OT: ok the maths one was too easy, try this

[djc]

Take in one step at a time;

A drinks 1/2: B drinks 1/4 (1/2 of 1/2) so ration A:B is 2:1

repeat that sequence for ever decreasing amounts; the ratio remains the same.

[dennis]

But the question asks what happens not what can you see. I expect you are like me and can't see what happens at the start.

[Bert Coules]

My approach was valid but I made an elementary mistake. The proportions consumed aren't 1/2, 1/4, 1/8 and so on, but 1/2, 1/8, 1/16... which does indeed add up to (approximately) two-thirds.

[ARW]

What about the students doing Media Studies?

[Tim Streater]

No, my solution relies on the pseudo-grav field caused by the fact that the truck is accelerating. I've no idea whether the pressure diff that should exist between front and back of the truck is significant or not, as I said in my post.

In fact I in any case doubt that, as a balloon released in the atmos moves upward immediately, and the pressure diff it would notice moving its first inch upwards is negligible.

[dennis]

So you now claim to have gravity moving the air along with the truck as it accelerates? I think its the pressure difference caused by the front and back walls myself assuming the truck isn't Earth like in mass.

Suppose its a very long truck with smooth surfaces (no air friction). Now it accelerates away. Why would the air inside move at all? So the forces on the balloon would be the tension in the string, drag in the stationary air and its buoyancy. Which way do you suppose it would go relative to the truck?

Like I said before initially the air doesn't move and the only force is going to move the balloon backwards. Only when the air starts to move is the balloon going to go forwards.

There are no correct answers in the quiz. Its an interview question to see how you think, or don't in some cases apparently.

[Tim Streater]

Don't be a dope, dennis. You claim to have a physics degree, how about applying that knowledge? The truck is accelerating. That makes the experience of anything inside the truck just the same as if it were in a gravitational field. That's basic relativity, Einstein.

A balloon in the earth's atmos will want to float upwards, simply because the density of the balloon and its contents is less than that of the air it displaces. If you don't believe that, try taking a balloon - any balloon, helium or not - and submerging it next time you have a bath.

The situation of the balloon in the truck is entirely *equivalent* to that of the balloon in the atmosphere. Ergo the effect on the balloon will be immediate once the truck starts to accelerate.

[dennis]

read the question and answer what is asked, dope!

It says what happens *when* it accelerates, not what happens *during* acceleration.

It doesn't take a degree its O level stuff.

You failed because you don't understand the difference between gravitational fields that directly act upon everything including the

*gas* and an engine which only directly acts upon the truck. You don't even appear to understand the hint I gave about it being a very long truck which should have made it obvious.

[Robin]

I'll stick my head above the parapet to agree (in part) with Dennis.

I agree with most of what you (Tim) and others say as regards the system in a steady state. But I'll own up that I thought there would be an initial period when the system was not in equilibrium. This was because I thought the air in the truck could not *instantaneously* reach its new equilibirum with the density gradient. I'm buggered if I know how to go about calculating how long it takes to achieve equilbrium 'cos I never did fluid dynamics but I'd guessed it must be of the same order of magnitude as the time it takes a pressure wave to propagate through the truck from back to front - say 0.01 seconds for a typical white van accelerating off for its next parcel drop[1]? That is on the assumption that the air is accelerated by the force on it by the truck - mainly the "piston" effect of the back of the truck[2]. Assuming acceleration of 3g and a string 1m long that'd suggest a balloon in the middle might move back perhaps 0.75mm.

I've covered the carpet ready for said head to be shot off :)

[1] well a 3m truck at 3g with speed of sound 343m/s [2] I wonder if the interviewee might gain extra points by discussing the difference between a conventional 21c truck driven through its wheels and a future truck powered by a local articial gravity field acting on truck and contents

[Martin Brown]

In the steady state yes. We are all agreed on that. However, the sudden transition from stationary to accelerating is a transient dynamic situation and the balloon cannot know it is in an accelerating frame until the forces caused by its new environment have time to reach it.

Once the van has reached its new equilibrium then yes the net bouyancy force now acts in the direction against the vector sum of gravity and the accelerating frame of reference.

