Ok, I’ve heard this riddle before but have never heard the actual answer…
An airborne airplane has a housefly standing on the seat. This will, of course, increase the gross weight of the airplane, but if the fly were flying, would the gross weight of the airplane be the same? My guess would be * no * , as I imagine myself on a bathroom scale holding a bowling ball, then tossing it up in the air. I guess that’s pretty mush the same principle. So, is the right answer…the weight of the airplane only increases when the fly lands? Yes?
Put your plane on the bathroom scale. Your bowling ball doesn’t have wings, displacing the air with downward force in a mostly-closed system of an airplane cabin.
I heard this one as:
A chicken farmer always stops his panel truck before the rickety bridge, gets out, and pounds on the side of the truck to agitate the chickens into fluttering around, so their weight won’t add to that of the truck as it traverses the bridge.
IANA physicist, but it would seem that in order for the housefly to fly, he must use his wings to thrust himself up, which would push the air in the plane down, which would increase the weight of the plane an amount equal to the weight of the fly. So my amateur answer is no.
Yes the weight of the plane would increase. And as far as the bowling ball and you on a bathroom scale, you weight not increase while the ball is in the air, but it would increase when you threw the ball up and when you caught it by more than the weight of the ball. On average the sale would show your weight plus the weight of the ball.
The chickens and flies are light. Imagine a scale place under the blades of a helicopter. It would show an increase when the helicopter takes off.
the bowling ball example is a good one; forget the effects of air for a moment.
For every action there is an equal and opposite reaction; when you stand on the scales with the bowling ball in your hands, the dial shows the weight of you plus the ball, when you start to accelerate the ball upwards, you will be exerting the same extra force downwards, so the dial on the scale will momentarily show extra ‘weight’, similarly, when you catch the ball again, you must exert upward force to stop it and your feet push down again. Very crudely, if you were to ‘average’ the dial readings over the whole exercise it would come to the same as the reading when the ball is resting in your hands.
There’s nothing magical about the fact that the fly is suspended in a fluid (air) inside a container (the plane); consider this: if it were a shrimp swimming in a sealed bottle of water - it would be absurd to suggest that the shrimp’s weight is only measurable when it touched the bottom of the container.
You weigh 80 kilos, and can juggle. You have three 1-kilo balls. Step on the scale, and begin juggling. Assuming the scale displays your continuously-sampled weight, what is the average weight it will display for you while you’re juggling the balls?
I posit this average will be near enough to 83 kilos as makes no difference.
Or to put it yet another way, the plane is a closed system; when the fly is at rest you would be weighing ([the plane plus a fly] and [some air]), when the fly is airborne within the sealed plane you are weighing ([the plane] plus [a fly and some air]).
Exactly. The easiest way to visualize it is that weight ALWAYS=mass X gravity. This is the definition of weight. This is the only definition of weight. If you have the same objects in two different situations, you have the same objects (duh). If you have the same objects, the total mass is the same. Weight ALWAYS equals mass X gravity. Therefore, the weight does not change. This always applies (to a closed system, like Mangetout sez).
Whoah, wait up a second, I just thought of a complicating factor; the mass of the closed system may remain constant in total, but if the fly moves from the floor of the plane up to the ceiling, the centre of mass of the system will be altered (moved up slightly) and will be subject to just a little less* gravity (because it will be further away from the Earth.
I sincerely doubt the effect would be anywhere near measurable though.
Gaaaah! There’s no reasoning with some people, I suppose.
To follow that weird logic toward conclusion, we should find that a bottle filled with water and a similar bottle with just a thin film of water in the bottom would weigh the same - after all, only the bottom layer of water molecules are in contact with the glass, so why should the others affect it at all? Hell, why should the scales register the weight of anything other than those few molecules of glass that are in contact with the load plate, no why should the load cell register the weight of anything other than the very bottom part of the load plate support… and so on; it is a journey into madness.
You get on board with a big balloon and a tank of helium, just enough to fill up the balloon. Once in flight you fill up the balloon and empty the tank. Now the helium is gone from the tank so the tank is lighter (because it was compressed and therefore heavier than air). The balloon is now buoyant (not flapping wings) and exerts upward force at the ceiling of the cabin.
Is the airplane lighter once I blow up my balloon?
No, the airplane isn’t lighter. The concept is very simple to repeat : In a closed system, mass[sup]*[/sup] (and therefore weight ) is conserved. If nothing leaves or enters the plane, the weight cannot change.
In your case, the weight of the helium when it was in the tank is exactly the same as the weight of it in the balloon; the tank is lighter but that weight is now in the balloon. The balloon is pushed up against the cabin, but it’s also pushing on the air around it. Considering Mangetout’s sealed bottle of water, it’s as if you had a sealed packet (or tank) of oil sitting at the bottom. If the oil leaks out, it (the oil) rises to the top of the bottle, but certainly won’t change the weight of the bottle system.
What does come into play here is pressure. Once the balloon is inflated, it displaces some of the air in the cabin. Since the air doesn’t leave the plane there is less volume for the same amount of air, thus the air pressure will increase.
The system you describe (inflating balloons) is used to raise sunken vessels in water. In that case, however, the fluid that gets displaced (water) can leave the boat system so the weight of the ‘boat’ can change.
One minor note : It’s theoretically possible in the chicken-bridge example for a chicken to take off before the truck is on the bridge and remain in flight during the crossing, thus lightening the load. This assumes that the truck, like every vehicle carrying live chickens I’ve seen, does not have an airtight chicken compartment.
[sup]*[/sup] Technically ‘mass’ includes energy as well. See Cecil’s column linked above discussing heat loss after eating (note that in that case it is not a closed system.)