Flies In A Bottle
Two flies are standing on the bottom of a closed glass jar, which sits atop a scale. According to the scale, the glass jar and flies have a combined mass of 100g. Suddenly, both flies lift off of the bottom of the jar and begin to fly around inside the jar. While the flies are in flight, what is the average reading on the scale?
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2 solutions
didn't read closed jar, dammit :-/
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I didn´t read " CLOSED "...too
Agreed, even picture shows its open
I would agree with the answer "Equal to 100g" if the flies were said to fly up and dwn only. But, as they fly around , there is a loss of energy to change direction so the resultant force caused by their flying movement would have components there are not vertical, making the average reading on the scale slighty less than 100g.
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perfect answer the force is not directed always downward , it is directed in all directions . hence the correct ans would be slightly less than 100g
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I dn't know where write my comment: Here ... Supposons qu'on dispose sur une "balance" sur lequel on dispose un "contenant" dans lequel il y a 50 tonnes d'eau et où nage une "baleine volante" d'également 50 tonnes. La balance affiche "100 tonnes". Tout à coup, la baleine s'envole dans les airs... Qu'affichera la balance ? 50 ou bien 100 T ? Tout le monde sait que ce sera 50 tonnes… Conclusion ? ...................... //// Suppose we have a "scale" for which there is a "container" in which there are 50 tons of water, where swimming and a "flying whale" also of 50 tonnes. The scale displays "100 tons". Suddenly the whale flies through the air ... What will display the scale? 50 or 100 T? Everyone knows it will be 50 tons… Conclusion ? ...................... Less than 100 Gr. is the right answer
What makes you think that? How is the force transmitted to the walls of the jar? Do you really think that this happens in a way that causes the AVERAGE (which is what the question asks for) net force from the flies' motion to be directed upwards, so that a lower reading is recorded on the scale?
Heitor Sanchez Fernandes, It may be true that energy is lost by flying laterally. However the pressure they exert in the vertical direction will still be the same. You are assuming that the resultant force is the same even if they are flying laterally and accelerating/changing direction etc. That is not correct. The resultant force for a fly that is flying at a constant altitude and also changing direction is actually GREATER than for a fly that is strictly hovering. The vertical component however, will be the same.
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The push caused by the flies' wings won't generate a laminar flow downwards, but a turbulent flow. This means that even if the flies are mostly applying a regular force downwards, the direction of this force is dispersed laterally while the air is moving, causing less pressure to the scale than if the flies stood still on the floor. The higher the flies fly, lower is the pressure applied to the bottom and higher is the pressure dispersed through the glass' walls.
This means that if the flies flew very close to the bottom, the scale would indicate a value very close to 100 (maybe even 100, depending on the scale's precision). The higher the flies flew, this indication would get lower. So if we consider the average, the correct answer would be less than 100.
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@Vinicius Valls – to gain height, the flies would need lift, so heavier than 100g?
it would be the same on average, but when the flies are flying downward it would be slightly less, and upward slightly more, no ? And flies also burn calories to fly so losing weight, although very very slowly :D
Oh, I see, that's right, thanks.
Exactly. And in reality, turbulence would redirect some air flow in the horizontal direction negating it's effect. I'm with you on slightly less in actual application.
That is incorrect. No insect flies by pushing the air down. Rather, they create a lower pressure above their wings (by removing air out of that place) which creates a life. More of less like airplanes. If they needed to push down and if the wind needed to hit the floor for them to fly, they would fall if they went out of a window on a tall building. The reason why the weight is unchanged is because the air inside the closed jar acts as a fluid, and since the jar is closed, the air has nowhere to escape. The weight on the measuring scale consists of the jar, the air inside it and the flies. It is a closed system, and it impossible to change the mass of a closed system, and thus the weight.
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That's not quite right .. the question doesn't ask for the mass, it asks for the average reading on the scale. The scale measures the force on it due to gravity, as well as any other forces. Suppose it were a larger closed jar, with a human jumping up and down. Do you really think the reading on the scale wouldn't change as the human pushed off and landed? Of course it would change, but the AVERAGE value over any reasonable time interval would be the total mass of the closed jar and contents, as you said.
but weighing machine wont account the weight of fly coz its hovering so no normal reaction thus wt. of fly should be reduced and rest follows your explanation (flying mechanism) implies less than 100g.
Untrue. The flies push the AIR down (not the bottom of the jar) and the air would not necessarily push the bottom of the Jar with the same force as the flies are exerting in the air. The air dissipates some of that force through turbulence (some of the up-pushing force keeping the flies up is transformed into heat in the air). The air is a viscous (albeit very little) and therefore transmission of force through it doesn't work quite that simply.