But the balloon can only know that the truck is moving when either the string length/speed of sound in the string or the distance to front or rear wall/speed of sound in the air has been exceeded.

Up to that point only the anchor point is accelerating forwards and because of air friction (drag) the balloon will initially lag behind the position of the anchor point even though its final equilibrium position will be entirely different. There is a minor point that a truck cannot sustain that constant acceleration for very long.

I am inclined on this occasion and very unusually to agree with Dennis.

[John Rumm]

The main point of contention here seems to be coming about as a result of a bit of classic dennis wiggling. He is choosing to interpret "when the vehicle accelerates" and being a far more narrow and close definition than the general tone of the question lends credence. i.e. by focussing only on the instant in time that acceleration begins, rather than the big picture of what happens during the the full period of acceleration - which was clearly the intention of the question.

This is true...

Indeed, as others have pointed out the speed of sound for the fluid in question is relevant - when you push one end of anything, the far end can't begin moving any quicker than that allowed by the speed of sound in that material.

However as your own sums demonstrate (even with the rather optimistic

3g, which seems rather too quick even for a powerful truck) the effect is negligible. You are also assuming that the 3g acceleration is applied "instantly" whereas in reality, the acceleration will ramp up from rest to the "final" figure over a short period of time as the clutch engages

- making any effect even smaller.

A very long narrow truck (i.e. a pipe) with a balloon filling most of its diameter, and very high acceleration, might be your best chance of observing any inertial effect - although this would still be indirectly due to air drag on the balloon rather than its own inertia (since the air displaced around it still has more mass than the balloon and its content).

Put your trunks on, I only have a water pistol ;-)

[John Stumbles]

I also started

You don't have to sum the series: each time round the first person gets twice what the second gets so ends up with 2/3 the whole

[Tim Streater]

No, the 3g can be applied immediately. Real life is not like the cartoon character who rushes off a cliff and then hangs there in space until he notices that he is now unsupported. He is subject to 1g the instant he is no longer supported. His acceleration doesn't "ramp up" to 1g, starting from 0g. His descent speed, by contrast, *does* ramp up.

[Scion]

John Stumbles put finger to keyboard:

Reminds me of the old joke:

An infinite number of mathematicians go into a bar.

"Pint of beer, please", says the first. "Half a pint, please", says the second. "Quarter of a pint please", says the third. "One eighth of a pint, please", says the fourth...

"You're all idiots", says the barman, pouring two pints.

[John Rumm]

If the truck were driven into by another, perhaps. A but a motor engaged with a clutch, will feather the power in over a short period of time.

[The Natural Philosopher]

the speed of sound is how fast the pressure wave from the back of the truck will transfer momentum to and accelerate all the air IN the truck.

[The Natural Philosopher]

That works until they set the question on the moon.

[The Natural Philosopher]

The length of time it does the other thing will be in the case of a truck only a millisecond or so.

And relevant only insofar as the third differential of distance with time is operational. I.e its not the acceleration that causes it to sway backwards for a millisecond, its the rate of change of acceleration.

IN a constantly accelerating frame, that reaction has completed.

[The Natural Philosopher]

The discrepancy is on account of dennis being a little bit right in that a change of acceleration is NOT the same as a constant acceleration.

Under constant acceleration, you are right, under changing acceleration, the inertial frame takes a few milliseconds to stabilise in its new vector. During that rime the whole truck cannot be considered as a single inertial frame.

It is not, it is slightly like a balloon in atmosphere with a bit of air turbulence.

The air in the truck will NOT immediately move at the same speed as the truck, any more than a piston coming down a tube immediately forces air out of the far end.

As I said, for perhaps a - well lets see how long a pressure wave takes to propagate - say - 6 feet, and I make it about a millisecond.

So, if we apply a step function of acceleration - equivalent to a constant force - to the truck, the balloon and air together will stay stationary for about a millisecond, before the air moves backwards displacing the balloon forwards, and a pressure differential between the air in the front and back of the truck is set up and maintained.

[Fredxxx]

Would the vessel still be called an AIRcraft?

I wonder how many planets or moons are known to have humans flying around in AIRcraft?