Enigmatic Code

Programming Enigma Puzzles

Puzzle #44: Elevator pitch

From New Scientist #3267, 1st February 2020 [link] [link]

On the way back from a party the other day, my daughter and I got into an elevator. I was holding a cup of water with an ice cube floating in it, while my daughter was admiring her helium-filled balloon as it floated above her on a slack string. Our only company in the elevator was a spider, dangling from the lift’s ceiling on a thin thread of silk. As the lift accelerated upwards, what did we see happening to the balloon, the ice cube and the spider?

[puzzle#44]

3 responses to “Puzzle #44: Elevator pitch”

1. Jim Randell 5 February 2020 at 10:41 am

More of a Physics question, but here are my thoughts:

When the lift starts accelerating upwards thing are generally going to want to stay where they are, so you would expect most things that have some freedom of movement to be observed to dip down initially (to an observer inside the lift), but there will be various other forces acting on them too.

The spider is tethered to the top of the lift, so will be pulled upwards by the thread. But as the lift starts to move the thread will elongate slightly, so initially the spider will appear to dip down slightly to the occupants of the lift.

If the cup is held steady (or placed on a shelf) the water in it will be pushed upwards, and the ice cube will be observed to sink slightly.

As for the balloon, I think the air in the lift will tend to stay where it is, but it can’t escape, so it will become denser at the bottom of the lift and less dense at the top of the lift. So the balloon will be observed to rise slightly towards the less dense air.

I think it would be difficult to do a practical experiment, as I don’t think most lifts accelerate for very long. Maybe a fast lift in a very tall building would be required.

• Jim Randell 6 February 2020 at 9:08 am

Having read up about lifts it seems that lifts accelerate at about 1m/s² and the fastest lifts get to about 20m/s, so there is potential for a considerable period of constant acceleration.

If the lift is undergoing constant acceleration, Einstein tells us this is the same as gravity being increased. Which means that the spider’s thread would be elongated slightly. There would be no effect on the floating ice cube, and probably no effect on the floating balloon. (The depth that floating objects sink to is independent of gravity).

• Jim Randell 9 February 2020 at 9:44 am

The official solution is the same as this one, that during a period of constant acceleration the spider’s thread elongates slightly, and the floating objects are unaffected. Disappointingly it doesn’t include a link to a slow motion video taken in a lift to show the actual observed behaviour. (I always like constructive solutions).

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