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Stupid science questions

  
  

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Wombat
20:33 / 30.01.04
Not only is it possible that some bit of the windscreen hits zero velocity but some bits may hit negative velocity.
It`s possible that due to conservation of momentum that atoms on the opposite side of the windscreen may break off.
I don`t know enough about the atomic stucture of windscreen glass or flies to give you an accurate prediction. Perhaps the patch will have a velocity that never touches zero (for large chunks of glass this is allmost certain). Perhaps parts hit negative velocity (being zero at two or more points).


In the area of effect of a fly on a bus.
My best guess is that some atoms of glass recoil to negative velocity, most atoms don`t hit zero velocity but simply slow.
The amount of atoms that would hit zero or negative is predictable to a very small error given the properties of the glass and the fly....to my knowledge no-one has ever done a large amount of research on the subject. An educated guess.
 
 
Wombat
20:44 / 30.01.04
Come to think of it.
Depending on the temparature of the bus, some bits of it are allready moving in the opposite direction. A fly would simply adjust the number of bits by a very small amount.
 
 
Smoothly
20:57 / 30.01.04
Thanks Mr. Spong. So is it best to imagine the windscreen as a big rubber sheet which absorbs the changing velocity of the fly, while maintaining its forward motion? Is this kind of 'rubberiness' a property of the molecular arrangement of all solids? I mean, would it make any difference if the bus were a solid diamond and the fly were a neutron, for example? Is this kind of elasticity universal? Is there any way it could be removed from the model?
 
 
Smoothly
21:19 / 30.01.04
Actually, thinking about it, I'm not sure if the rubber sheet model helps me at all. I mean, there will still be a point where the sheet it at maximum 'stretch'. So we've still got a moment where the 'bus' is moving at 50 mph while at least one point within it is stationary. That's really what I'm struggling to visualise. I can see how there can be systems within systems - that the windscreen is composed of smaller objects all vibrating and moving in their own way (like people walking around on a planet...that's spinning round a sun....that's careening through a galaxy...that's whirling across a universe....etc). Is it just that a if I imagine the bus/fly collision from a kerb-side perspective, I have trouble grasping how within the object speeding past me, part(s) of it can be standing still.
Am I making sense at all? I'm not pissing about, I'm really struggling.
 
 
Wombat
23:13 / 30.01.04
Perhaps a better model from a kerbside viewpoint is a lot of rubber balls held together by rubber bands. breakable rubber bands.
Hmmm. My explanation is so bad I feel like I`ve just told you a porky.
*grin*
Tell me why this is important to you.
Then I can create a lie to suit your needs.
Sorry. Current physics models defy human understanding.
If it could be put into words we wouldn`t use maths.
And just because you can express it in maths doesn`t mean it works.

In the fly/winscreen case. I suggest you do a little research into conservation of momentum and conservation of enegy. Then take a pinch of salt.
 
 
Smoothly
22:39 / 31.01.04
Thanks for bearing with me Mr. S. Why this is so important to me kinda eludes me, now that you ask. It's not *so* important to me. I suppose we all build up models in our head of how things are, and although these are always going to be imperfect and metaphorical we want them to make sense of things. I think that the way we do this is quite interesting in itself (I'm sure that people go about understanding things in very different ways - we're never taught methods of understanding at school, afterall. It seems to me that things are just explained to us in different ways until we say 'I understand!'; and our word is taken for that without much thought being given to what it means. But I digress - that could be a thread all on its own).
One technique i use to understand new things is to liken them to things I already understand, and a kind of exaggeration plays a role in that (making the micro macro); hence thinking of a bus windscreen as a big rubber trampoline. That helped me visualise how the flexibility of the bonds between atoms even in 'solid' objects might change my intuitive picture of collisions. But then I realised that that wasn't really the problem I was having. Because even if I think of the collision of, say, two snooker balls as if they were two rubber balls (with a certain amount of 'give' during the impact), the point at which direction changes (ie. the point at which there is no more compression) they are (it seems to me) as good as solid. So how can one ball be moving if it is in contact with another that isn't? I know I'm having trouble explaining myself, and sound like the idiot's idiot... We see collisions all the time and know what flies don't stop buses, but I somehow just don’t ‘get’ how a stationary thing can be fixed to a moving thing.
 
 
tom-karika nukes it from orbit
19:05 / 01.02.04
With the fly, yes it will be true that the windscreen and the fly will deform. But at some time, bits of the fly must go from one direction to the other. The bits may lose some of their original energy to the deformations, the 'spring' or the rubber sheet.

