Measuring tube velocity with air bubble?

[furtivefelon]

Here is a question i can't figure out, it's a challange question we suppose to research..

Question: to measure acceleration, a bent arc-shaped sealed glass tube filled wtih water is used. there is a little air bubble inside. Explain the method of measurement in detail, and find the relationship between position of the bubble and acceleration of the tube.

i'm not expecting anyone to give me complete answer, but if anyone could point me to the right material (a name of a specific topic/law would be suffice) i would be forever grateful :D

I think it should be under hydromechanic.. though not sure what exactly i should be looking at..

thanks alot!

 

[Astronuc]

Have you ever used a carpenter's level?

Hints:

Think of bouyancy and gravity, and force and acceleration?

 

[lightgrav]

most people call those a "level" because the bubble is at the top of the arc, in the middle of the tube length, if it just resting on a level surface.
Why do you think the bubble is on top?
What will happen to the water if the glass tube is accelerating leftward?

 

[furtivefelon]

i had used carpenter's level a long time ago, i know that the bubble is on top of the level because the density of air is way less than the density of water, therefore, less dense substance floats on top of the more dense ones because of the pressure under the water is also larger than the top..

I would imagine when the arc is in motion, bubble would go backwards for a bit and become still again.. I can't imagine how that would measure the velocity of the tube though.. the only way i can think of that would make the bubble continuously move would be turning the arc continously, so that the bubble would rise to the top constantly, and therefore that constant motion would be a measurement in velocity (though it would seem to be way too complex and out of the context here.. )

i'm also reading up on Archimedes' principle (a search for bouyancy and gravity revels that), i don't see the relation between archimedes' principle with the task of measuring the air bubble containing vessle and the measurement of it's velocity..

May i get another hint or so? Since I'm pretty much stuck at this point in time..

 

[lightgrav]

you don't want to measure velocity, you want to measure acceleration!

When you start out in a car, accelerating forward after a red light,
does the air in the car shift closer toward the back window,
or does your head shift closer to the back window?

Does this depend on how hard the driver steps on the gas?

Have you added Force vectors in 2-d yet? there's a big difference between external contact Forces and the gravity Force.

 

[furtivefelon]

everything is beginning to make sense now... can't believe i was that stupid as to misread acceleration as velocity..

So if the tube moves forward while the bubble is stlil in a inertia state, we can then carefully reach desired acceleration, and record the max displacement of the bubble in the tube (though it would seem pretty inaccurate to me), then if we want to measure the acceleration, we can then read off the scale..

Though does the curvature of the tube matter? since on the question it said it's an arc...

 

[lightgrav]

the bubble will point in the direction of the sum of contact forces.
If it accelerates to the right at "¼g" = 2.45 m/s/s , the bubble will
be on the right-hand side, where the arc slope 14 deg. from horizontal.

a level is maybe better than a weight-on-string to measure angles;
since the weight-on-string isn't damped, it will oscillate easily.

 

[furtivefelon]

mmm.. i thought when arc accelerates to right at some acceleration, the bubble will point to the left? How is it that bubble will point to the right?

and what is a weight on string? is it some kind of pendulum?

 

[furtivefelon]

I still don't quite understand how to calibrate the scale to measure the acceleration.. I do imagine however that the bubble will move backwards as the tube accelerate forward (however, according to lightgrav, it will accelerate forward??).. Though, is there a reliable way of calibrate the scale so to measure at least approxmately the acceleration? Can someone please help me, thanks alot!