BS: Free falling

Subject: BS: Free falling
From: TheBigPinkLad
Date: 08 Jul 05 - 05:20 PM

"School officials in Victoria, Australia, say it's too hard for students to calculate equations using the constant 9.8 meters/second/second [32 feet/second/second] — the acceleration of gravity at Earth's surface — so it's changing the Year 12 physics exam for the Victorian Certificate of Education to use a rounded-off figure of 10 m/s/s. Close enough? No: "The difference could cause a parachutist or bungie jumper to plummet into the ground, or the launching of a rocket to fail," say people who actually understand physics. After hearing the criticism, the Victorian Curriculum Assessment Authority announced that it would not penalize students who used the correct figure."

So if you're right you're right and if you're wrong you're right.

Subject: RE: BS: Free falling
From: Liz the Squeak
Date: 08 Jul 05 - 05:34 PM

Yet another reason to remain unbungeed and firmly buckled into my aeroplane seat!!!

LTS

Subject: RE: BS: Free falling
From: JohnInKansas
Date: 08 Jul 05 - 06:10 PM

BPL -

9.8 m/s^2 = 32.15 ft/sec^2

At grade 12 they should be able to explain when it's appropriate to use roundoff values, as you did in your conversion (0.4% error). (?).

Agreed that there's something fundamentally wrong with testing students on whether they've learned something, and then implying on the test that it's not important enough to actually learn it correctly, but that seems to be what school boards do.

John

Subject: RE: BS: Free falling
From: Sorcha
Date: 08 Jul 05 - 06:29 PM

Sounds like something Kansas might do.....

Subject: RE: BS: Free falling
From: GUEST,Jon
Date: 08 Jul 05 - 06:41 PM

Oh well... It was 9.81ms^-2 when I was in school.

Subject: RE: BS: Free falling
From: gnu
Date: 08 Jul 05 - 06:43 PM

Let's start at the start. The earth's gravitational force related to mass is 9.81 newtons per kilogram at sea level. Then, the students will easily follow the arithmetical representation of acceleration. Or, you could throw the stupid ones off the school roof.

Subject: RE: BS: Free falling
From: Bill D
Date: 08 Jul 05 - 06:50 PM

oh, RIGHT! and next pi will be set at 3!

Subject: RE: BS: Free falling
From: gnu
Date: 08 Jul 05 - 07:02 PM

Or we'll have pie at 3.

Subject: RE: BS: Free falling
From: Amos
Date: 08 Jul 05 - 07:26 PM

Pi at three will realoly do wonders for our "shock and awe" campaign. When we aim our missiles at Syria or perhaps Iran, we'll blow up Bethlehem. That'll teach 'em!! L:>D


A

Subject: RE: BS: Free falling
From: Bill D
Date: 08 Jul 05 - 07:47 PM

an interesting historical note on trying to legistate pi

Subject: RE: BS: Free falling
From: Peace
Date: 08 Jul 05 - 11:51 PM

Cake are squared, pi are round.

Subject: RE: BS: Free falling
From: JohnInKansas
Date: 09 Jul 05 - 12:38 AM

Bill D -

I was going to comment that a very bad book that keeps popping up on the sale tables at Barnes and Borders relates to the "mysteries of pi" and cites some 30 separate instances in which legislatures have proposed requiring that pi be exactly 3. So far as I recall none of the bills passed.

Surprisingly, I don't think that Kansas is included in the list, although I wouldn't be surprised if it had happened here.

Sorcha -

From recent - and historical evidence - it would seem that literacy is not a requirement for being a member of a Kansas School Board -- or of the Kansas Legislature.

John

Subject: RE: BS: Free falling
From: Bill D
Date: 09 Jul 05 - 12:45 AM

nope, John, not literacy NOR logic....

Subject: RE: BS: Free falling
From: Leadfingers
Date: 09 Jul 05 - 02:24 AM

Free Falling ?? Who would want to PAY for Falling ???

Subject: RE: BS: Free falling
From: Bunnahabhain
Date: 09 Jul 05 - 03:21 AM

There are only a few of these important irrational numbers that stupid folk, and schoolboards or state legislators run into very often.

Most of them are hidden away under plain names, such as e,i, h, and G, so Kansas will never notice how untidy they are. The speed of light, c, is fairly much immune to rounding, unless you're from a country that thinks science in imperial units is a good idea.....

Subject: RE: BS: Free falling
From: JohnInKansas
Date: 09 Jul 05 - 03:44 AM

If those writing the tests really believe that the "concepts" can be taught without the need to know accurate values for the constants, the exam should state:

"Use the value g = 9.8 m/s^2 etc,"

so that all those taking the test will be working from the same info.

Then they can penalize those who don't read the instructions, instead of just those who don't know any physics.