But, whilst the fly is in direct contact with the bus, it's velocity changes from left to right. Whether the windscreen is slightly deformed or not is not really a problem, if the windscreen is attached to the fly at the same point as the fly changes direction, the windscreen must be stationary. And if the windscreen is stationary, the whole train (or was it a bus?) is stationary.

My point is that whether energy is lost in the colission or not, whether one or the other of the colliding objects is deformed, if one object changes direction, the other must be stationary.

But is the bus only stationary for an infinitely small amount of time? There may be an 'Instant' when the bus is stationary, but is the duration of that 'Instant' 0?
 
 
Wombat
20:44 / 01.02.04
The bus doesn`t have to hit zero velocirty at any time.
No part of the wind screen has to hit zero velocity at any time.
It depends on the nature of the collision.
Glass is fluid-like (amporphous silicon). The bonds are weak. So the impact has more effect on a small area. For harder substances the impact would effect a larger area to a lesser degree.

If someone threw a marble at you when you were sprinting
The marble would stop and reverse direction.
At no point would you stop.
Your slow down would be negligable.
A piece of you would slow down in the area of impact to a much larger degree than the rest of your body.Still not hitting zero velocity.
An atom of the marble may interact with your body long enough to slow it down to zero or lower velocity.On the wider scale of things this is negligable. It`s of low probability but possible.

If someone threw a marble at a eprfectly hard substance. The entire object would slow down a fraction. But wouldn`t stop.

I hope this helps. Think of throwing a stone into a large diamond...think of throwing a stone into water.
 
 
Smoothly
11:20 / 02.02.04
But, whilst the fly is in direct contact with the bus, it's velocity changes from left to right. Whether the windscreen is slightly deformed or not is not really a problem, if the windscreen is attached to the fly at the same point as the fly changes direction, the windscreen must be stationary. And if the windscreen is stationary, the whole train (or was it a bus?) is stationary.
...But is the bus only stationary for an infinitely small amount of time? There may be an 'Instant' when the bus is stationary, but is the duration of that 'Instant' 0?

You asking me or telling me Tom-Karikar? Yes, that is exactly how I'm thinking about it. Much less to do with conservation of momentum and more about simple velocity. Trying to simplify, I suppose I'm wondering which of these is false:

1. At some point in the collision, the fly has a velocity of 0.
2. At this point the fly is joined to the bus.
3. Two objects that are joined together cannot be moving at different velocities.

Now I know 'joined' is is an imperfect term because, in a sense, a bungee-jumper is joined to a bridge, but is still moving. And I understand that atoms in solid objects can be seen as being elastic in a similar way. But I suspect that this a distraction from the nub of the problem I'm having because the instant I'm interested in is the same instant that any such elasticity becomes irrelevant. In the same way that in the bungee-jump system, the elasticity of the rope matters when considering how the jumper slows (or gets catapulted back), but at the point at which the jumper changes direction, the rope is (for that instant) no longer stretching. It might as well not be stretchy at all, in that instant, no?

[tangent]I always suspected that my confusion and misunderstanding in this specific example a part of a more general confusion about infinity (hence me thinking it might be a mathsey problem). For example (and maybe someone can answer this as a side question), I learnt at school that a retarding force acts on a body in proportion to its acceleration (eg. G-forces?). But as an object moves from rest there must be a change in velocity from 0 m/s to 'some' m/s, and no matter how small 'some' is, that would be an infinite increase in velocity, resulting in - I would have thought - an infinite G-force. So how can things get moving at all?[/tangent]
 
 
grant
17:49 / 02.02.04
Uh, maybe it would help if you understood that "velocity" is, in part, a measure of time. So if you're breaking up the fly/bus transaction into discrete moments of time, you're already futzing with perceptions of velocity.

In other words, as soon as you take a specific moment in time, you've transformed velocity from motion into potential energy.

