It is obvious, the answer given is wrong for the starting condition and correct for steady state acceleration. The balloon will first swing back relative to the truck before settling to a lean forwards. It will bob about between the two states for a bit.
Another way to look at it is a that 'balloon in air' responds negatively to gravity' And that includes pseudo gravity due to acceleration, from which it is indistinguishable. I.e. the force of aceleration 'feels like' tilting the car upwards at the front, heavy stuff slides to the back, the balloon however point upwards along the line of gravity+acceleration vector.
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not so. speed of propagation is speed of sound. The balloon will seek the locally nearest thing to 'lowest density' it can find.
So its finite then and what I said is true.
then you may have noticed wrong. The video doesnt begin with him starting the car.
Your intuition would be correct for a weight hanging from a string, however in this case, the "weight" is actually the air displaced by the balloon rather than the balloon itself. So the acceleration will be felt by both balloon and surrounding air, but the air will move back with more force (F = ma) than they balloon due to its greater mass.
Thanks for that: fascinating. I'm obviously missing something fundamental in the milk-drinking question: at first glance the amounts drunk would seem to be 1/2 + 1/4 + 1/8 + 1/16 and so on, but unless my maths is even worse than I think (which is entirely possible) I can't make that add up to 2/3.
Can someone explain in numbers of one syllable please?
Bert Coules put finger to keyboard:
I thought of it this way:
Each "round" is Person A drinking, then Person B drinking. Person B always drinks half of what Person A drank. Therefore if Person B has drunk one unit, Person A has drunk two units. Out of 3 units, Person A has drunk 2.
I drink twice what you drink. So the ratio is 2 to 1. That's true each time - all the way to the end*. So I get 2/3.
It's not a question of there being "heavier" or "lighter" bits of air. A helium balloon, when released, doesn't just float, it floats
*upwards* because the earth's gravitational field pulls on the air, which can come down *under* the ballon, forcing it up as it does so. This has nothing to do with that air being heavier than other air, but the fact that the air is heavier than the *helium*.The *instant* the truck starts to accelerate, the same conditions apply now in a horizontal direction and so the balloon will *immediately* start to move to the front.
In principle there should also be a pressure differential in the air (higher pressure at the back of the truck), just as there is in the atmosphere, but whether that is significant for an ordinary truck accelerating as only an ordinary truck can, I don't know.
Nothing to do with the speed of sound, either.
What is a "two-draw filing cabinet" ???
That series should add up to 1.
If you think of it as a two player game.
Whatever A drinks then B drinks half as much on his turn.
A drinks 1/2 + 1/8 + 1/32 + 1/128 + ... B drinks 1/2(1/2 + 1/8 + 1/32 + 1/128 + ...
The whole is therefore divided into three & A gets 2 parts.
Variants can then include each player drinks 2/3 of the remaining liquid which is a bit harder to get right. It was beer in my day.
Thanks for all the replies. Stupid of me: I was shooting past the requirement to drink only half of what remains each time.
On 04/12/2013 08:44, dennis@home wrote: ...
Carefully worded to weed out the obsessively pedantic IMO :-)
Colin Bignell
I would probably taken more care had I actually been applying for a university place, but that approach was good enough for my purposes, as was thinking back to the last time I was in an aircraft at 38,000 feet, on a clear day and remembering how far I could see, to guestimate the horizon from the options offered.
Colin Bignell
I couldn't remember the density of air, but I could remember the atomic weights of O2 and N2; that at STP 1 mol of a gas occupies 22.4 litres; and for an ideal gas at contant pressure, volume is proportional to the absolute temperature (although a rough figure could be got without that correction) and work it out that way.
I also just knew it was in that range from previous experience.
SteveW
Isn't that RTP? 22.4l for STP?
SteveW
No it won't, there will be a compression of the air at the rear where the air is pushed by the wall. The rest of the air will still be stationary. (There is also a reduction in pressure at the front.) That compressed air will then act on the air in front until it reaches equilibrium. Prior to that the balloon sees nothing changing in the air and is pulled by the string. That would cause it to move down and towards the rear of the truck as that force will be instantaneous.
Its a powerful truck as stated in the question. No details are given as its to provoke discussion as we are doing. It may be able to do 100G for all we know.
Anyway your solution requires that its significant enough cause the balloon to float to the front so it would be measurable.
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There are plenty of other vids on youtube that demonstrate that this is not the case though.
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