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# The Line

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### #31 shrooma

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Posted 29 May 2013 - 02:01 AM

Stellar, on 29 May 2013 - 01:41 AM, said:

Just pointing something out, because the physics I'm seeing people argue here is horrendous:

The force opposite to the floors falling due to gravity is the Earth getting pulled up to the floors that are falling... now continue.
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opposite force, yes, but wouldn't an applied force only count if the two were in contact?

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### #32 Stellar

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Posted 29 May 2013 - 02:07 AM

And if you want to draw a force diagram showing all the complementary forces in this instance, it'll get quite complex and messy, since you can always make it "more complex". Realistically, you do not need to even consider Newton's 3rd law in this instance since what matters is how much force is getting applied vs how much force it can hold.

The frame of the building can only hold so much force before breaking. When an object suddenly impacts another object, it transfers some energy to it. In other words, the object getting impacted slows down (decelerates) the impacting object. This can cause the force to be *much* greater at the instant of impact.

Back to the example of the scale. When you stand on the scale, it gives you a certain reading. This reading is proportional (dependent) on your mass in the presence of gravitational acceleration (F=mg). If you were to fall from 10 meters onto the scale and impacted the scale with a velocity of 18.6 m/s, what would happen? You would be essentially instantaneously stopped. Brought back to a speed of 0. For ease of simplifying the math, lets say that it actually took 1 second for the scale to slow you down (a huge simplification). That means you were accelerated at a rate of 18.6 m/s/s in the opposite direction to your fall. Hence, your scale would show a reading proportional to F=m*18.6 or, in other words, F=2mg. So, for that 1 second, your scale would read more than your actual weight, until everything came to rest.

In the example above, if we were to draw a free-body diagram with the complementary forces as per Newtons 3rd law, what would we see? Well, initially, we'd have a force pointing downwards applied to the falling person, and an equal force pointing upwards applied to the Earth. During impact, we would have a force peaking at F=m*18.6 pointing up on the person and the same force pointing down on the scale/Earth until it came to rest, at which point you would have the an upwards force equivalent to F=(mperson + mscale)g on the person, and that same force pushing down on the scale/earth.

You would also, throughout, have the gravitational force of the scale pushing down on the scale and up on the Earth.

Thats the scenario in a nutshell.

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### #33 Stellar

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Posted 29 May 2013 - 02:09 AM

shrooma, on 29 May 2013 - 02:01 AM, said:

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opposite force, yes, but wouldn't an applied force only count if the two were in contact?

I'm not sure I know what you mean by "count". An opposite and equal force is *always* present. All that this means is that you dont have one object that's fixed. Both move. When the Earth's gravity pulls an apple down towards the Earth, it also pulls the Earth towards the apple. The only reason we don't "notice" this is because the mass of the apple is so small compared to the mass of the Earth, which means that the apple will accelerate and move at a faster speed than the Earth, which will accelerate so slowly its essentially negligible.

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### #34 flyingswan

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Posted 29 May 2013 - 09:35 AM

Stellar, on 29 May 2013 - 02:09 AM, said:

I'm not sure I know what you mean by "count". An opposite and equal force is *always* present.
The forces are only equal if the objects are in contact.  After the initial drop, there is a growing layer of crushed floors between the upper and lower blocks.  This layer is falling, like the upper block.  This means that the situation is no longer symmetrical between the two blocks.  The force on the lower block is greater than the force on the upper block by the amount of the force on the layer of crushed floors.

The force on the lower block is resisting the fall of both the upper block and the crushed layer.  The force on the upper block is just resisting the fall of the upper block itself.

Edited by flyingswan, 29 May 2013 - 10:12 AM.

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### #35 Stellar

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Posted 29 May 2013 - 11:00 AM

flyingswan, on 29 May 2013 - 09:35 AM, said:

The forces are only equal if the objects are in contact.

No, you are wrong. The forces Newtons 3rd law talks about are always equal, regardless of whether they are in contact or not.

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After the initial drop, there is a growing layer of crushed floors between the upper and lower blocks.  This layer is falling, like the upper block.  This means that the situation is no longer symmetrical between the two blocks.  The force on the lower block is greater than the force on the upper block by the amount of the force on the layer of crushed floors.

The force on the lower block is resisting the fall of both the upper block and the crushed layer.  The force on the upper block is just resisting the fall of the upper block itself.

You are correct here, but the forces you speak of here are not the forces that Newton's 3rd law refers to.

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### #36 Little Fish

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Posted 29 May 2013 - 11:26 AM

aquatus1, on 29 May 2013 - 01:37 AM, said:

Be snarky somewhere else.  In this thread, support yourself or beat it.
as per newtons third law, my snarky is only a response to someone else's snarky.

