Infinite pressure on infinitesimal area?

[Fullmetal_Potato]

So for a story I'm writing, there is a character with the ability to absorb force and store it (the force never impacts but its absorption works like pausing a movie). The force can be released (or resumed) through use of a circular space called a "rune". The character can control the size/area of these runes. In some cases, they can create a rune of an infinitesimal area (or you could just say the smallest area possible if that works better for answering the question). Since pressure is a force over an area, then any force applied to an area of infinitesimal size would create infinite pressure. My question is: what are the effects and consequences of applying infinite pressure to something (or you can use the smallest area possible and some unit force for calculation (like 1 Newton) if that works better). What effects happen when applied to different substances or objects like walls, buildings, air, even people. I'd like to see what happens in this scenario to see different possibilities of how this character uses this ability.

 

[russ_watters]

It sounds to me like you are describing a spear.

 

[jrmichler]

And if that spear has zero diameter, it will go through anything, but do no damage in the process.

 

[Fullmetal_Potato]

And if that spear has zero diameter, it will go through anything, but do no damage in the process.

ok then what would happen if instead of an infinitesimal size it would be the smallest possible. Not zero, but extremely small, like atomic or subatomic level?

 

[AidenFlamel]

ok then what would happen if instead of an infinitesimal size it would be the smallest possible. Not zero, but extremely small, like atomic or subatomic level?

Again, most likely nothing would happen. The chances of "hitting an atom" are really low, so the force released would probably just keep going until it dissipates or hits something... which could be really far away. Unless the ability of your character also makes him/her able to precisely point that force to, let's say, an atomic nucleus, then maybe it would be strong enough to "cut trough" it, but I don't really know how much energy we are talking about here, and even if it goes trough it, that doesn't necessarily mean it will separate in nuclear fision. Maybe the neutrons and protons are still being hold by the strong force.

Hope this is useful for you in some way, I really like the concept you are working with, so keep going!

 

[jrmichler]

It would fail by elastic buckling at very low force, because it would be an Euler column (search that term for the equation and discussion). Pick some numbers and plug into the Euler buckling equation. Start with the dimensions and theoretical modulus of a carbon nanotube, then go science fiction from there.

 

[stevendaryl]

In stories by I think Larry Niven, there was some kind of thread that was extremely strong but only a few molecules in diameter. The storyline implied that it could slice through anything. From the discussion, it seems that maybe there is an optimal diameter size for such a thread. Too small, and it would slice through an object without actually cutting it, and too large, it would lose it's cutting ability.

 

[Svein]

Check out "Billiard Ball" by Isaac Asimov.

 

[pervect]

So for a story I'm writing, there is a character with the ability to absorb force and store it (the force never impacts but its absorption works like pausing a movie). The force can be released (or resumed) through use of a circular space called a "rune". The character can control the size/area of these runes. In some cases, they can create a rune of an infinitesimal area (or you could just say the smallest area possible if that works better for answering the question). Since pressure is a force over an area, then any force applied to an area of infinitesimal size would create infinite pressure. My question is: what are the effects and consequences of applying infinite pressure to something (or you can use the smallest area possible and some unit force for calculation (like 1 Newton) if that works better). What effects happen when applied to different substances or objects like walls, buildings, air, even people. I'd like to see what happens in this scenario to see different possibilities of how this character uses this ability.

This is a rather late response, but the thread just caught my eye.

Force is the rate of change of momentum, with respect to time, so if you "absorb a force" for some time period $\Delta t$, you are absorbing a net amount of momentum p = F $\Delta t$.

The consequence of this is that by absorbing momentum from a massive object, and imparting it to a less massive object, one can create energy, i.e. it violates the conservation of energy, the hypothetical ability as stated allows one to create a perpetual motion machine.

The amount of momentum absorbed will be $m_1 v_1$. The amount of momentum restored will be $m_2 v_2$. The amount of energy absorbed at low velocities where relativistic efects are not important will be $.5 m_1 v_1^2$. The amount of energy restored will be $.5 m_2 v_2^2$. Because $v_2 >> v_1$, absorbing momentum from a massive object and restoring it to a less massive object will create energy.

One possible way around this difficulty is some mechanism to balance the energy. This would imply that one would need an external energy source to restore absorbed momentum to an object less-massive than the one one absorbed it from. Similiarly, absorbing momentum from a fast-moving but not-very-massive bullet and tranferring it to a more massive object would release energy.

