The Flies
Two identical jars A and B each contain a fruit fly of equal mass. The lids of the jars are tightly closed. In jar A , the fly is sitting; in jar B , the fly is flying at a constant speed in a horizontal circle.
The jars are placed on weighing scales to see which jar weighs more. Which jar will show a greater reading on the scale?
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6 solutions
Shouldn't Jar B have a higher reading because of relativistic effects - the mass-energy of Jar B is higher.
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Ha ha.
But consider this suggestion -
If the fly in jar B starts at rest and then spins up even to relativistic speeds, the two readings will still be the same. Remember that mass and energy are equivalent, and the total mass-energy inside the jar does not change.
But if the fly were replaced by an electrical insect drone and fed energy from an external power source (perhaps via wires through the lid of the jar) then the mass would increase! Of course the increase would be undetectable at everyday speeds.
With v F L Y < < < c any relativistic effects would be undetectable. If the fly were able to break the sound barrier, ( ≈ 3 0 0 m/s), then the sonic boom might cause a momentary jump in the scale reading, but flies can't even travel that fast. :)
We generally do not talk about the relativistic effects on macroscopic objects like flies which fly at speeds much smaller compared to the speed of light. I think it would be nitpicking and over complicating the problem statement unnecessarily to include the assumption that relativistic effects are ignored.
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Why is it evaluation in extreme cases is considered "unnecessary"? Either make clear the assumptions used, or take the counterexample for what it is--a proof your solution is WRONG.
"Good enough" may be fine for building a bridge, but when you're discussing in the abstract, you have to define your domain VERY precisely. Failure to do so is either laziness or short-sightedness.
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@Joshua Nesseth – Well, then there will be so many things for the author to mention, like, 1) The fly does not fly at relativistic speeds 2) The fly does not spin with relativistic speeds 3) When the fly flutters its wings they don't catch the static charge and even if they do ignore the electromagnetic radiations they may cause. 4) Due to the motion of fly, no heat is generated and escapes from the jar. and maybe much more.
Yes, I think that assumption needs to be stated. Because really, it could be equal, less, or greater depending on the acrobatics of the fly.
Bonus question2: Which jar would have weighed more if the lids of both the jars were open? The fly in jar B is going in the horizontal circle and the fly in jar A is sitting inside it.
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I think that we won't be able to predict what would happen if the lids are open. When they were closed , we were certain that all the forces on the air molecules must be equalised by the walls of the container while here the system is too complex to predict what would happen.
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I think if the lids were open then the fly will still push the air down with a force equal to its weight but the air won't be able to transfer all that force to the bottom. Thus, the weight of jar B should be less than jar A in this case.
Air molecules striking the bottom of the jar are going to be nearly the same on both accounts, whether the fly is flying or not. The acceleration of the fly also will have little effect. The assumption that the air molecule that the fly pushes off of will travel in a straight line to the bottom of the jar is a bit idealistic.
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It's not that all the air molecules are being pushed downward in a straight line, but that in equilibrium the net downward force of the air on the jar is equal to the weight of the fly. I've added the word "net" as a qualifier to "force" in my solution for sake of clarification.
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Not against this. But still not convinced. If the fly is sitting on the bottom of the jar, there is a normal force pushing up on the fly from the scale. I guess the idea that the fly is part of some closed system is the caveat here. Thanks for the response.
I think the reading should be noisy but on averaging over a decent time duration we should get the result that the reading of Jar A and B is same.
You are talking about molecules - then you probably need to take into affect the air molecules friction on the jar and the resultant energy loss through heat because of it. Any energy loss by this process will result in a slightly less 'weight' on that side. Tough to measure though
Bonus question1: How will the reading of the weighing scale change if the fly accelerates upwards? (Lids of the jars are still closed)
Well, I think I agree with Brian Charlesworth; there must be some assumption on the acceleration of the fly. I agree that the mass does not change, but the question asks whether the reading (i.e., the force measured by the scale) would change. I answered the question correctly (the reading will not change), but because I thought: well, the problem does not say whether the jar has air or not. If it had air, then why cannot I assume the air is moving (just as the fly would?). If can assume the air is moving and not changing the reading, why would the fly?
An everyday analogy of this problem is an elevator/lift. I can imagine myself in a lift that is stopped, I jump, and, although we are in a 'jar', by jumping we momentarily exert some force that will change the position of the lift, and thus the reading.
If the fly is flying in circles at a constant speed (thus still needing an accelaration), why wouldn't the reading change? Well, if the circles are orthogonal to the direction of gravity, those forces would not affect the scale, but if the circles where on a different plane, then I think it would., however, the forces when flying orthogonal to gravity will affect the pressure at the sides of the jar, wouldn't these forces distribute and still change the reading (assuming unbounded precision).