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Technically, yes, however the entire purpose of this example is to show the compounding increase of energy achieved by a falling object as opposed to one at rest.  Newton's 1st Law is about balanced forces, such as forces at rest.  Newton's 3rd Law is about forces interacting.  Newton's 2nd Law, however, is about forces which are unbalanced, such as collisions and impacts, which is what we are dealing with.

So, what I am attempting to show in this example, is that a slab of concrete that exerts X amount of force while at rest (while simultaneously receiving X amount of force from the slab it is resting on, as per Newton's 3rd), is going to gain dramatic amounts of energy after falling (acceleration due to gravity).  At the moment that these two slabs contact (interact), the bottom slab (which was pushing upwards with X amount of force) is now being pushed downwards with a slab that has X times 5, 10, 15 times as much force as before.  Sure, it can try to push back with the same amount of force, but whether or not it actually succeeds in doing so is another question altogether.

the bolded bit is incorrect as per newtons third law. it does not "try to push back with the same amount of force" nor is there a question of whether it succeeds or not in exerting the force - it DOES push back with same force. if the falling slab impacts the stationary slab with say, a force of ten billion trillion newtons, then the stationary slab will exert the same ten billion trillion newtons on the impacting slab. this is an important concept to acknowledge because you are implying that the stationary slab will be the only slab that fails (breaks), when in fact both impactor and impactee will fail (break). if you are thinking that only the impactee will fail then your model is analogous to a steel slab falling on glass slabs. again this is important since the 10 storey falling block of wtc1 will be destroyed after the first 10 "floor impacts", leaving 90 intact storeys vs 20 fragmented storeys which is a different problem altogether (less than 20 actually since a lot of debris is not going to do any impacting).

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I want an acknowledgement from you that you understand the academic side of it first.
yes i understand simple physics, how about you? do you understand that two objects impacting will exert the same force on each other at the same instant?

Edited by Little Fish, 29 May 2013 - 11:29 AM.

### #37 Little Fish

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Posted 29 May 2013 - 01:04 PM

shrooma, on 29 May 2013 - 12:27 AM, said:

Force=Mass x Acceleration.
gravity & acceleration are both interchangeable and indestinguishable from each other.
a 50kg object at rest doesn't have the same mass characteristic as an accelerating 50kg object, which is why aquatos made the analogy of a weight at rest and an accelerating body. so your saying that gravity acting on mass as a constant is wrong. that's why you experience accelerative g-forces, not because you've suddenly become heavier, but because you've gained energy, E=Mc2 remember. the more energetic, the more mass, which is why only massless bodies can achieve light-speed, because the faster something is moving, the more massive it becomes.
i have no idea what you are trying to say. and i did not say the bolded bit. i said gravity was constant in the context of the discussion.

"you can't properly apply newton's third law to the problem of the collapsing floor due to momentum."
newton's third law is a law. you don't get to pick and choose when it applies. it applies because it is a law. however, on its own it doesn't determine what happens to the motion after collision.

"the floor underneath the collapsing floor may respond with an equal force"
there is no "may", it does as per newtons third law. a law of physics cannot be broken.

"but as the floor underneath's collapse point is well below the force being applied, there is no way for it to be sustained, so it WILL collapse."
whether it collapses or not does not negate that the stationary slab exerts the same force on the impacting slab.
do not assume that i mean to say it will not collapse- i did not say that.

### #38 aquatus1

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Posted 29 May 2013 - 01:07 PM

Little Fish, on 29 May 2013 - 11:26 AM, said:

as per newtons third law, my snarky is only a response to someone else's snarky.

I don't care who's snark it is.  If you haven't supported your claim, you don't get to snark.

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the bolded bit is incorrect as per newtons third law.

No, there is no conflict with Newtons 3rd law.  I can't completely understand what you think the purpose of the 3rd law is.

Quote

it does not "try to push back with the same amount of force" nor is there a question of whether it succeeds or not in exerting the force - it DOES push back with same force.

Yes, it does, to the extent that it has force to push back with.  Once the opposite forces have been equally matched, the objects come to rest.  If, however, there is still energy left over, that energy will force continued movement until such time that it finds equilibrium as well.  Whether you like it or not, the 3rd law is about interactions.  Its purpose is to define (for lack of a better word) the two forces that are interacting; it forbids the existence of a single force.  The 3rd law does not deal with the force and acceleration of a single object, unlike the 1st Law.  It deals with the net result of the forces involved, the action and reaction of the objects.

Newton's 3rd Law is less a law and more a description of forces interacting.

