# B A fly in an elevator

1. Jun 20, 2017

### lavoisier

Suppose that a fly flies into an elevator and hovers in mid-air. The doors close and the elevator goes up.
In analogy with a similar example (link), I imagine that the fly will travel up, it won't fall to the elevator floor.
And I guess this is because the 'air' in the elevator, which is what the fly pushes down with its wings to create an upward force counteracting its weight, is carried up as well.
However, if I stand in the elevator, the force that is counteracting my weight is the reaction of the elevator floor, which is equal to my weight at the beginning, and temporarily increases as the elevator accelerates.
This is felt as some additional pressure under my feet. If I am carrying a heavy sack of potatoes, for a moment it will 'feel' heavier.
Is this correct so far?
Now, if this is true, doesn't it imply that the air in the elevator will undergo some compression, i.e. for a brief moment there will be 'less' air near the roof of the elevator than near the floor?
And if so, doesn't that affect the fly's ability to hover at a certain level, i.e. won't we see it go down for a brief moment as the elevator accelerates?

2. Jun 20, 2017

### sophiecentaur

The air is being pushed up the same as your feet. The effect of the rising floor would be like an enormous loudspeaker, with a very low frequency pulse on it. The speed of sound in the air would be so high compared with the elevator speed that the displacement could be considered to be the same throughout the lift (a tiny fraction of the wavelength of the 'pulse).

3. Jun 20, 2017

### Staff: Mentor

The fly isnt floating, it is flying. It flaps its wings to counteract its weight. What just happened to its weight?
Yes, but this is negligible for the acceleration of an elevator.

4. Jun 20, 2017

### rcgldr

Treating the elevator as a sealed container, this already happens when the elevator is not accelerating, due to the force from gravity. The pressure of the air at the top of the elevator will be less than the pressure at the bottom of the elevator, and this pressure gradient results in a net downforce exerted by the air onto the elevator equal to the weight of the air in the elevator.

As posted by russ_waters, what happens to the fly's weight if it accelerates upwards to match the upwards acceleration of the elevator?

5. Jun 25, 2017

### lavoisier

Unfortunately I did not manage to convince any fly to travel with me in the elevator, so this still remains a theoretical question for me.
I think the point about the weight is clear: the fly flaps its wings, i.e. it pushes some air down, to create a corresponding force pointing up that serves to counteract its own weight. That allows it not to fall down but instead hover in mid-air. A bit like a helicopter would do.
What is not clear to me is whether there is a difference between me and the fly when the elevator starts going up.
Surely an upward force is applied to the elevator, to cause it to go up in the gravitational field and to go from rest to a constant speed. Some work must be done for the potential and kinetic energy of the whole thing to increase, right?
I may be considered part of the elevator when I'm standing in it, so the upward force is applied to me as well.
The fly, on the other hand, is not 'touching' any part of the elevator: it is only touching the air in the elevator. Is the air going to apply a force on the fly in the same way as the elevator floor applies a force to my feet?
I know this is pretty basic stuff - it's obvious that my physics is extremely rusty, and some concepts were never clear to me in the first place

6. Jun 25, 2017

### SlowThinker

Let's imagine a drone. The air flows through the rotors quite quickly, certainly much faster than an elevator. I believe the same applies to a fly.
Thus the speed of air has little effect on the lift generated.
Even if the elevator moved very fast, the drone needs to generate power to increase its altitude and thus potential energy in the Earth's gravity field. It needs to work harder in a rising elevator than in a stationary one. The exact amount depends on its actual size, rotor speed etc.

7. Jun 25, 2017

### Drakkith

Staff Emeritus
Yes it is. The same way that your torso isn't touching the elevator, but the force is transferred up through your feet and legs.

8. Jun 25, 2017

### Staff: Mentor

Not on its own, no - it's just air. The wings have to apply the force to the air, needed to keep the fly hovering.

9. Jun 25, 2017

### Staff: Mentor

I think that sounds more like the situation where you have a floating balloon instead of a flying fly...

10. Jun 25, 2017

### Drakkith

Staff Emeritus
How so?