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I think we are considering the motion of the air into account. When the fly flies in a horizontal circle then it pushes the air downwards with a force equal to its weight and then the air exerts an equal extra force on the jar. Hence, the reading of the scale remains the same.
The fly would not be able to stay airborne in a vacuum, so since it is stated that the fly is flying in circles in jar B we can assume that there is air inside it. And you are correct that when the fly goes in circles at a constant speed there is acceleration, but this acceleration is purely centripetal, and thus this acceleration does not have an effect on the air, (and hence the jar). The fly, in the process of flying in a closed jar, pushes the air in many directions but the net force on the jar is that of the fly's weight directly downward.
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I understand that to stay in vertical equilibrium, the net upward force exerted by the the air molecules on the fly must be equal to the the fly's weight, and by Newton's third law, the fly must be exerting a downward force on the air particles equal to its weight, but I'm having trouble seeing how we know that the net downward force on the container produced via air molecules colliding with the sides and base of the container must equal this force that the fly exterts on them. Could you please explain this?
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@Alan Fruge – It's a closed system, so if the air "supports" the fly with a force equal to the weight of the fly, then this force must in turn be supported by the jar, the result being that the scale reads the combined weight of the jar and the fly.
It might be easier to consider a similar experiment with a goldfish in a bowl of water. On one side the goldfish sits on the bottom, and on the other it swims slowly in circles. It seems more intuitively clear in this case that the two sides will have the same reading, but fundamentally there is no difference with the fly scenario.
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@Brian Charlesworth – Thank you so much, the goldfish analogy really helped. Due to the particulate nature of a gas, I guess it felt a bit unnatural for me to think of the air occupying the space between the fly and the bottom of the container to be like a column of sorts in equilibrium from the forces on the top of the column (from the weight of the fly) and the total upward normal force acting on the base. I was initially trying to visualize the problem in terms of momentum changes through collisions and kinda confused myself lol. I also feel like it was more natural for me to do this with a fluid like water, because in a liquid, the molecules are closer together and it's easier to see it as "layers" of planes of water stacked up on top of each other, kind of when caluculating the total pressure acting one side of a container (calc 2 lol).
@Alan Fruge – We can approach the question in another way. The center of mass of the jar plus enclosed air plus the fly is not moving even when the fly is flying in the horizontal circles. Hence, the net force on this system must be zero. The upward force exerted by the scale must balance the weight of the jar. Therefore, the reading won't change.
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@Rohit Gupta – Thank you, this also makes sense especially when recalling that gas is a fluid too XD
@Rohit Gupta , @Brian Charlesworth ; right, thanks to both, I now see that in the case the fly is flying in circles the net force of pushing the air is equivalent to that of the fly's weight downwards.
I think that the assumption that the fly pushes the air to stay aloft is inaccurate. Some of the lift comes from the flow of air over the wings and the air pressure difference above and below. This creates a local circulation which I don't think is communicated to the scale. An large scale example of this is a plane, which takes off when it reaches a certain forward velocity, and stays aloft by supplying only enough energy to overcome friction. The thrust generated by the engine is perpendicular to gravity, and unlike a rocket motor, contributes nothing to lift.
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Interesting. I'm not sure if a plane is a good comparison since the flight dynamics are quite different and the system isn't closed. Birds would make for a better example, and I remember MythBusters did a similar kind of experiment with birds inside a closed trailer, (resting on the floor compared to flying around). They found that there was no difference in the weights, giving empirical evidence for the present answer. While there may be a "local circulation" initially, once the closed jar B system reaches equilibrium the downward force on the jar must match the force keeping the fly aloft, (Newton's Third Law), which must in turn match the weight of the fly.
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Actually, the local circulation I mentioned was from the underside of the wing to the topside. In any case, my point was merely that if any of the lift on the fly results from this small pressure differential, it subtracts from the action reaction lift that registers on the scale. I did not see the MythBusters you refer to, but average size birds weigh a few ounces and average size trailers weigh 1000s of pounds. That must have been a very fancy scale! In any case, some birds can glide for extended intervals without flapping their wings (unlike flies) and none of their weight is transmitted to the floor then.
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@Tom Capizzi – Here is the MythBusters video. I felt sorry for the birds. While the in-flight data was noisy the average weight reading was the same as when the birds were sitting. The helicopter data was even more convincing. I like one of the last comments from the guys: "There's no free lunch". :)
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@Brian Charlesworth – I watched the video. The experiment seemed more theatric than scientific. The birds spent a lot of time hovering, which does require action/reaction lift. But the precision of the scale was not clear, and there was no baseline to actually compare to. We needed to see the reading when the truck was empty. And the motion of the birds was not in a horizontal circle at constant speed, like the fly. Same objection to the helicopter test.