And yeah, your mention of Zeno is appropriate, since it's possible to keep reducing the moment of collision to smaller and smaller transactions - the fly's head smushing back into its own thorax, for instance, or all that atomic stuff you're getting into up there.

But basically, when you've got the energy going in one direction that is suddenly forced into the opposite direction, it gets transformed into (or reconceptualized as) heat. A stationary thing isn't "fixed" to a moving thing, it just swaps energy with the moving thing.
 
 
grant
17:53 / 02.02.04
Oh, and there's no reason the fly would need to have a velocity of 0. It just goes from flying at -2mph to +50mph at the moment of collision. The change in energy is converted to heat (and sound and "deformation of the objects).

This discussion may help with basic terms, and this ppt/pdf file may give more of an idea of what goes on during inelastic collisions.
 
 
Smoothly
19:07 / 02.02.04
Ahhh. Grant, you diamond. I wasn't considering all the full consequences of looking breaking things down like that. I wasn't really thinking about the difference between any old short period of time, and an infinitely short period of time (ie. no period of time at all).

Ahhhh, that indefinable moment of 'understanding' I was musing about earlier...

I was assuming the 'moment' at which the fly was moving at 0 m/s was a moment of some (albeit minute) time. But of course it's not; it's an infinitely short part of the transition between -ve velocity and +ve velocity. And I can see how 'infinitley short' differs in nature from mere 'very, very, short'.
Honestly - *that's* where I was going wrong. How humiliating.

I think I try to think about things in graphs too much, when in fact I can be pretty thick about graphs.


'Oh my God! They'll die instantly!'
'Everybody dies instantly. You're alive, you're alive, you're alive, you're dead.' - Steven Wright.
 
 
Lurid Archive
00:31 / 03.02.04
Oh, and there's no reason the fly would need to have a velocity of 0. It just goes from flying at -2mph to +50mph at the moment of collision.

But isn't there something a little disquieting about the notion that velocity (or even speed) does not vary continuously with time? For a start, try calculating the force experienced by the fly at the moment of collision. If there is an instantaneous jump in velocity, the answer is either undefined or infinite, which amounts to much the same thing I suppose.
 
 
UnTaMeD
07:35 / 03.02.04
I have another question:
Think about the road runner cartoon when wile coyote is stood on a falling rock at a very high velocity. when it reaches the floor he dies and then goes on to use his acme weapons. If wile coyote was to jump from the rock moments before it hit the ground, would he experience a less damaging landing, similar to that of jumping off a 6 foot wall?
 
 
Smoothly
11:20 / 03.02.04
UnTaMeD - I think that if he can achieve some relative upward motion in jumping (ie. taking off some of the downward speed) the impact will be (fractionally) softer. However, I'm not sure that, in jumping, his legs won't merely propell the rock downwards faster still, and not affect his own velocity. Intuitively, I imagine the size of the rock might be a factor here.
Either way, I think that without his Acme rocket-pack, he's fucked.
 
 
tom-karika nukes it from orbit
14:30 / 03.02.04
The relative sizes of the Coyote and the rock are crucial here. If they are both the same size, then they will both recieve the same proportion of the Kinetic Energy the Coyote puts in by pushing down with his legs.

But if the rock is massive compared to the coyote, the Coyote will carry away most of the kinetic energy. When a collision occurs, (defining this separation as a collision, which it sort of is really...) the least massive particle always carries away the larger proportion of the kinetic energy. The particle with the most kinetic energy is the fastest, and so the push downwards could make an appreciable difference to the coyotes final impact speeed.

Of course, if the reverse is true and the rock is smaller than the coyote, the coyote gets very little of the kinetic energy he puts in, and the rock gets lots of it.

Thats why firing a gun doesn't hurt so much as being hit by a bullet. In the collision, where the bullet and gun get energy from the explosive charge, the bullet is many hundreds of times lighter than the gun and the person holding it. The bullet gets all the K.E, and the gun gets very little.
 
 
grant
17:48 / 03.02.04
Well, also, Wile E. Coyote can't jump upward at anything near the velocity of the rock (and himself) going downward. His legs aren't that strong. Same thing with jumping inside the falling elevator the moment before it crashes into the skyscraper's basement floor. It's going a lot faster down than up.