John

Subject: RE: BS: Free falling
From: Doug Chadwick
Date: 09 Jul 05 - 04:31 AM

The difference could cause a parachutist or bungie jumper to plummet into the ground, or the launching of a rocket to fail


The parachutist's calculations would suggest that he was going to arrive on the ground earlier than would actually be the case, in which case, he would release his parachute earlier. Using the rounded up figure builds in an additional safety margin.

The bungie jumper will only fall as far as the bungie will stretch. With the same mass but an increase in the value of "g" you get an apparent increase in weight. If the bungie is set for this heavier calculated weight, the lighter actual weight will make it stretch less and thus keep him further from the ground.

Similarly for the rocket, if the propulsion system is designed to meet the calculated values, it will more than cope with the actual.

DC

Subject: RE: BS: Free falling
From: Shanghaiceltic
Date: 09 Jul 05 - 07:20 AM

Even 9.81 m/s2 is not accurate. I use 9.8165, why because when I am doing calibrations using mass I have to and if I need more accuracy I use an even longer version of G.

To add to the complication the G figure above is standard G there is also local G. The variation of G increases as you get towards the equator, you'd weigh slightly more at the equator than you would at the poles. It also varies due to whatever is under the ground near you locally, large amounts of iron bearing rocks and underground oil have a small effect on G.

Rounding up is just not on, bet when these kids grow up they would not round up the level of their pint if it has been delivered slightly short in measure.

Now I will go away and find a clean anorack and go trainspotting.

Subject: RE: BS: Free falling
From: gnu
Date: 09 Jul 05 - 07:43 AM

Pray tell SC, what the hell are you doing that needs an accuracy of 1/981,650 of a kg? BTW, I would have rounded that to a millionth of a kg, but, I don't want to start anything.

Subject: RE: BS: Free falling
From: JohnInKansas
Date: 09 Jul 05 - 02:12 PM

A bit of browsing found that nearly all of the standards orgs that one would expect to have copies of the SI definitions want money before they'll let you see a copy. I also found quite a number of examples of college course material in which the profs made some rather vague, misleading, and sometimes outright wrong statements about the MKS (SI) system, but that's probably to be expected. Some of them appeared quite old – like me.

US NIST SI is the United States Department of Commerce, National Institute of Standards and Technology, NIST Special Publication 330 which is the "United States version of the English text of the seventh edition (1998) of the International Bureau of Weights and Measures publication Le Syste`me International d'Unite´s (SI), including Supple´ment 2000: additions et corrections a` la 7e e´dition (1998)." Free .pdf, 814 KB, 77 pages, if anyone wants a download. The next revision won't be until 2007.

I find that Shanghaiceltic is probably illegal, although that may depend on where he's doing the calculations:

3rd CGPM, 1901 (CR, 70): declaration on the unit of mass and on the definition of weight; conventional value of gn†
…
3. The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s2, value already stated in the laws of some countries.

980.665 cm/s^2 would be 9.80665 m/s^2, in a country where that legal "standard local acceleration due to gravity" is defined. 9.8165/9.80665 = 1.00100442, or a 0.1% error – very sloppy (tsk, tsk, tsk).

There is sufficient variation in local "g" to require correction in precise calculations, but for almost anything I can think of on the earth's surface 9.8 m/s^2 should be close enough (9.81 if you're fussy). It should be noted that the definition of a "standard g" has absolutely no significance within the basic SI system, and was inserted only to clarify the "kilogram weight" (or kilogram force) unit still in use in 1901. While the concept is still okay if your just buying a lump of lard, "kilogram force" is a denied, abrogated, prohibited, illegal, unlawful, disreputable, and horribly offensive notion in "scientific" work, and should never be used.

The legal definition of a local "g" has no significance if you're using a true "balance" scale, since you compare mass to mass, and variations in local g affect both masses equally. If you use the constant to calibrate a spring scale (not legal for trade in most US areas) you would "get more for your money" by buying at high altitude – but not much.

John

Subject: RE: BS: Free falling
From: gnu
Date: 09 Jul 05 - 03:08 PM

Like I said in my first post... (not just a pretty face ya know).

And, further, when you throw the stupid ones off the school roof, and measure the volume of the yelps when they hit the ground, although they will all hit the ground at the same velocity, when the data is analysed with respect to yelp volume and mass, the ones of greater mass will be found to yelp louder, within a certain statistical error. This demonstrates the relationship between gravitational force and mass in a "hands on" manner. Acceleration is then just a hop, a skip, and a jump away, so to speak.