@Tom Capizzi – Even if we consider the pressure difference below and above the fly's wing, still its weight must be transferred to the floor. Imagine the fly is gliding and has its wings stretched and the pressure below the wing is greater than the above. The air will apply a force on the wings in the upward direction due to this pressure difference. This force will equal to the weight of the fly. An equal force the wings will exert on the air. Thus, the air will receive a force in the downward direction equal to the weight of the fly.
Even, the airplanes exert a force on the air equal to their weight, in a level flight.
The lift in the airplane is generated by the push of the air. Unlike birds/flies the airplanes do not flutter their wings although due to the aerodynamic design of their aerofoils, they eventually push the air down and generates a lift.
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Actually, the lift on a wing is caused by the shape of the cross-section. The air travels farther over the top of the wing than over the bottom, and the higher velocity results in a decreased pressure. It is this difference in pressure times the area of the wing which creates lift. It's the Bernoulli effect.
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@Tom Capizzi – I am afraid this is also a myth. Here is an article.
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@Rohit Gupta – Thanx. That article was informative. Guess I learned it wrong.
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@Tom Capizzi – You didn't learn it wrong. The shape of the wing does indeed generate lift, but not enough to keep the plane in the air.
Shouldnt there be a note showing the jar has air in it To avoid the concept of vaccum
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The fly would not be able to fly in a vacuum, so the fact that it is flying makes it implicit that there is air in the container.
This is not correct. The jar A should be weightier. Flying or not flying the entire content of jar B is the same, but because the fly is flying it looses energy, the air in the jar gets warmer, then the jar itself gets warmer and eventually the heat is being conducted away from the jar B, and the jar gets lighter.
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Wow...thank you!
It should be noted--and correct me if I'm wrong here, as I was not a physics major--isn't this an issue of differential rates of heat loss, rather than one losing heat and the other not? In other words, the fly at rest also is losing mass, just at a far lower conversion of an easily transmittable form (i.e. into heat energy)?
Think about this for sometime:
We know that the speed of an object is directly proportional to its mass from experimentation and the famous formula of E=mc^2. This change in mass happens at all times irrespective of the speed of the object. We say that the mass only starts increasing when the speed is near 3*10^5 m/s but that is the time when the change starts becoming noticeable. So if one fly is at rest in a jar and the other one is continuously moving at a constant speed, then the weight of both the flies should not be the same. The one that is flying should have greater eight than the one who is sitting.
P.S. The change in mass may not be noticeable in the weighing scales as their least count is very less. If a weighing scale with a higher least count is taken then the change in weight even though is small will be noticeable.
The force due to the movement of the fly is an internal force in the jar fly system causing no change in the weight of the system as Newton's second law reads F(external)=ma
What if the fly is accelerating upwards or downwards? Will that change the reading?
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What if we compare the closed jar and opened jar, both without the fly in it and assume the lid doesnt affect the weight? Will the closed jar be heavier than the opened jar?
E=mc^2. The total energy contained in jar B is larger, because of the kinetic energy of the fly and the air.
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It is not fair to use relativistic concepts on macroscopic objects like flies and jars.
I fully agree with you. Nobody can forget Special Relativity
The fly is converting stored energy into kinetic energy, so Jar B has greater kinetic energy, but less non-kinetic energy.
The fly is converting stored energy into kinetic energy, so Jar B has greater kinetic energy, but less non-kinetic energy.
If the lead of jar is tightly closed than how fly will breath and move! Its wring question, if jar will open & fly will move then weight will not be differ.
Wouldn't Jar B be loosing energy in the form of heat?
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Why do you think so and how will that affect the answer? Shouldn't we be thinking about the forces instead of energy and heat?
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Given the assumptions of equivalent jars and initially equivalent fly masses, if Jar B is loosing energy (in the form of heat) faster than Jar A, then Fly B must be loosing mass (in the form of heat) faster than Fly A. Fly B would eventually weigh less than Fly A, and the reading on the scales (if they are sensitive enough) should show that Jar A weighs more
(At a faster rate than Jar A)
Charles Lindbergh asked this question in "The Spirit of Saint Louis," but the fly flew out the window before he could figure it out.
I think that initially, the spring in the balance will have to balance the weight of the jar + weight of the fly (quite clear) and in the second case, the spring in the device has to balance only the weight of the jar (as the fly is flying and not exerting any force on the bottom of the jar and ultimately the surface of the weighing machine). So, the reading should be higher initially. If we assume the mass of the fly to be negligible as compared to that of the jar, then option seems to be correct. Otherwise, option A seems correct to me. Please give it a thought and let me know where I am wrong.
What if the fly is circling around at 0.1 times the speed of light? The mass of the fly will be higher than of the static one. Will the weight of the jar be then felt as larger too, by the scale?
The fly would be immediately vaporised at such a speed in air...
That would be interesting video.