That said, the flies would also be exerting a greater force than their gravitational force downward, only a portion of which is transformed into lift due to inefficiency. Therefore the answer is it is impossible to determine with that level of information.
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no, you are making it too complicated .. the problem asks for the AVERAGE reading on the scale. Whatever the instantaneous forces transmitted to the scale from the flies' motion may be (they'll clearly be larger at the instant a fly takes off from the bottom of the jar, and a bit smaller if it is hovering near the top of the closed jar), they'll cancel out over any reasonably long time interval, so the average reading on the scale will be 100g. You can guess the right answer by just thinking about the mass of a closed system being conserved, but that explanation is too simplistic.
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That's actually not too complicated. Fluid mechanics (which belong to classical mechanics) teach us that a turbulent flow has heat and momentum transfers. The momentum transfer can be represented by the shear stress, calculated in the direction normal to the flow. This momentum transfer slightly changes the direction of the main flow through its theoretical path, decreasing the probability that the particles originally dislocated by the flies flapping their wings would ever exert vertical pressure over the glass bottom. This probability decreases as the distance between the flies and the bottom increases, because the events are chained.
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@Vinicius Valls – The system is contained, except there is heat loss as the flies flap their wings. The scale probably cannot measure this. it should read 100g until enough energy escapes through the walls of the glass. Energy, thus mass will slowly escape, very slowly I think. The flies cannot in reality "just keep flying". They are expending energy. They are still being registering on the scale even if they are flying just as the air inside is being registering. Any extra energy due to metabolism goes into turning and such. They still have to push down enough to keep flying.
@Vinicius Valls – Hmmmmm .... I don't think that works out for a closed container, at least not for a long-time average. Consider the following modification, which works in the effects of turbulence in a different way. Suppose that instead of flies, you have a small fan suspended in the center of the jar, supported by rigid attachments to the jar walls. The fan blades are directed do that the air flow will be directed vertically up or down (depending on the direction of rotation). By your logic, when the fan is operated at a constant speed, if the flow is directed downward, the reading on the scale should be lower than when the fan is at rest (and vice versa). This is because the full force exerted by the fan against the rigid mounts will be transmitted to the jar walls (and thus the scale), but only a fraction of the opposing force exerted against the displaced air would be transmitted to the inner surface of the jar, due to turbulent losses. I don't think it works that way .. otherwise you could fly a neutrally buoyant zeppelin around by running a thrust fan INSIDE of it, and I am pretty sure that won't work.
Firstly, mass and weight are not the same thing. One is how much space an object takes up. I don't think a scale could really measure mass. So, that being said, I would assume they mean weight. How much weight is being applied to the scale.
The flies sitting on the bottom of the jar would be a constant weight, which would be the 100g.
The flies then begin to fly around. This is what I am not getting. If they were hovering, I would understand that the weight would be 100g. But what if they go higher? Would they not have to push more than their weight in a downward force to go up and less to go down? In turn, changing the weight constantly?
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That is precisely why the question requests the "average reading on the scale" .. because the force exerted by the flies on the jar, or the air in the jar, changes with time, but the time-averaged value remains 100 g.
it is similar to a helicopter. Then a helicopter fly around it and you stand at the land when the helicopter flies around do you feel the pressure?(when the distance of helicopter and you is very high)... so i think is less than 100g
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agreed, but you wouldn't feel much pressure anyway, because it would be spread over a wide area. what a nice way to test this though, take a mini remote helicopter on a spin, on a scale, in an airtight container!
so the mass have to change by time because the wing of the flies swing up and down
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There is also dissipation of pressure because the jar is not closed. It should at least be less by 1/5 or more because of geometry....
So this is a disguised statistical mechanics problem?
but dont they have to applie a stronger force to lift their weight up? So it should be more than 100, even so a little bit?
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Yes, but think about what they are pushing against ... it's always the air, which is in contact with the walls of the closed jar. So, you can think about them zipping around making little wind currents that push on the walls of the jar ... sometimes those tiny forces have a resultant that adds to the force on the bottom of the jar, and sometimes their resultant subtracts from the force on the bottom of the jar. That is why the question asks for the AVERAGE reading on the scale ... all those little variations will cancel out over time, and the AVERAGE reading will just be the total mass of the system (assuming the scale is properly calibrated).
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That is correct, like Agastya Bellad mention it on top. But there is one observation that is interesting, even if fly spent their energy on flying and making oscillations, average mass will stay the same, but if they spent their energy, they should lose some "weight"?
