Fruit flies in a bell jar

Question

You place a bell jar on a scale and the scale registers x grams. You then trap y grams of flying, non-landing fruit-flies in the bell jar. What does the scale register? x grams? x+y grams? Something in between? Assume that the weight of the fruit flies is significant enough that it wouldn't be lost in the error of the scale's output.

My intuition is that it registers something in between. Clearly the fruit flies are exerting downward force on the air around them and that force is at least in part being transmitted down to the floor of the bell jar and thus to the scale. However I feel like some of those air molecules will lose this coherent downward movement on their way down and energy will be lost to heat.

edit: Although this looks like homework, it isn't. I just tried to state it in a clear way. I was asked this by someone and found that I couldn't answer with confidence.

What happens to the momentum of the air molecules that are lost as heat? — BowlOfRed, Oct 22 '14 at 23:27
@BowlOfRed A good question. Would you then say that the answer is x+y grams because of conversation of linear (downward in this case) momentum? — Zaius, Oct 22 '14 at 23:40
possible duplicate of A flying fly inside a sealed box on a scale — Brandon Enright, Oct 23 '14 at 00:35

t.c · Accepted Answer · 2014-10-22T23:50:29.130

1

$W = x + y$ if the fly is hovering, $W>(x+y)$ when the fly is flying upwards (i.e. accelerating up), $W<(x+y)$ when the fly is accelerating down, and $W = x$ if the fly is free falling (accelerating at g) (assuming there is no air resistance).

Air is a fluid. If you replace air with honey and flies with fishes that prefer to swim in honey than water, you can clearly see that when the fish pushes the honey beneath it in order to swim (accelerate) upwards, the reaction force would be downwards, so the scale registers a higher reading than x+y. Another way to look at it is that since momentum is always conserved, by swimming upwards, it gains momentum in the upwards direction, so something has to gain momentum in the downwards direction - which is honey in this case.

edited Oct 22 '14 at 23:50

answered Oct 22 '14 at 23:43

t.c

1,542

So assuming that there are enough flies to statistically average the up and down flapping motions to an "overall hover", the answer would be a roughly constant x+y grams? – Zaius Oct 22 '14 at 23:47
@Zaius Yes, in that case the air is supporting the flies, and the jar is supporting the air. – rob Oct 22 '14 at 23:48
@Zaius Yes - or if the fish dies and got stuck in honey its weight would simply be x+y – t.c Oct 22 '14 at 23:52

Fruit flies in a bell jar

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