Physics and Magic, what else do you need?

[Fenix_of_Doom]

Some people start complaining when you mix physics with magic, if your one of those people, get out of this thread.

At Fax's maga-crab thread my attention was drawn to an interesting physics debate, I however do not wish to derail that thread so I made a new one, I'll give you the start-up.

A small pile of pebbles does not cause 1000 damage. 'Tossing them onto a solid surface' doesn't necessarily include the tarrasque itself (leaving aside the assumption that the boulders retain the same velocity as the pebbles).

After that, it's pure physics, unless you think that heavy stone won't fall, for somewhat reason. Why, they suddenly turn anti-grav or something? They will actually fall faster, not slower.
Unless you have gm that magically turns them into the styrofoam or haven't learned physics at all, that results will be exactly the same under any sane gm - several tons on heavy matter splatting one crab.

emphasis his, but very fitting in context.

Psst- all things fall at the same speed regardless of weight. Simple phyics :P

Pssst - that works only in open space. Simple physics

And now, go and make your homework on effects of air friction and how volume relates to surface area

and why dont you go home and calculate how little effect air friction actualy has on something as dense as stone?

You know, your little theory [Aristotelian, btw] was refuted by guy named Galileo Galilei almost 500 years ago.
Yeah, go ahed, pick one stone weighting 100 g and other weighting 1 kg and drop them from a reasonable height.
You know, level of teaching has fallen significantly during the last 20 years, what I was in elementary school - that was one of the first physics experiments conducted here, and to not kno... ech, whatever.

If you guys are reading what I'm reading then Trixie has now proven himself wrong, congrats on that BTW.

But that was just for fun, I'm actually going to ignore all that and instead I'll try to guess what Zincorium meant.
When magic and physics meet things sometimes get a little difficult, so let's start at the basics, when an object falls it will gain speed thus it gains kinetic energy. The formula for kinetic energy is as following: E=0.5*m*v^2
this means that if the mass of the falling pebbles would increase by a factor of 4.000 and the energy constant that the speed would decrease significantly.
in context of the pebble throwing this would be no problem if the command word was use at the same time you drop the pebbles but it would be a problem if you use the return to original size when it hits something method.

Now I know myself, so chances are I made a mistake or missed a factor somewhere, so comment or post your own magic/physics calculations here.

[goat]

Well, the magic effectively produces mass from "nowhere".

If the "nowhere" views the shrunken object as being stationary, and simply introduces the mass into the same reference frame as the object, completely "ignoring" the rest of the universe around it, then it would make sense for it to be initially travelling at the same speed as the small object from the viewpoint of an external observer. It would then accelerate at whatever rate was appropriate for the external conditions.

[daggaz]

Well Fenix, your math is correct. You are going off of the principal of Conservation of Energy, from which the Conservation of Momentum (mass*velocity) is derived.

Of course, suddenly pounding a ton of extra mass in magically violates the conservation of energy by default, but like you said, its magic.

So yeah, if you allow the magical introduction of mass, but want to conserve energy after the fact, then the resulting velocity will be reduced. Also, there is a huge problem with the fact that the mass is instantaneously introduced (leading to an instantaneous shift in velocity and therefore acceleration) but that is a singularity that can be just as well ignored and described away by magic. Note that the velocity cannot be reduced to exactly zero, regardless of the mass increase. Also note that gravity will begin accelerating the new mass immediately, so its not like the boulder is gonna just hang in mid air.

And for the record, that guy did prove himself wrong. Quite funny, actually.
Gravity accelerates all mass at the same rate, depending on the mass of the two interacting bodies, based off the gravitational constant 'G'. On earth, this results in a more or less constant value of 'g', or 9.81.. etc.. meters per second squared. Its not an exact constant tho, and ultrasonic aircraft actually make use of gravitational maps when flying their highspeed missions, especially over large mountain ranges and oceans, where the differences are most prominent.

[goat]

Also note that gravity will begin accelerating the new mass immediately, so its not like the boulder is gonna just hang in mid air.

Actually, in theory it should. Gravity is still bound by a maximum speed of c.

Edit - I mean, the distance between the new mass and some (ANY) existing mass will likely make that a hideously small amount of time. But for a tiny fraction of a second, it should just sit there.