Of course, since we are talking absolutes, or, rather, pure numbers, forget the statistics and let's just say, the bigger they are, the harder they fetch up (Not "the harder they fall". This is clearly wrong, as proven centuries ago, by Galilei, 1564-1642... of course, he was imprisoned in 1633 for throwing stupid pupils of off the leaning tower of Pizza in order to measure acceleration. Much higher than a school.)

Now, if... excuse me... there's a sale on beer this weekend and I am conducting another experiment... I'll be back, within an error margin of...

Subject: RE: BS: Free falling
From: JohnInKansas
Date: 09 Jul 05 - 05:02 PM

gnu -

I'm not sure the bit about the big 'uns yelping loadest is quite right. You can't hurt a flea by throwing him up agin' a wall, but do it with an elephant and all you get is a great big "sploop."

Little kids bounce pretty good, but it knocks the wind out of the big ones.

John

Subject: RE: BS: Free falling
From: gnu
Date: 09 Jul 05 - 05:06 PM

EXACTLY... more mass, more force, bigger yelp. But, if yer gonna throw elephants off the roof, give time for the chilluns ta git clear.

Subject: RE: BS: Free falling
From: Shanghaiceltic
Date: 09 Jul 05 - 08:11 PM

Sorry I put in a 1 where their should have been a zero *blush*

We use accurate values of local G as we are calibrating pressure controllers using dead weight testers (AKA piston guages). We work to an accuracy of 0.0015% when we use the piston guage to calibrate a device of 0.01%. We use mass to correct a pressure measuring device that has an electrical output, therefore the mass has to be corrected.

If you use hydrostatic level sensors then you must also correct when calibrating as the pressure is generated by the column of liquid acting on the electrical sensor and that column unlike gas has a mass.

Makes a difference when measuring the level of oil or gasolene when measuring tank levels in terms of total tank contents.

Local G in China varies by as much as 2% north to south.

Subject: RE: BS: Free falling
From: gnu
Date: 09 Jul 05 - 08:34 PM

2%... wow!!! That is amazing.

Subject: RE: BS: Free falling
From: Azizi
Date: 10 Jul 05 - 01:01 AM

What the heck did y'all say?

Never mind. Even if you explained it to me in 'plain English',
I probably still wouldn't get it.

Math didn't like me [or vice versa]..I was lost after "Algebra II".

That's why I'm impressed.

Really.

Subject: RE: BS: Free falling
From: Azizi
Date: 10 Jul 05 - 01:03 AM

I just lied. I was lost after Algebra I.

I never made it to Algebra II.

I'm in awe of men and women who have a mind for math.

My mind wasn't made that way.

Subject: RE: BS: Free falling
From: Peace
Date: 10 Jul 05 - 01:19 AM

For some reason, I don't think this is what Tom Petty had in mind!

Subject: RE: BS: Free falling
From: gnu
Date: 10 Jul 05 - 09:59 AM

Well, the results of my beer research are evident upon reading my posts of yesterday.

Elementary analysis clearly shows that beer will make you fall from grace.

Further, observations I have recorded this morning indicate that the mass of beer consumed has a directly proportional asymtotic effect upon blood pressure in the brain and also has an inversely proportional asymtotic effect upon brain activity. While other effects exist, these are ignored for simplification. (See below, "hangover")

Unfortunately, these observations are only qualitative at present. Until actual measurements are taken, a quantitative value for the relationship between beer mass and hangover (the term commonly used for a collective of effects) cannot be determined.

Future study, after initial discussions with my research team, points toward determination of a value defined as beers per hour per hour, the terminology of which might be "acceleration due to stupidity". Once this value has been determined, we can use it to express beer mass in terms of force, as related to how hard the beer(s) hit one. The proposed terminology for the unit of force is "Bud".

Practical use of the knowledged gained might include a rating system for brands of beer. For instance, one Moosehead Dry Ice Beer would have a rating of 4 Bud. Other applications are open for suggestion.

On-going research in this area is suspended at present in favour of more pertinent investigation. Specifically, how many cups of tea does it take to reverse the effects of a dozen CBuds (Canadian Buds).... oh, me head... anyone get the license number?

Subject: RE: BS: Free falling
From: Jerry Rasmussen
Date: 10 Jul 05 - 05:50 PM

You beat me too it, Peace. I must admit that I far prefer Tom Petty's version... The Heartbreakers are one of my very favorite bands..

Maybe I'll change my Mudcat name to Understanding.

Then we can be Peace and Understanding. What a combination!

Jerry

Subject: RE: BS: Free falling
From: Azizi
Date: 10 Jul 05 - 08:40 PM

Don't forget the "Love".

Not that I'm nominating myself for that name,

but I'm just sayin....

