, zero distance and zero gravity are two different concepts. Zero distance refers to the distance between two objects, while zero gravity refers to the absence of gravitational force. Zero gravity can occur at any distance, not just at zero distance.

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