[Dervag]

Actually, in theory it should. Gravity is still bound by a maximum speed of c.

Edit - I mean, the distance between the new mass and some (ANY) existing mass will likely make that a hideously small amount of time. But for a tiny fraction of a second, it should just sit there.

You mean the Looney Toons artists were right all along?

Yaay!

[Zincorium]

Not much need to guess, really.


I was going off of the 'pebbles hitting a solid surface' trigger, where the pebbles remain pebbles until they have hit ground and stopped. Going by this version of the spell, there is no acceleration* of the boulders once they've changed from pebbles.

If they've hit the ground, the energy of the pebbles is so low that when applied to the much greater mass of the boulders, the impact would be less than impressive.

Edit:
*Acceleration in the layman sense. I know the reduction in speed caused by the pebbles hitting ground is also a type of acceleration. But the people who know that probably understand what I was trying to say anyway.

[daggaz]

Actually, in theory it should. Gravity is still bound by a maximum speed of c.

Edit - I mean, the distance between the new mass and some (ANY) existing mass will likely make that a hideously small amount of time. But for a tiny fraction of a second, it should just sit there.

We are talking on the order of picoseconds, or probably less. This is less than the time it takes interatomic interactions to occur. Symantics aside, the rock will begin to fall immediately. In fact, the rock will begin to fall in less time than it takes light to bounced back and forth, and in far less time than your optical cells can fire nerve signals off in, let alone before they reach your brain.

[Kaelik]

Well the big question is terminal velocity. It doesn't matter how fast gravity accelerates an object if it has time to reach terminal velocity. I would think that with the height we are talking about it would certainly reach that level. My big question is does Shrink Item decrease it's mass?

Assuming it does then the terminal velocity of (lets pretend) a sphere is going to be decreased by the larger diameter, but increased by the larger mass. I therefore don't know how to compare the terminal velocities of the two particles.

[goat]

I was going off of the 'pebbles hitting a solid surface' trigger, where the pebbles remain pebbles until they have hit ground and stopped. Going by this version of the spell, there is no acceleration* of the boulders once they've changed from pebbles.

Ah! So, in this trigger, does the magic occur at the instant of the first point of contact, or once the energy has been transferred?

If the pebble expands instantaneously (which is only as absurd as the mass from nowhere) upon any point of contact, the rear of the pebble may not yet have stopped moving, and still contain all of its initial kinetic energy! If the expanded rock is moving at the same speed, it will still have a massive amount of force to bring to a rest.

BUT, this brings other problems to mind. Which way does the pebble expand? Does it "explode" out in all directions? Grow only away from the struck surface? I'm not actually sure the spell description provides information on what happens if it tries to expand into too small a gap.

[Fenix_of_Doom]

Not much need to guess, really.

It was guessing because I'm not a mind reader, but it was what I like to call a calculated guess.
As the rules don't mention anything like this you could technically use any of the following rulings:
1 the new mass has the same relative energy as it had when you cast the spell
2 the new mass has the same relative energy as the shrinked remains
3 the new mass has no energy at all since the spell doesn't mention it does(so cold damage then? ).

edit:

My big question is does Shrink Item decrease it's mass?

yes it does, by a factor 4000 no less, check my original post for the link.

[goat]

Symantics aside...

Good lord man! This is theoretical physics! Semantics can NEVER be put aside.

[Zincorium]

It was guessing because I'm not a mind reader, but it was what I like to call a calculated guess.

I just meant you could, y'know, ask me what I meant. Given that what someone means is very hard to calculate.

My belief, and my point, is that the speed of the pebble will probably not be retained, only the kinetic energy possessed by that pebble, which when the greater mass is taken into effect, results in a very slow downward moving boulder.

Really, the fact that you have a boulder lying on top of you would outweigh (no pun intended) any kinetic energy that the boulder retained from the pebble.

This is assuming that by hitting they mean any contact with a solid surface. If they meant that it activates when the object is resting on a solid surface, and they very well might have, then it is of course going to be motionless.

[daggaz]

Assuming it does then the terminal velocity of (lets pretend) a sphere is going to be decreased by the larger diameter, but increased by the larger mass. I therefore don't know how to compare the terminal velocities of the two particles.