That said, in toon physics, surprising things are often possible.

Back to this:
, try calculating the force experienced by the fly at the moment of collision. If there is an instantaneous jump in velocity, the answer is either undefined or infinite, which amounts to much the same thing I suppose.


I'm not sure I understand how this is a special case. At the moment of collision, the force is being converted from velocity into other forms of energy (smushing the fly). The fly's force also has an effect on the bus, slowing it down, but the mass of a fly and the mass of the bus are so very different that that slowing force is infinitesimal. Then, the fly's body is swept along by the bus as it continues to move in the opposite direction.

Might be easier to picture a linebacker running into one of the TV cameramen on the sidelines -- the camera guy gets carried along by the force of the collision, but they're both going to get bruised up, and the linebacker is going be slowed down instantly.

Is there some tricky thing I'm missing here?
 
 
Lurid Archive
19:47 / 03.02.04
The fly's force also has an effect on the bus, slowing it down, but the mass of a fly and the mass of the bus are so very different that that slowing force is infinitesimal.

Don't they feel the same force?

Force is a measure of the rate of change of momentum (via Newton's second law which is surely good enough for us here) so tells you how quickly the fly's velocity changes (proportional to its mass). So if it instantly changes velocity, that gives you an infinite force.

(Here I am using "instant" to refer to the fact that a change in velocity happens in literally no time.)
 
 
grant
16:52 / 04.02.04
Don't they feel the same force?

Force is a measure of the rate of change of momentum (via Newton's second law which is surely good enough for us here) so tells you how quickly the fly's velocity changes (proportional to its mass). So if it instantly changes velocity, that gives you an infinite force.

(Here I am using "instant" to refer to the fact that a change in velocity happens in literally no time.)

Hmm. OK, my understanding of Newton's 2nd Law is F=ma or force = mass times acceleration.
So according to that measure, on the first question, I'm not sure they do, although that seems counterintuitive. I think the collision involves both masses becoming one mass, so the end result is a single force felt equally, but as long as they're separate, the force of the bus will be vastly greater than the force of the fly because it has a vastly greater mass.

Maybe the difference between velocity and acceleration might help, since the only acceleration that's experienced here is by the fly, whose velocity goes suddenly from -2 to +50mph... which is a 52 mph/(unit time) acceleration. Technically, in this conceputalization, the bus experiences no force since it never accelerates. In the real world, the bus experiences some force, but only at a miniscule level, because of the vast difference in masses.

The second question, though, involves that "/(unit time)" part of the acceleration figure, which is kind of tricky to me. I'm not sure an instant change in velocity will give you an infinite force, I think it'll just change the units you use to measure the acceleration. But that's just a hunch after two minutes of staring at the screen and wrinkling my brow.

It seems that there's something "infinite" about every force, since every acceleration involves (potentially/depending on frame of reference) a moment when an object is stationary, followed by a moment when it's not. That's what acceleration is.

Apparently, acceleration is always an average, understood as change in velocity during a specific unit of time.

As a note, elsewhere on that last linked Q/A site, I discovered that the English unit for mass is the "slug" and that a Kleenex box on the back dashboard of your car will probably have enough force to kill you in a 60 mph collision. The figuring in that set of equations, by the way, gives an arbitrary .01 seconds for the period of a collision between the Kleenex box and the back of a skull.
 
 
grant
17:05 / 04.02.04
Oh, and the physics term for this sort of force from an inelastic, near-instantaneous collision is "impulse," understood as "Ft" which I never knew before.

Calculating the impulse exerted on an object by some force is generally pretty easy and uncomplicated - impulse is always the product of the force and the time the force is applied. Since it is always the product of a force and a time, impulse has units like "Newton seconds"

Example:
A force of 5 Newtons acts on a ball for 4 seconds. How much impulse was exerted on the ball?


Answer: 20Ns.
You learn something new every day....
 
 
Lurid Archive
18:57 / 04.02.04
I think its Newton's third law that says they experience the same force, grant. Although I always lose track of those forces. I think that the bus experiences a force, even theoretically, though it is very small compared to the mass of the bus so essentially irrelevant, making it slow down by a very tiny bit.