Delete his tidallythis is the correct solution .
E=mc^2 so the kinetic enegery of the fly will give the jar more mass.
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It is gaining the kinetic energy but it is losing the muscular energy.
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I get that but a clock that is ticking will weigh more than a clock that isn't. Just like atoms, the mass of the individual pieces will be less then the mass of the combined pieces. Anything object moving will have a greater mass than the object being stationary, it's physics!
I personally voted for A because I thought the air would get hotter by friction. Maybe that was a little too much :/
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I was thinking that the slight agitation of the air would cause it to expand slightly causing the air to have slightly lower pressure, inducing it to 'float' in the cooler surrounding air outside the jar. Conservation of energy-- the fly exerts energy, burning up it's fuel-- the energy is going somewhere-- why not beating up a few air molecules?
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I don't see how air can expand in a sealed (tightly closed,as the problem states) container, giving the strange result to lower its pressure. What I may say is that the container also gets "colder" with time, however in an equilibrium situation the temperature inside would still be higher than case A.
Both jars are closed systems. As long as there is no vertical acceleration or deaccelerearion by the fly within the system they are equal in total mass.
What if the fly is having a vertical upwards acceleration? Which Jar will weight greater?
If the fly were traveling in a horizontal circle, wouldn't it be exerting a centripetal force perpendicular to gravity, thus offsetting the downward force of its mass, causing Jar A to read heavier than Jar B?
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As you said the centripetal force will be perpendicular to the gravity, why should it offset the downward force of gravity?
What if the jar was a cage or a closed box and the fly was a bird? imagine a boxing cage and it is covered with a big box which is being weighed. And you are climbing to the top of the cage, would the weight of the box change ? what if you are jumping from the top of the cage, would the weight of the box change now? I think it would change now!!
so the answer is certainly wrong i guess.
what if fly is exerting a force upward to lift the bottle? so i think in reality things are different!!!
you guys were dealing with mass not weight i guess
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There is a difference between a cage which is open for the air to pass and a closed box. In the case of the former, the reading of the weighing machine will change. However, in the latter case, moving in horizontal circles will not alter the reading. Although, if the boxer jumps, falls or accelerates vertically then the reading will change.
E=MC**2, the fly is expending energy which gets absorbed as heat by the air in the jar. That heat eventually leaves the jar into the universe. Thus jar B is loosing energy and is thus losing mass. Jar B should weight less. Am I being picky?
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I agree (also hotter air means less dense air, which will mean that jar slightly 'floats' more in the surrounding non-heated air than the other jar. Answer : A.
I think that initially, the spring in the balance will have to balance the weight of the jar + weight of the fly (quite clear) and in the second case, the spring in the device has to balance only the weight of the jar (as the fly is flying and not exerting any force on the bottom of the jar and ultimately the surface of the weighing machine). So, the reading should be higher initially. If we assume the mass of the fly to be negligible as compared to that of the jar, then option seems to be correct. Otherwise, option A seems correct to me. Please give it a thought and let me know where I am wrong
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No, it is not correct to say that the flying fly does not apply any force to the bottom of the jar. The fly pushes on the air to keep afloat. This force is transferred to the bottom through the air. Hence, the two jars weigh equal.
Weight is a measurement of the force exerted downward. Since they are the same mass, and the gravity is the same, neither fly weighs more.
However, if the fly was flying upwards or downwards, more or less force would be exerted downwards, and thus weight would change. A good example of this is if you have a bathroom scale. If you step onto it and stand there, it measures your standard weight. However, if you jump off of it, or place your foot and exert pressure downward, the weight displayed increases.
The flying fly is not in direct contact with the bottom surface of the container. How is the weight of the flying fly getting transmitted to the weighing pan?
Are they suggesting that we have the same weight exertion, whether flying or not flying? That the flying fly rides on a mass of air and then uses it as a chair, and still exerts downward pressure on the pan? Physically, of course the systems are equivalent, they do contain the sama mass, but I am still puzzled as to how the fly can exert that pressure on the spring while in the air. :)
when the fly is moving on the jar with constant velocity thus means its "net" acceleration is zero hemce its centre of mass is fixed therefore the body will be assumed to be in the "case A" condition so, there will be no change in the reading!! thats it!! thank you!!
I like your approach to the problem. The center of mass of the complete system does not accelerate vertically and hence the vertical forces will remain the same and so does the reading.
According to the relative theory of mass moving larger than the static mass
If the fly in jar B is hovering in place, then the net force that it's flapping wings exerts on the base of the jar via air molecules will be precisely equal to it's weight, in which case the two jars will weigh the same.
Note that If the fly is accelerating upwards or downwards then the force it exerts on the base of the jar will respectively increase or decrease, at least temporarily, so an assumption needs to made that the fly in jar B isn't doing any acrobatics during the weighing.