The smaller force does not magically generate more energy out of nowhere.  Force is a variable used to calculate interactions between objects based on their mass and velocity.  It doesn't reflect any particular quality of whatever example we use.  We can put a jeep on top of a grape and claim that the forces are equal and opposite, but that doesn't mean that grapes have the power to hold up jeeps.  Once the upward force of the grape is matched by the downward force of the jeep, the jeep still has plenty of energy left to keep moving downward, thanks to gravity.  If, however, we place the grape on top of the jeep, even though gravity is giving the grape extra force, it still doesn't have enough force to move the jeep.

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if the falling slab impacts the stationary slab with say, a force of ten billion trillion newtons, then the stationary slab will exert the same ten billion trillion newtons on the impacting slab.

Only in the sense that the net force between the two objects is equal and opposite.  In other words, the impacting slab is being pulled towards the stationary slab with ten billion trillion newtons of force, and the stationary slab is being pulled towards the impacting slab with ten billion trillion newtons of force, as per 3rd law, however, when contact occurs, we have to determine the

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this is an important concept to acknowledge because you are implying that the stationary slab will be the only slab that fails (breaks), when in fact both impactor and impactee will fail (break).

How am I implying that when I specifically removed energy at every interaction?  I gave the falling mass a "bounce.  I calculated the reduction in speed of the falling mass due to the impact.

And there is no "breaking" involved here.  Two objects, two movements, one with a logarithmically growing increase in energy, and one with a mathematical increase in energy.  Two forces impact, the smaller force cancels itself out on the larger force, and the remaining force continues in the path it was taking before being interrupted.  Just because the direction they are taking is "down" (because, you know, gravity), doesn't change those characteristics.  If this was in space and we were talking about a rocket accelerating towards some stationary satellite, the same would apply.

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if you are thinking that only the impactee will fail then your model is analogous to a steel slab falling on glass slabs.

There is nothing in these formulas that reflects different properties of the objects involved.

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again this is important since the 10 storey falling block of wtc1 will be destroyed after the first 10 "floor impacts", leaving 90 intact storeys vs 20 fragmented storeys which is a different problem altogether (less than 20 actually since a lot of debris is not going to do any impacting).

That is a different argument altogether, and not the one I was demonstrating.  If you wish to discuss that scenario, I will be more than happy to, however, first let's finish the example that is actually on the table.

Don't change the variables randomly and then argue the results of the original are wrong.

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yes i understand simple physics, how about you? do you understand that two objects impacting will exert the same force on each other at the same instant?

Do you understand that Newton's 3rd Law is not an iron rule dictating that all forces interacting with each other are magically equal, but rather that its purpose is to define the net forces involved?  In other words, that the energy due to momentum in each body will be retained in one way or another, not that the energy of each body is inherently equal?

### #39 aquatus1

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Posted 29 May 2013 - 01:20 PM

flyingswan, on 29 May 2013 - 09:35 AM, said:

After the initial drop, there is a growing layer of crushed floors between the upper and lower blocks.  This layer is falling, like the upper block.  This means that the situation is no longer symmetrical between the two blocks.  The force on the lower block is greater than the force on the upper block by the amount of the force on the layer of crushed floors.
The force on the lower block is resisting the fall of both the upper block and the crushed layer.  The force on the upper block is just resisting the fall of the upper block itself.

This is more a question of elastic vs inelastic collisions.  In the example I have presented, I am using a combination of both depending on which system I am calculating.  As I mentioned before, this is a simple example to demonstrate one single aspect of physics, that of the logarythmic increase of energy due to gravity.

The thing about the actual WTC collapse (or, for that matter, any collapse) is than an avalnche situation does not readily lend itself to simple physics.  There are both elastic and inelastic collisions, there are unusual gravitational effects in play, the main body alternates between acting as a solid and acting as a fluid, and mass is alternately gained and lost, affecting momentum in both negative and positive ways.

Avalanches are, basically, every aspect of mechanical physics jumbled up into one chaotic package.  Unfortunately, there is a lot of confusion from people who don't recognize how many different types of forces are at work here, and how things that seem like they are common sense change when physics go wild.

For instance, there are people talking about air friction acting as a cushion, or at least a significant variable of some kind.  As it turns out, in avalanche scenarios, air can act as a cushion (absorbing energy), as a lubricant (increasing energy), and it can even act as a multiplier of mass!

### #40 Liquid Gardens

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Posted 29 May 2013 - 01:45 PM

Little Fish, on 29 May 2013 - 11:26 AM, said:

again this is important since the 10 storey falling block of wtc1 will be destroyed after the first 10 "floor impacts", leaving 90 intact storeys vs 20 fragmented storeys which is a different problem altogether (less than 20 actually since a lot of debris is not going to do any impacting).