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@Стеван Грубач – Well, if you are talking about metabolic conversion, then the total mass is unchanged .. whatever waste products are excreted by the flies will remain in the jar, and mass is conserved. If you are making the more esoteric point about relativistic mass-energy conversion, then you could say that, since the processes in the jar are spontaneous, a TINY amount of rest mass (in the form of enthalpy changes in chemical bonds) was converted into heat. In that case, unless the jar was a perfect thermal insulator, that energy could be lost from the system as heat, resulting in a tiny reduction in the rest mass of the system. :)
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@David Moore – Exactly what I had in mind, dissipation is inevitable, tho we can lower it to the minimum but still. So in one way this proves lows of conservation and in other hand inability to make perfect preservation of energy or possibility to make something like perpetuum mobile. ;)
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@Стеван Грубач – I answered "correctly", becauase I was expecting that answer was expected. But I really think it would show less than 100g. The scale only measures 1 side of a complex 3d closed system. How flies fly and how force is dissipates throug air to the sides and top of the box and the aerodynamics are all very complicated, I'm sure. In a really simple world or a properly defined problem(well it does mention a scale which measures mass, but it should elaborate on its accuracy and operation, as it could be an expression used for a normal scale), the answer would be 100g.
The flies can not just throw air down, the air will circulate down first and then upwards in a constant circular motion to compensate for the vacuum created above the flies, on top of this, the higher they fly inside the jar the less pressure arrives to the bottom of the jar due to the fact that the pressure will be cushioned and dispersed through the increasingly remaining mass of air. Though there are other valid theories to contest the answer, with just these two, combined or not, I think that there´s no chance for the scale not to move.
The answer is 100g of course. Flies and 100g makes you lose your mind. Now change the question like this :
If there are 2 fish in a closed jar with full of water have a combined of 5kg. Suddenly the fish swim to the top of jar. Then what is the average reading on the scale ?
Easy right ?
the fly can fly so as your idea can still be an idea or can fly away
Take note that what is asked is the AVERAGE.
this is wrong, it is specified that the jar is closed. Further the weighing machine calculates by the displacement of spring attached to it. Only if the fly stands on it, the reading will appear. May be the closed jar may read some weight as told by you.
firstly was the weight of the jar included when the zero was set =so the 100 grams is just the flies weight ? secondly i refute the claim that the downthrust of wings is equal to the weight of the flies ?
The answer brilliant provides is incorrect. It would be 100g only if the fly was not exerting more force than necessary to keep it flying. A flying fly is either exerting exactly its weight or more than its weight to fly, so on average it would be more than its weight. It would not be equal to its weight. One of the answers should have been larger or equal to 100g, that would be the most correct answer.
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No, that's not quite right. You have to think about what the flies are pushing against as they are moving around .. it's the air in the jar of course. So the motion of their wings causes tiny pressure waves, which propagate in all directions .. depending on the vertical component of their motion, the instantaneous pressure differential between the bottom and top inner surfaces of the jar (which is the thing that will change the reading on the scale) can be either positive or negative, and on average it will be zero.
You can think about it another way .. take a series of snapshots as the flies are flying around inside the jar. Clearly, the total mass in each snapshot must be the same. Now figure out the force vectors required to move the flies from one snapshot to the next ... as a simplification, we'll assume those forces are exerted against the walls of the jar directly. Isn't it clear that over any reasonably long time interval, the net force in any direction will balance out to zero?
This would be true only if the whole force produced by the flies was transfered to the air and from the air to the glass bottom. However, the flies generate a turbulent air flow, causing part of this force to dissipate through concurrent air current vectors, heat and finally the glass walls.
Let's break it down in few moments: T-0: The flies are standing still at the bottom. Scale indicates weight = 100. T0: The flies take off. Due to the momentum conservation, the same force used to take off is applied to the bottom of the glass. Scale indicates weight > 100. T1: The flies reach a threshold height H in which the force inflicted by the flow they produce is totally dissipated, generating no impact on the scale measurement. Scale indicates weight < 100 T1+: Any flight path produced by the flies above the H height, or any flight path produced below the H height if the flies are accelerating downwards (in other words, not producing enough lift to cancel the gravity) will leave the scale indicating weight < 100.
The only two situations where the average measurement indicated by the scale would be >= 100 would be when the flies are below H, descending and breaking when the flies are below H and climbing up.
Can we build and test it
we are not given a degree of sensitivity for the scale; and with 100g given, we have to assume the scale operates +/- 1g. Which is a terrible scale. Even kitchen scales operate with a sensitivity of 0.1g. Amazon has .001 scales available for less than $20.