Not true, sorry. Terminal velocity is a function only of the surface area and subsequent drag of a material. Gravity accelerates two different masses at exactly the same rate, regardless of size or shape. But the air does play a part (note that now we arent talking about the accelerating force, but the decelerating force, or drag).

Aerodynamic drag has the most to do with the shape and, especially, the surface area of the falling object. It is also directly related to the square of the velocity. The ultimate velocity is independant of mass. So, two different massed objects will speed up to a certain point, but at some point the velocity^2 * surface area begins to quickly overtake the force of gravity, and you end up with an equilibrium falling speed.

Obviously, items like a human body or a parachute or much harder to model mathematically, but if you take the case of two spheres its much easier. Two spheres of the same size and different mass will fall at exactly the same rate, and reach the same exact terminal velocity. Two spheres of different sizes and the same mass will reach different terminal velocities.

This is why the terminal velocity for human beings (i think its about 144 miles per hour, but i might be mistaken) is only an estimate. You are assuming roughly the same shape and size, and disregarding the differences in mass. (think of your friends at school who are more or less the same size as you, but might be a bit more heavierset).

[Ulzgoroth]

It might reasonably conserve momentum instead. Since we cheerfully disconserve both with various spells (at least from a naive view of local physics) expecting either one to prevail seems equally valid. Conservation of momentum would make the KE actually go down when the rock un-shrinks.

It could conserve velocity instead, but that would make abuse trivial. Just toss and talk...

Of course, the intended trick was to un-shrink the stone and let it fall, which works fine with any of those.

[bosssmiley]

Fenix - did you honestly hive off a whole new thread just to up the count on your catgirl cull? Are you trying to powerlevel by rampant nekocide or something?

[Gashad]

"When magic and physics meet things sometimes get a little difficult, so let's start at the basics, when an object falls it will gain speed thus it gains kinetic energy. The formula for kinetic energy is as following: E=0.5*m*v^2
this means that if the mass of the falling pebbles would increase by a factor of 4.000 and the energy constant that the speed would decrease significantly."(this is supposed to be a quote)


That the stone would decrease in velocity would be a violation of newtons first law( an object will reman at a constant speed or at rest unless an external force acts upon it.) As no forces are added by the spell, it would continue to accellerate downwards until reaching terminal velocity.

[Ulzgoroth]

Not true, sorry. Terminal velocity is a function only of the surface area and subsequent drag of a material. Gravity accelerates two different masses at exactly the same rate, regardless of size or shape. But the air does play a part (note that now we arent talking about the accelerating force, but the decelerating force, or drag).

Aerodynamic drag has the most to do with the shape and, especially, the surface area of the falling object. It is also directly related to the square of the velocity. The ultimate velocity is independant of mass. So, two different massed objects will speed up to a certain point, but at some point the velocity^2 * surface area begins to quickly overtake the force of gravity, and you end up with an equilibrium falling speed.

But the force of gravity (not the acceleration from gravity) is proportional to mass. Two outwardly identical objects will experience the same drag when falling at the same speed, but if one has more mass it will experience more gravitational force and thus have a higher terminal velocity.

[goat]

But the force of gravity (not the acceleration from gravity) is proportional to mass. Two outwardly identical objects will experience the same drag when falling at the same speed, but if one has more mass it will experience more gravitational force and thus have a higher terminal velocity.

This is very true, and just like my point above about the speed of gravity, completely meaningless in this conversation.

Excellently done.

edit - I say completely meaningless, I suppose if we were dealing with a block of degenerate neutron matter it could be important. Two dozen cubic feet of that would weigh over 50*10^15 kilos, enough for significance.

edit 2 - I say significant, thinking about it, it would only be another few micrometers a second...

[Zincorium]

That the stone would decrease in velocity would be a violation of newtons first law( an object will reman at a constant speed or at rest unless an external force acts upon it.) As no forces are added by the spell, it would continue to accellerate downwards until reaching terminal velocity.

Objects in motion will remain in motion until acted on by a net force. Speed and what constitutes an outside force are not part of the first law.