Why do you think this, that the damage will be equal beyond the first impact between the blocks, what happened to the mass of the crushed stories in between?  Isn't it exerting a force/have energy that the remaining lower block must withstand but not the remaining upper block?

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### #41 Little Fish

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Posted 29 May 2013 - 02:41 PM

Liquid Gardens, on 29 May 2013 - 01:45 PM, said:

Why do you think this, that the damage will be equal beyond the first impact between the blocks
because every experiment i have seen shows it, that's why i think it.
why do you believe what you believe? show me one experiment that shows an object can crush another identical object and survive without suffering the same damage that it inflicted, or better still, an experiment to show an object crushing 10 identical objects.

"what happened to the mass of the crushed stories in between?"
it's still there, some will be between the two rigid blocks, some will freefall off the sides and some will be freefalling between the blocks.

"Isn't it exerting a force/have energy that the remaining lower block must withstand but not the remaining upper block?"
the notion that the upper 9 storey block is just freefalling whilst only the loose crushed material of 2 storeys is compressing the 99 storeys below is silly on its face, if you are trying to say that only the crushed material from the first impact is crushing the rest of the building, then you are claiming that the collapse of just the top storey (floor 110) would crush the entire building, so in order to demolish the entire wtc tower, it would be enough to just blow up the top floor (floor 110) and the resultant rubble would crush the entire building, i'm sure you'll agree that is absurd.

### #42 Little Fish

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Posted 29 May 2013 - 02:59 PM

aquatus1, on 29 May 2013 - 01:07 PM, said:

Force is a variable used to calculate interactions between objects based on their mass and velocity
you are confusing momentum with force.
force = mass x acceleration
momentum = mass x velocity

### #43 Little Fish

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Posted 29 May 2013 - 03:32 PM

aquatus1, on 29 May 2013 - 01:07 PM, said:

Newton's 3rd Law is not an iron rule dictating that all forces interacting with each other are magically equal,
I never stated that, but it is an iron rule that 2 colliding bodies exert the same force on each other.

"but rather that its purpose is to define the net forces involved?"
no, newton's third law is not that, nor does it have a purpose, it just is.

"In other words, that the energy due to momentum in each body will be retained in one way or another, not that the energy of each body is inherently equal?"
not sure what you are getting at. conservation of momentum determines the motion after collision, is that what you are getting at?

### #44 Liquid Gardens

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Posted 29 May 2013 - 04:09 PM

Little Fish, on 29 May 2013 - 02:41 PM, said:

"what happened to the mass of the crushed stories in between?"
it's still there, some will be between the two rigid blocks, some will freefall off the sides and some will be freefalling between the blocks.

"Isn't it exerting a force/have energy that the remaining lower block must withstand but not the remaining upper block?"
the notion that the upper 9 storey block is just freefalling whilst only the loose crushed material of 2 storeys is compressing the 99 storeys below is silly on its face, if you are trying to say that only the crushed material from the first impact is crushing the rest of the building, then you are claiming that the collapse of just the top storey (floor 110) would crush the entire building, so in order to demolish the entire wtc tower, it would be enough to just blow up the top floor (floor 110) and the resultant rubble would crush the entire building, i'm sure you'll agree that is absurd.

You kinda dodged the second question above; although I agree that the notions you are talking about above are absurd, it doesn't have anything to do with anything I said.  If some of the mass of the crushed stories, which is constantly growing as the collapse continues, is freefalling as you admit, then the answer to my question is obviously yes, the remaining intact lower block has to withstand a force, that provided by the mass of the falling middle crushed stories, that the upper block does not.  Thus the forces on the intact lower block and the intact upper block cannot be equal past the first collision, in general.  So then it follows that the resultant damage from these forces, in general, should not be expected to be the same on the lower block and the upper block as the forces are not equal at those two separate points.  Thus, I don't know why you think the damage would be equal and that a failing floor in the lower block, after the first stories have been crushed, must also result in a crushed floor in the upper block.

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### #45 flyingswan

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Posted 29 May 2013 - 07:11 PM

Stellar, on 29 May 2013 - 11:00 AM, said:

No, you are wrong. The forces Newtons 3rd law talks about are always equal, regardless of whether they are in contact or not.
Oh dear me, what an admission.  You have no idea at all, do you?

Unless you are considering forces that operate at a distance, like gravity, the "equal and opposite" forces only apply at the point of contact of the two bodies.  If the bodies are not in contact with each other directly, but only through a third object, then you have two separate situations, two pairs of equal and opposite forces, and these two pairs are not equal to each other.  If you have three blocks stacked in a vertical column, do you really think that the force between the middle and bottom block is the same as the force between the middle and top block?

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