One thing I am more sure of is that this

Maybe the difference between velocity and acceleration might help, since the only acceleration that's experienced here is by the fly, whose velocity goes suddenly from -2 to +50mph... which is a 52 mph/(unit time) acceleration.

isn't quite right. You have to divide the 52 by the length of time it takes to cause the change in velocity (and also mutiply by the mass of the fly). A constant miniscule force can cause an increase in velocity over a century, say. But it takes a larger force to cause the same change in a few seconds.

So if a change in velocity happens in no time, you get an infinite force.

BTW - acceleration is a kind of average, especially in the real world. In the theoretical world, you have instantaneous acceleration via calculus.
 
 
grant
17:19 / 05.02.04
Ah. I never took calculus. Those strange symbols....
 
 
Lurid Archive
08:26 / 06.02.04
Its just about averages taken over infinitesimally short times. Nothing to be scared of.
 
 
tom-karika nukes it from orbit
14:35 / 07.02.04
I think I may have to resort to drawing a graph...
 
 
tom-karika nukes it from orbit
15:04 / 07.02.04
OK, I've put a graph Here.

I've put the original velocity of the fly as being -2 mph, and the velocity of the bus as being +50 mph (ie. in the other direction).

I'm trying to say that the velocity of the fly (and hence the bus) does reach zero, albeit for a length of time which is also zero. I don't think it has anything to do with exerting an infinite force, as you cannot affect the motion of an object over 'No time'. You have to measure force over a time period in order to have any affect on an object's velocity.
 
 
Cloned Christ on a HoverDonkey
15:25 / 07.02.04
I'm not sure that graph is entirely correct, as I don't see in my interpretation of events the fly actually slowing down and then speeding up in the opposite direction.

I feel the gradient of that slope should be infinite, ie vertical. The fly doesn't slow down, then speed up, it simply changes velocity from -2mph to +50mph instantly, the apparent infinte acceleration being explained away by the fact that the fly is no longer intact, and the overall effect of bits of fly flying every which way, the window deforming and the bus slowing down infinitessimally all act to cancel each other out.

In other words, looking at the fly and the bus as two distinct, irreducible objects is inherently flawed. The bus and the fly need to be considered as collections of tiny objects, whose overall momentum and energy is conserved in the impact (save a minute amount of heat dissipation and sound as the fly breaks apart). There isn't just one interaction between bus and fly, but countless interactions between loads of different (extremely tiny) objects.

View them as a system as opposed to two discrete objects and it all makes sense. Well, to me anyway.
 
 
Cloned Christ on a HoverDonkey
15:32 / 07.02.04
Another, almost contradictory, way of looking at it is by considering there to be only two dicrete objects, but by defining their spatial co-ordinates as being where their centres of gravity are.

When the fly hits the windshield, it is deformed, thereby altering the position of the fly's centre of gravity within itself. It is entirely reasonable to believe that this centre of gravity is perfectly stationary for a measurable length of time, due to the fact that the centre of gravity of the fly is shifting as the fly deforms, eg, the centre of gravity of the fly is shifting towards its head as the head shifts towards its tail.

Am I making sense?
 
 
Lurid Archive
17:34 / 07.02.04
Tom-Karikar

That definitely won't give you an infinite force - the force is (essentially) the gradient of the line(s) you have drawn. You only get an infinite force with an instantaneous increase.

I think the issue is really about the relationship between the velocity of the bus and the fly. The paradox arises because you would naively model one or both of these as points. I think this goes away if you allow a more three dimensional model that includes compression effects.

About forces being an average....

This is certainly true if you want to measure them, but there is a notion of instantaneous forces. I mean, it's what Newton used to show that planetary orbits are elliptic.
 
 
tom-karika nukes it from orbit
10:05 / 08.02.04
No, you are right, there is no infinite force. The force exerted on the fly is directly proportional to the gradient of that line.

As for the false-model of the fly and bus as indestructible, non-deformable particles, well that is true also.

So how about if I now say that the graph is for one atom at the front of the fly, and one atom at the front of the bus. Now, you can deform atoms, you can wrench them apart and bond them together. But not at 50mph. So some constituent part of the fly will obey the rule of that graph. Doesn't really matter if the head being crushed cushions the blow to the body. For the body of the fly, the graph will be a slightly different shape. In fact, because of this effect, the 'corners' of the graph should be slightly rounded. But this doesn't matter, it should still go through zero, whatever it's shape.