Momentum is conserved, and as momentum is a product of mass and velocity, a change in mass would violate the conservation of momentum unless the velocity drops. The object in question does remain in motion, albeit drastically slowed from an outside perspective, so no violation of newton's first law occurs.

[daggaz]

But the force of gravity (not the acceleration from gravity) is proportional to mass. Two outwardly identical objects will experience the same drag when falling at the same speed, but if one has more mass it will experience more gravitational force and thus have a higher terminal velocity.

The problem is one of limiting factors. The point is, the velocity squared term completely outstrips differences in mass, so a small (or even fairly large) difference in mass between two objects has a very negligable effect on terminal velocity. Remember, when dealing with two diff masses, say 50 lbs and 200 lbs, its not the difference between them, its the difference between the mass of the entire earth and the object, and the same difference from the other object. Because of how you compute g, this comes out very very close, whereas the aerodynamic drag factor completely outstrips this term with only small changes in surface area. (remember,
g is G*(m_object*mass_earth)/r^2 (and G is really really small) while the drag is a coefficient*v^2.) That is why you have a general terminal velocity for anything, regardless of mass, as long as it shares a close enough shape and surface area. Parachutes and feathers and falling pieces of paper are obvious deviations due to the dramatically different shape and surface area, as well as the extremely light mass.

Sorry Goat, but you are wrong as far as practical interpretations go. (although entirely correct, if you count things out to the further decimal places... problem with this is, the uncertainty in the measurements often exceeds this very small margin of proof. In other words, a heavier mass will have a faster terminal velocity technically), you just cant measure it accurately.

[Chronos]

The problem is one of limiting factors. The point is, the velocity squared term completely outstrips differences in mass, so a small (or even fairly large) difference in mass between two objects has a very negligable effect on terminal velocity.

Uh, no. Terminal velocity has nothing to do with energy, only with forces. The drag force on an object is equal to the object's surface area times its velocity squared times a factor which depends on the object's shape. The force of gravity is equal to the mass of the object times the acceleration due to gravity. Terminal velocity is the velocity at which these two forces are equal: s*A*v^2 = m*g. Solving this for v, we have v = sqrt((m*g)/(s*A)). In other words, if you have two objects with the same shape and area, but different masses, then the heavier one will have a higher terminal velocity, in proportion to the square root of the mass ratio. Thus, for instance, if the heavier object has four times the mass of the lighter one, it'll fall twice as fast. If the heavier object has 100 times the mass, it'll fall 10 times as fast, and so on.

In the case we're looking at here, each of the object's linear dimensions increases by a factor of 16, so its area increases by a factor of 256. Its mass, meanwhile, is proportional to its volume, and thus increases by a factor of 4096 (this is the "approximately 4000" referred to by the spell). So the boulder will have a terminal speed of sqrt(4096/256) times that of the pebble, or 4 times.

[Ulzgoroth]

I'm not going to dispute your aerodynamics, but the math you're doing with them is wrong. Likewise, your conclusions from the formula for gravitational force (not g...g is gravitational acceleration normally).

The formula is correct, but if you actually look at what it says, that 200 lb object has exactly 4 times as much gravitational force on it as the 50 lb object. And thus the same acceleration, of course. If a factor of 4 is trivial is trivial to you... The difference of mass between the object and the earth is utterly irrelevant, unless you think I'm factoring in the acceleration of the earth toward the falling object (I'm not). Which exists, but is trivial for reasonable masses.

If drag is indeed proportional to v^2, and these two masses have the same coefficient, the heavier one will have twice the terminal velocity. This is trivial. There is no such thing as a 'general terminal velocity'. For objects of identical surface, terminal velocity rises as the square root of mass.

[Kurald Galain]

Aside from all the catgirl splattage, Mage: the Ascension has the best answer to this. Physics is just another kind of magic, that happens to work because the Order of Reason convinced most of humanity that Reality does indeed work like that. Which means that in certain deserted areas, your jet plane will be taken down by a flying carpet, because Consensual Reality over there has a different paradigma.

[Leon]

a large supply of female humanoid cats

[Gashad]

Objects in motion will remain in motion until acted on by a net force. Speed and what constitutes an outside force are not part of the first law.

