# B An infinitly dense human body

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1. Sep 13, 2017

### manuel chaparro

Hello,

I've been watching too much anime. I know that isn't the best way to ask a question scientific in nature, but visualizing bizarre situations is one of the best ways to come up with interesting questions.

Anyways, in order to break a rock by compressing it with your hands, you would need to apply force on the rock, right? Force is determined by mass times acceleration, right? I guess I can't change the acceleration of my hand when I try to press down on the rock, so in order to apply more force, I'd need to change the mass, right? (Here a little note: I assume that you can indeed change the acceleration, I can't imagine how I would in this scenario, but I assume you can.)

So, back to changing the mass. Mass is defined by volume and density, right? I want to keep my size, so let's say that volume can't change in this equation, so what would need to change would be density, isn't it? But If I increase the density, I also increase the mass. If I increase the mass, I increase the weight (on earth), and if I do that, then my hand, which keeps getting heavier, will be pushed towards the ground or even rip my skin, break my bones and fall to the ground on its own.
I would like to avoid that. So, lets say that not only the hand but the whole body gets denser uniformly.

Then:

1) Would an denser hand be indeed able to break a rock by applying pressure on it?
2) If the whole body got dense enough to be able to break a rock by trying to compress it, would it be able to keep its structure? I mean, would limbs collapse under their own weight, or would the body keep whole?

and

3) If the body got dense enough to break a rock, would it also mean that it'd go through the planet due to it's own weight? Or is the ground able to withstand the weight? (Keep in mind that we would be talking of a human-shaped object that would weight, well....a lot. ( I guess I should be adding numbers to this)

Well, that would be what's been bothering me. I know it's a waste of time since matter can't change it's density just like that, but...

mmmm....

Can I change the mass of something by changing it's density, but without changing it's volume? I don't think it can be done, right? I mean, the density of something is inherent to it's enviromental conditions and it's state, right? (Whether it's a solid, a liquid, a gas...and conditions such as temperature etc.)

Ok, no. It's too complicated now. Simply help me answer the three first questions, and if there is a way in which I can change the density of something without altering it's volume, please let me know.

2. Sep 13, 2017

### rootone

Mass is mass.
It can be more or less dense only depending on how much space you want it to be contained in.

3. Sep 13, 2017

### manuel chaparro

Sure. But I mean, if I want to keep the same volume, would mass change? Only if I change it's density. But, can I change the density of something without changing it's volume?

4. Sep 14, 2017

### willem2

Force = mass x acceleration just isn't useful when you want to break something by pushing against it. The rock doesn't move, so acceleration is 0 and it doesn't matter what the mass is.

Force = mass x acceleration is useful if you want to hit a rock with a hammer. To increase the mass you use a bigger hammer, and to increase the acceleration you swing the hammer faster. Because the hammer and the rock are very hard, the hammer will have to accelerate very quickly to lose its speed when it hits the rock, and this will produce a very large force. The force that the rock exerts on the hammer to make it stop is equal to the force that the hammer will exert on the rock.

5. Sep 14, 2017

### Drakkith

Staff Emeritus
F=MA is a mathematical equation relating force, mass, and acceleration. It is not a definition of force. Besides, if it were, you would never be able to apply a force if your acceleration was zero, no matter how much mass you had.

No, density by itself is useless. Your body would need to be physically capable of exerting enough force through your hand on the rock to break it. The density of your hand is not directly related to its ability to exert a force. You would need to drastically change the physical makeup of your muscles, tendons, bone, and skin in order to be able to exert this force and keep your skin and other tissues intact. What the final density and makeup of your body would be, I have no idea.

6. Sep 14, 2017

### manuel chaparro

Thank you.

7. Sep 14, 2017

### CWatters

When you hit a rock with an object the "a" in F=ma is the deceleration of the object as it strikes the rock. This depends to some extent on the rigidity of the object. A soft squishy hand will have a longer stopping distance and hence a lower deceleration then something like a hard iron hammer of the same mass.

So for a fictional/anime purposes only (eg Don't try this at home folks!) you could have the super hero dip his hand in liquid nitrogen to freeze it really hard. That would increase rigidity, and the force with which you could hit the rock :-)

PS: It's a toss up if the frozen hand or rock would shatter first.

8. Sep 14, 2017

### Drakkith

Staff Emeritus
I'm betting on The Rock to win that match.

9. Sep 14, 2017

### manuel chaparro

Ok, so it's been made clear that using F=m.a isn't the right formula for this. So what formula would apply? I was thinking about Pressure= force/area (or something like that), but again, I have the problem with F as, just like you mentioned it, there's no acceleration.

10. Sep 14, 2017

### Mr Anderson

F = MA won't work here because A in this formula is average acceleration over a distance. There would be two main momentum periods, T = before your hand reaches the rock, T = After your hand reaches the rock. At T(Before), A can be whatever you like, at T(After), A = 0 since you can't push through the atoms of the rock AT ALL. You will not be traveling any distance into the rock with your hand because your hand cannot displace the atoms of the rock.

This is because the atomic and molecular bonding in rocks follow various crystal structures and lattices which provide significantly higher density than general animal organic tissue. Density and hardness are not the same thing. You should be looking at this from a hardness perspective. In that regards, diamond would be the hardest, non synthetic, crystal, (which is used for digging through rock, btw, along with high pressure water cannons). Even if your hand were fully made of diamond, just smashing it again the other rock would do nothing, since that is a super inefficient way to transfer energy when your objects are non-compressible.

If one of your objects had infinite density, it would be a black body, basically a small black hole. NOT the best thing to have around other objects. It will tear apart the other object(s) at the atomic level, just by being close enough.

This all boils down to an energy transfer problem. Simply heat the rock up to its melting point ~1500 K, 2000 K if you want to be sure. Slip on a well insulated glove and have fun slapping your rocks! Just a quick FYI, due to the nature of bonding in rocks, their compressibility is already pretty close to their limit meaning you will be able to reduce the volume (and hence, increase the density at the same time) by a marginal amount, if any, since you would need the rock to form shorter bonds in a more densely packed crystal structure, which is usually very hard to do since crystal structure often depends on the atomic composition of the rock. You won't be able to change that just by slapping it. You MAY be able clear out some of the mistakes in bonding (removing impurities from the crystal structure) but this will most likely not be the case. Actually, it is much more likely to be the opposite. Since you are messing with the surface of the rock, you'll be adding more impurities and more chances for the crystal structure to have imperfections, making the atoms in the rock actually take up MORE space and cause the rock to be LESS dense. LOL

Basically, done in this way, by hitting a rock with your hand, you would actually make it less dense and have a higher volume.

Hope this helps!

:)

- Some weird Chemist wondering a Physics Forum.