In all honesty, if flies at rest give a measured weight; then flies in motion, exerting force on the inside the glass jar (biochemical reactions transforming stored energy) then heat outside the jar will be slightly inequal to the inside; and an exchange will take place. The actual weight will change. Whether our terrible kindergarten scale will measure it is the question.
this is a challenge of recognizing misdirection, not mechanical physics.
F=ma, what if they accelerate upwards at a high acceleration? The force of lift of each fly will be above their individual weight. Thus the overall force will be above 100 g. If their acceleration just equalled gravity, they would float, not fly. Wrong?
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It asks for the "average reading on the scale" ... you are right that the instantaneous resultant of the force vector from the flies' motion can point in any direction, however, since the container is closed, and the files are flying around (i.e. changing direction to avoid collisions with the walls), over time those forces will average out to zero.
I thought the air also has some negative space (called vacuum) which helps flies to fly in the air without any resistance (by air). and the mass of the air particulate also accommodates the mass of the flies. Now, according to the solution mentioned, flies push the air downwards to with the force, equal to the gravitational force generated by the mass of the files while at rest. So, according to this theory, when an aero-plane travels above any one, does the person below it feels the weight of the plane (approx 1000 to 2000 kgs) by its downward pressure and gets crushed???
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I think you need to think more carefully about the differences between compressible and incompressible fluids, and how forces are transmitted through them ...
It seems you agree it is impossible to determine, because you have serious needs to include the expression "on average". So, in some situation it will be more than 100g, in others less, that on average it tends to be 100g. F..., i just realised the question is "average reading"... You are right! I will beat myself up.
I don't think air is so rigid to pass on any displacement right down to the jar bottom.. Air molecules are loosely arranged, so it may allow a certain extent of compression without exerting any force on the jar..
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How would that work? Remember that we are talking about the long-time average of a closed system, and you have to conserve energy, momentum and angular momentum. Certainly at the instant the pressure wave is created near the wings of the moving fly, it is not in contact with the jar, but over time that disturbance will propagate to the jar walls, at which point it will cause a fluctuation in the scale reading, and be reflected, and then register as a different fluctuation the next time it hits a wall. Energy dissipation in the form of turbulence will convert some of the energy used to create the disturbance into heat, but I think any fluctuations caused by pressure waves bouncing around inside the jar have to balance out in the long-time average.
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Most of the energy will be dissipated through walls and ceiling, or exist in mini air currents within the jar. Before, the flies were touching down. Now they are flying, by exerting on average forces equal to their weight right below them. With that as a center of energy dissipation and a relatively huge jar filled with non compressed air it doesn't take much to assume the physics and mechanisms involved are too many and too complicated not to cause losses on that scale read. It's too simplistic to think it would read the same, even on average.
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@Nick Zafiridis – I don't think so .. but I do see why your analysis might lead you to that conclusion. Think about it another way ... suppose I have a jar filled with air, and another jar that has been evacuated but is otherwise identical to the first. If I measure their masses, they will be different, with the difference being equal to the mass of the air. So, according to your logic above, only things touching the lower surface of the closed container will register on the scale, but in the gas filled container, only a tiny fraction of the molecules are in contact with the lower surface at any given time, yet the mass of all the contained gas molecules registers on the scale. How can you explain that? Why is that case any different than the one under consideration here?
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@David Moore – The tiny difference would indeed exist because of the air, but even then I'm not sure all the air in the jar is weighed, due to air mechanics I'm not aware of. This means air could be pressuring against walls or the ceiling, especially if you consider warmer or more active air molecules would be nearer the ceiling. I'm not so sure a jar of air would behave like one with water or solid matter. I'm more certain when it comes to the flies case. Most of the weight read is from them, since air is so light. Even if in your example the scale would read the weight equivalent to the whole mass of the air, in this case that weight is too little to affect the average. Also, complex aerodynamics while flies fly increase the chance of air pressuring against otheer directions.
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@Nick Zafiridis – Well, I can tell you for sure that it's the entire mass of the contained gas that is measured, just as if it were water or solid matter. Furthermore, it's not that small of a difference, particularly if the gas is under pressure .. for example, you can easily tell just by lifting it whether a SCUBA tank is full (~200 atmospheres) or "empty" (where empty means it just has one atmosphere left inside it).
Anyway, the full mass of the gas is registered on the scale because the gravitational force on the gas molecules slightly increases the force of collisions with any object when the molecular velocity has a downward vertical component, compared when when the it has an upward component. This difference is measured consistently, even though all of the molecules are undergoing thousands upon thousands of collisions every second, and most of them never even touch the lower surface. The net result of all of those tiny differences is accurately registered on the scale, so I don't think there will be any issues with measuring the net vertical component of the increased velocities of air molecules that have been driven downwards by the fly's wings. The steady state value of the downward force is essentially the same as when the fly is sitting on the bottom of the jar, with the difference being due to the tiny amount of energy lost to heat via friction, which is negligible compared to these other considerations.