11. Jun 25, 2017

### SlowThinker

If the fly was massless, and it was pulling a massless string attached to the floor at a force equivalent to a fly's weight, then yes, in an elevator moving up, the massless fly would need to work just as hard as in a stationary elevator to maintain the pull.
But in the real scenario, the fly needs to pump some energy into its potential energy, so it must work harder.
A baloon is more similar to the massless scenario.

12. Jun 25, 2017

### Drakkith

Staff Emeritus
The fly (and everything else in the elevator, including the air) is now moving upwards at a steady velocity. That means that the force exerted by the fly on the air is identical to the force exerted prior to the elevator accelerating up to speed. If the force exerted by the fly is identical to when the elevator was stationary, then no extra energy is being expended by the fly. The energy to move the elevator and all of its occupants upward against gravity is provided by the elevator's motor.

13. Jun 25, 2017

### SlowThinker

I'm afraid you're wrong. A helicopter that is rising at a steady pace generates as much force as a hovering helicopter (it is not accelerating upwards, only rising), but needs more power.
The fly in an elevator is a fairly tricky scenario and I guess it will remain unsolved until someone tries it with a drone, but I believe that my arguments are valid.

14. Jun 25, 2017

### rcgldr

The original question asks what happens after the doors close and the elevator goes up. This would include an initial upwards acceleration of the elevator.

15. Jun 25, 2017

### Drakkith

Staff Emeritus
Yes I know. I was replying to SlowThinker's post, which I thought was about the non-accelerating portion of an elevator's ascent.

Of course. Just like the elevator motor needs to use power to perform work and raise the elevator and its occupants against gravity. Are you suggesting that the pilot of a helicopter, who is just sitting in a chair, is somehow performing work to raise himself against gravity?

I don't agree. I've ridden an elevator many times in my life. Once the initial acceleration is over, I've never had to exert more of an effort to remain standing than I had to when stationary. I just did an experiment in which I rode the elevator in the building I'm currently in from the ground floor to the top floor, a height of about 50 ft, in 12.8 seconds. That's roughly 9500 Joules spent over 12.8 seconds to get to the top floor, for a power of 742 Watts. 9.5 kJ is about 2.26 kCals, or 2.26 "food" calories. That's about the same energy required to run 120 feet.

I did not just run nearly half a football field worth of distance in 12.8 seconds. I didn't even break a sweat while standing in the elevator.

If you're thinking that the situation is different because the fly has to perform work on the air, then just think about the situations prior to and after the acceleration upwards. Both situations involve the fly hovering in air that is stationary with respect to the elevator. There is no acceleration of the general mass of air in either case. The forces exerted by the fly on the air are identical in both situations. If all of these things are the same, how could the fly be expending more energy in one situation than the other?

16. Jun 25, 2017

### SlowThinker

No but he's not flapping his wings inside the helicopter either.
A fly sitting on the floor of the elevator does not perform any work, a flying one does.

I admit I'm starting to have doubts. Your arguments seem valid but I can't see a flaw in mine either.
I would be glad if someone could present sound reasoning either way.

17. Jun 25, 2017

### Staff: Mentor

When you say: "The same way that your torso isn't touching the elevator, but the force is transferred up through your feet and legs." it implies to me that the force the air provides to the fly changes on its own as the air accelerates with the elevator. Technically it does, but the amount is so small it only shows up as buoyancy, which can't keep a fly aloft. If the fly makes no adjustment, it accelerates toward the floor (in the elevator's reference frame).

Last edited: Jun 25, 2017
18. Jun 25, 2017

### Staff: Mentor

This doesn't make a lot of sense to me. String or not, the only scenario where the object doesn't change its elevation more than via a minor amount of pressure gradient in the air is if the weight equals the buoyancy: the balloon scenario.
That is because it is moving through the air as opposed to moving with the air.
It isn't a tricky scenario (and is a common and well documented question), but sure it would be fun if someone took video of a drone in an elevator. You can also try hovering a drone in a moving car . Balloons don't work as well, but if you have helium balloons they will move opposite the gravitational vector in the car (meaning of you turn right you will feel yourself pulled left, but the balloon will move right).

19. Jun 25, 2017