Momentum is conserved, and as momentum is a product of mass and velocity, a change in mass would violate the conservation of momentum unless the velocity drops. The object in question does remain in motion, albeit drastically slowed from an outside perspective, so no violation of newton's first law occurs.

I disagree, for an object to change in velocity it must either accellerate or decellerate(duh). Accelleration = Force/mass. hence if force = 0, accelleration(or decelleration in this case) equals zero, and hence the speed of the object would not change.

Besides Newton in his first law emphesises constant velocity, hence if the speed has changed a force needs to be applied.

[daggaz]

I disagree, for an object to change in velocity it must either accellerate or decellerate(duh). Accelleration = Force/mass. hence if force = 0, accelleration(or decelleration in this case) equals zero, and hence the speed of the object would not change.

Besides Newton in his first law emphesises constant velocity, hence if the speed has changed a force needs to be applied.

Zincorium is entirely correct if you accept in this world of magic
that conservation of energy, and thus, momentum, is conserved. If the energy is conserved, the object WILL slow down when it's mass is increased. That is pure and simple physics. But if we dont follow the conservation of energy, anything can happen, it is up to us to define things.

And that is the crux of this entire thread. Without defining the paramaters where physics and magic meet, we really have nothing to discuss without endless arguments, as everybody will be arguing about different things. (unless they are arguing about pure physics, as those parameters have already been defined).

EDIT oh and ha ha, sorry for the above posts. That is what you get when you argue physics while incredibly drunk (sorry, we had a huge dorm party last night)

[Gashad]

Zincorium is entirely correct if you accept in this world of magic
that conservation of energy, and thus, momentum, is conserved. If the energy is conserved, the object WILL slow down when it's mass is increased. That is pure and simple physics. But if we dont follow the conservation of energy, anything can happen, it is up to us to define things.

last night)

I disagree that it is that simple. The earth velocity towards the rock could increase instead, since that would still mean total momentum was conserved.

Even though this would have the same problem as previously with velocity changing without a force, which would be evidence for your statement that without parameters we cannot get any clear answer, as either the law of conversion of momentum is broken, are newtons first and second laws would be broken.

[Fenix_of_Doom]

Fenix - did you honestly hive off a whole new thread just to up the count on your catgirl cull? Are you trying to powerlevel by rampant nekocide or something?

Yes, that's the true reason didn't you hear the catgirls are taking over the world with the new 4th edition, we MUST STOP THEM .

I disagree, for an object to change in velocity it must either accellerate or decellerate(duh). Accelleration = Force/mass. hence if force = 0, accelleration(or decelleration in this case) equals zero, and hence the speed of the object would not change.

Besides Newton in his first law emphesises constant velocity, hence if the speed has changed a force needs to be applied.

it only keeps constant velocity if unaffected by outside forces, I would say the release of a shrink spell is definitely an outside force.

[Citizen Joe]

You can draw energy from a source other than kinetic.

When you let compressed air expand rapidly, the temperature drops. Thus the pebble to boulder may result in the boulder suddenly becoming much colder.

You may draw from the nuclear forces that hold the matter together. This actually works best to negate the cheese. I.e. To expand the boulder's mass, the strong forces within the pebble become very weakened. So much that on impact, it shatters easily into powder. Thus doing no more damage than a mere pebble would have done.

[Enzario]

Besides Newton in his first law emphesises constant velocity, hence if the speed has changed a force needs to be applied.

Aye, but Newton, though ahead of his time, did not catch up to 21st century advances in physics. One question you must look at in this situation is what will remain constant: kinetic energy or velocity? In some ways, we must assume that kinetic energy stays the same, since the spell only adds MASS, not energy. In that case then, you would have the same amount of energy propelling the pebbles (your toss) being transferred into boulders. The boulders would then hit with the same force of your (underhand?) toss, plus the energy gained by acceleration due to gravity in the time since their expansion; if you set the trigger for their expansion to be their impact on said tarrasque, balor, PPDC, etc., the only damage you would be doing would be the placement of said large rocks on top of them.

All done in the name of research. If the catgirls ever take over the world, I'll be tried for my war crimes. (jar of cookies if you can get that book reference; hint: Michael Crichton)