As the first part of the fly, the first atomic surface, interacts with the first surface of the screen, it experiences a force. The force accelerates the fly, from -2 to +50 mph. And as it does so the velocity of the fly (or one of it's constituent parts) must at some time be zero. You cannot accelerate from -2 to 50 without going through zero. An acceleration can be very, very sudden, but never instantaneous.

I could, given enough data and a supercomputer, draw graphs of every single velocity of every single atom in that fly. Some of them would not obey that graph at all, as bits of fly zoom out into the atmosphere. Some of them would obey it closely, and these are the ones which at some time reach a velocity of zero.

Steve Dubplate: How could the fly, or any part of it, change direction instantaneously? It must take time, hence the graph having a slope.

The thing with instantaneous force being used to show that the orbits of planets are elliptic is also correct. This is just plain calculus. (Though in those days it was very new...) The derivation, as I've learnt it (I think this is the right one) does the math using 'real' (ie. big, measurable intervals) of time, velocity, angle and therefore acceleration, and shows that as the interval in time approaches zero, an expression can be given for the force acting on the body at that instant.

Taking this back to the fly, I can do the same thing with my graph. I can take the derivative of that graph, ie. it's gradient, and I will get a constant value, from which I can work out the force. That is the force exerted at any one instant on the fly. But if I exert that force over 'zero time', I cannot accelerate the fly.
 
 
Cloned Christ on a HoverDonkey
10:18 / 08.02.04
I agree.

Yes, an instantaneous change of velocity like that would imply infinite acceleration and hence infinite force, which is obviously bollocks.

Your 'zero velocity for zero time' theory is the only plausible explanation.
 
 
tom-karika nukes it from orbit
11:51 / 08.02.04
Aha...
 
 
lukabeast
03:07 / 12.02.04
I remember reading something about the possibility of there being a second "brain" in the stomach region? Is this hokum?
 
 
tom-karika nukes it from orbit
17:14 / 12.02.04
Yes, there is a previously-unknown dense knot of nerves in the digestive tract. It could be responsible for some low-level physical reactions, and even some sorts of emotional reaction. It is described in more detail Here. I'm not quite sure about the provenance of the site, it's mainly concerned with whatever 'Aikidoaus' is, not general anatomy.

I think calling it a 'Brain' is a bit of an overstatement, it's not really comparable to the thing encased in the skull.

I find it amazing that this has been missed for so many years, although it was first seen by Leopold Auerbach, a neurologist in the 19th century. What other little anatomical quirks may have been overlooked?
 
 
Cat Chant
10:41 / 13.02.04
Well, the internal parts of the clitoris are apparently still not featured in "Gray's Anatomy" and some people think this may account for women complaining of impaired sexual response after hysterectomies, what with the surgeons not realizing the bulk of the clitoris is "in there"...

Here is my stupid science question. I have accepted that I will never understand how electricity works, with the electrons and everything, so let's leave the big question aside, but on a smaller level, how come people tell me I will be electrocuted if I turn on a light switch with wet hands? I know water conducts electricity, and I see how the light switch must be completing a circuit inside my wall, so the idea is that the electricity is going to travel through the water to my hands instead of up the wire to the lightbulb as it should, but, you know, the switch is plastic, and it's between me and the electricity. So how wet would my hands have to be for me to be electrocuted by turning on a light switch? How likely is it? Wouldn't I have to, like, deliberately drip water into the cracks in the lightswitch?
 
 
tom-karika nukes it from orbit
12:00 / 13.02.04
The voltage could be enough to jump the air gap between the wet hand touching the plastic and the electrical terminals in the switch. The distance is probably less than a centimetre. The drips would really cause the problem. They might leave a connected trail of water from your finger to the terminal as they move through the cracks, and that would form a circuit.

I'd say that if your hands were dripping wet, you might have an appreciable (>5%?) chance of being electrocuted. But I'm not volunteering to experiment to find this out exactly.

The probability of electrocution is low, but the number of times that you operate a light switch is large, so it will almost certainly happen to someone...
 
  

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