The later case where energy released occurs in nature. One can imagine a bullet hitting a massive object. The bullet slows down, transfering it's momentum in an inelastic collision to the larger object. This process releases energy, typically in the form of heat. The stopped bullet will become hotter due to this heat energy.

 

[Fullmetal_Potato]

This is a rather late response, but the thread just caught my eye.

Force is the rate of change of momentum, with respect to time, so if you "absorb a force" for some time period $\Delta t$, you are absorbing a net amount of momentum p = F $\Delta t$.

The consequence of this is that by absorbing momentum from a massive object and imparting it to a less massive object, one can create energy, i.e. it violates the conservation of energy, the hypothetical ability as stated allows one to create a perpetual motion machine.

The amount of momentum absorbed will be $m_1 v_1$. The amount of momentum restored will be $m_2 v_2$. The amount of energy absorbed at low velocities where relativistic effects are not important will be $.5 m_1 v_1^2$. The amount of energy restored will be $.5 m_2 v_2^2$. Because $v_2 >> v_1$, absorbing momentum from a massive object and restoring it to a less massive object will create energy.

One possible way around this difficulty is some mechanism to balance the energy. This would imply that one would need an external energy source to restore absorbed momentum to an object less-massive than the one absorbed it from. Similarly, absorbing momentum from a fast-moving but the not-very-massive bullet and transferring it to a more massive object would release energy.

The latter case where the energy released occurs in nature. One can imagine a bullet hitting a massive object. The bullet slows down, transferring its momentum in an inelastic collision to the larger object. This process releases energy, typically in the form of heat. The stopped bullet will become hotter due to this heat energy.

the way the ability is meant to work is that you could say in a sense that it freezes the force in time and resumes it at a later time in a different position. kinda like pausing a movie, moving the TV then resuming the show. or you could think of it as sending that force forward in time to a different location. Keeping the same momentum, but changing in position and applied area. If you think of the ability like that would it change things? or does the same problem remain?

 

[Fullmetal_Potato]

In stories by I think Larry Niven, there was some kind of thread that was extremely strong but only a few molecules in diameter. The storyline implied that it could slice through anything. From the discussion, it seems that maybe there is an optimal diameter size for such a thread. Too small, and it would slice through an object without actually cutting it, and too large, it would lose it's cutting ability.

that sounds nice, that actually gives me some ideas. For one, if the ability evolves in a way as to control the shape and not just the size of the area of the force release then that could lead to the creation of weapons like blades that only cut in a single moment before disappearing. I'll have to check those stories out but thank you.

 

[Fullmetal_Potato]

Again, most likely nothing would happen. The chances of "hitting an atom" are really low, so the force released would probably just keep going until it dissipates or hits something... which could be really far away. Unless the ability of your character also makes him/her able to precisely point that force to, let's say, an atomic nucleus, then maybe it would be strong enough to "cut trough" it, but I don't really know how much energy we are talking about here, and even if it goes trough it, that doesn't necessarily mean it will separate in nuclear fision. Maybe the neutrons and protons are still being hold by the strong force.

Hope this is useful for you in some way, I really like the concept you are working with, so keep going!

thanks for that response. The character could theoretically have the ability to cut with that precision, her abilities are tied to giving more and more influence to two entities that represent Apathy and Rage, the more influence they gain also gives the character extra computational power in her mind and increases in her reflexes. Given enough power the character could cut with that much precision but at the risk of the expanded control of either entity allowing one to gain full control for a time. Even if the cut atoms cannot cause nuclear fission, the slicing capability gives something quite intriguing.

 

[Fullmetal_Potato]

Check out "Billiard Ball" by Isaac Asimov.

I went and checked it out, though I'm not sure what its relation to the question was. I'm not that well versed in physics so if you could explain the relation id appreciate it.

 

[Fullmetal_Potato]

It would fail by elastic buckling at very low force, because it would be an Euler column (search that term for the equation and discussion). Pick some numbers and plug into the Euler buckling equation. Start with the dimensions and theoretical modulus of a carbon nanotube, then go science fiction from there.

Then what about with much larger forces like a punch from someone with the strength of the average bodybuilder, or even the force from an impact or collision with a high-speed truck or 18-wheeler. Would forces like these be large enough to suffice, if so, then what would the effect be?