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@David Moore – If you're sure it's ok. Even if the weight of the air inside registers on the scale steadily, it's the weight of the flies I'm worried about. You could be right, but I'm not sure. Yes, on average the downward force is the same. But I don't know if it would be registered on scale, because of the air dispersing it. The difference with the jar only filled with air is, that the weight of the flies isn't added to that of the air, probably. I feel like in theory what you say should be correct, but because we are dealing with air, there are a lot of losses due to mechanisms we are not considering.
I dn't know where write my comment: Here ... Supposons qu'on dispose sur une "balance" sur lequel on dispose un "contenant" dans lequel il y a 50 tonnes d'eau et où nage une "baleine volante" d'également 50 tonnes. La balance affiche "100 tonnes". Tout à coup, la baleine s'envole dans les airs... Qu'affichera la balance ? 50 ou bien 100 T ? Tout le monde sait que ce sera 50 tonnes… Conclusion ? ...................... //// Suppose we have a "scale" for which there is a "container" in which there are 50 tons of water, where swimming and a "flying whale" also of 50 tonnes. The scale displays "100 tons". Suddenly the whale flies through the air ... What will display the scale? 50 or 100 T? Everyone knows it will be 50 tons… Conclusion ? ......................
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And what will it be as the whale is accelerating up out of the water? It will have to exert a downward force that will be registered on the scale. So, some of the time the scale will be reading >100T, and other times it will be reading <100T ... the AVERAGE reading (which is what the problem asked for) will be 100T.
If the air is in laminar flow, sure we can assume force is exerted straight down to the bottom of the glass and register on the scale, but this is most certainly turbulent flow, meaning that the force would be spread throughout the jar unless it was infinitesimal in height. The answer is an average below 100g
If the flies are just sitting then the pressure exerted by the flies is less than when they fly inside and pushing the air downward then obviously the pressure increases due to their motion.
Average can't be equal.
the figure shows it's an open jar!
Scales don't measure mass, they measure force. The force exerted on the scale would change with changes in position of the flies due to flight.
If the flies are in flight or at rest on the bottom or under the lid of an enclosed jar, then the air they are pushing downwards just to hover (or stay still in the event they are crawling on the bottom or under the lid) would be equal to their body mass and thus would register their weight (the force of gravity working on their mass) plus the weight of the jar on the scale.
The reason for this is because the downwards rushing air pushes against the glass bottom of the jar, pushing into the scale with the same force as if the flies were standing on the bottom of the jar, not flapping their wings at all.
The weight would be greater than 100g if the flies had a change in upwards momentum; if they went up, the wings would have to provide MORE than their body weight in thrust, which would push the glass jar down harder, registering a greater weight until they resumed hovering, or hit the lid of the jar and couldn't rise any further, which would bring the force exerted on the scale back to 100g.
If they attained an altitude and slowly descended, their wings would provide less force than their body weight, registering LESS THAN 100g in the beaker, until the flies either hovered or landed on the bottom of the jar.
If the flies flew in a side-to-side movement, there would still be a force equivalent to the flies weight pressing into the scale, and would be the Y component of the force vector generated by the fly; there would also be an X component that would would exert a lateral force on the bottom of the jar, but not enough to move it.
These are just my thoughts; I'm no physicist.
I answered "correctly", becauase I was expecting that answer was expected. But I really think it would show less than 100g. The scale only measures 1 side of a complex 3d closed system. How flies fly and how force is dissipates throug air to the sides and top of the box and the aerodynamics are all very complicated, I'm sure. In a really simple world or a properly defined problem(well it does mention a scale which measures mass, but it should elaborate on its accuracy and operation, as it could be an expression used for a normal scale), the answer would be 100g. What if you stand right below and right at the center a massive swarm of birds/locusts/whatever flying around? Would you on average feel the force of even half of their collective weight? No.
if the flies descended at a constant rate, then the change in acceleration would be 0 and hence no change in force (than currently showing when flies are in air, hovering) would register, right?
If the jar is closed, then the flies will exert a force by pushing air downward in order to lift themselves. So the force remains constant on average.
It makes sense if you remember that flies fly by pushing air down. If the air can't go down through the floor of the jar, then the floor of the jar must stop that air. On average, this force applied to the air by the jar is the same magnitude as the force applied from the flies to the air (which is the weight of the flies).