Subject: RE: BS: Free falling
From: Azizi
Date: 10 Jul 05 - 09:05 PM

More on the off topic comments about names:

At the beginning of the first session of this after-school program I conducted, I asked the children to introduce themselves. Three young girls told me they were sisters. The first one's name was "Faith". The second one's name was "Hope". And the third one's name was ....."Grace".

If I had been a betting person, I would have sworn that the name for the third sister would have been "Charity". And if I had bet on that, I would have lost. But, still "Grace" fits that pattern....

So....back to my post up above, I hasten to say that I wasn't asking to be a part of your singing duet or song writing team. My role would be to applaud your creative works.

Anyway, I'm sorry for the digression...I'm finished. There'll be no more interruptions from me.

I'll just sit here in the corner and marvel at the songs you folks compose, listen to the songs that you sing, and try to figure out what you mean when you talk about "falling free" and other heavy duty subjects.


Peace, Understanding, and Love!


Azizi

Subject: RE: BS: Free falling
From: gnu
Date: 10 Jul 05 - 09:11 PM

Awww.... by the Grace... lovely, Azizi.

Subject: RE: BS: Free falling
From: sixtieschick
Date: 11 Jul 05 - 12:08 AM

Azizi--it took me 2 1/2 years to scrape through Algebra I with a "D." That was it for math for this chick.

M.

Subject: RE: BS: Free falling
From: sapper82
Date: 11 Jul 05 - 12:46 PM

Only just found this thread, but in the UK it's been rounded to 10 for a long time for up to A Level!

Subject: RE: BS: Free falling
From: GUEST,Art Thieme
Date: 11 Jul 05 - 12:58 PM

My life on the road singing and playing folksong gigs, while trying to keep my calendar full, has always been, pretty much, a lot like this free falling you mention here. Mainly, it was the only way to do it from where I sit. It meant being my own boss---and it was the only way to go.

It's what this freedom thing is all about. Like Kris Kristofferson said, It's just another word for nothing left to lose. Quite exhilerating!

Art Thieme

Subject: RE: BS: Free falling
From: TheBigPinkLad
Date: 11 Jul 05 - 02:27 PM

Haven't had time to drop back in on this thread till now. JohninKansas 06:10 PM: it's not my error ... I'm quoting.

I've thought about this and while it might cause problems if someone used a sloppy value for the acceleration of gravity, I think for the intents and purposes of the exam it's fair enough. One would hope, thought, that the kids are made aware that the value has been rounded.

Subject: RE: BS: Free falling
From: MarkS
Date: 11 Jul 05 - 05:29 PM

Got it.
So when I tune my guitar to "A" equal to 454 hz at the 5th fret instead of 440hz, I can tell the others, "I'm not out of tune, I'm just fine in Victoria, Australia."

Subject: RE: BS: Free falling
From: Amos
Date: 11 Jul 05 - 05:49 PM

Azizi:

It ain't that hard once you get used to the notion that your body's weight is a measure of force, which you apply to your bathroom scale with the help of gravity. Unnoticed under usual day-to-day circumstances, gravity is accelerating your body toward the center of the Earth, roughly. Fortunately, you have floors, sidewalks, and the surface of the earth itself to prevent this acceleration from happening, but if you jump off a step stool at, say, one meter (a yard more or less) high, and then jump off a table that is 6 feet high, you will notice a dramatic difference in the force when you hit. That's the same force as your bathroom scale measures, but since you don't leap onto your scale from a foot up, I hope, it measures the force you apply to it in a more genteel manner.

If you were on the moon, your weight would be much less. Your scale would show you it was so.

But your body's mass would be the same. Mass is essentially the tendency of a body to resist acceleration, according to some definitions. Anyway, an object may weigh one thing at sea level in North Carolina, another thing on the Moon, and something else at the top of the Himalayas, but the mass of the object won't vary.

This value of "g" is just an approximation of how much acceleration (speeding up from zero start) gravity puts on an object when it falls freely. It starts at rest, so its speed is zero meters per second. The gravity field instantly starts acting on it so that after one second its speed is about 9.8 meters per second. After two seconds, it is going 10.16 meters per second. Every second of free fall increases the speed of the object falling in Earth's gravity by another 9.8 meters per second. This rate of speeding up is called "accelerating at (9.8 meters per second) per second". Or, 9.8 meters per second squared, speaking loosely.

Hope that helps.

Amos

Subject: RE: BS: Free falling
From: Azizi
Date: 11 Jul 05 - 05:58 PM

Amos, thanks for breaking this down in 'regular English'.

But I confess that I'll have to read this again to really "get it" 'cause my concentration was thrown off track by this sentence:

"If you were on the moon, your weight would be much less. Your scale would show you it was so."

Alright!! Fly me to the moon!

[Not that I need to lose alot of weight... I'm just sayin..]


LOL!!!

Subject: RE: BS: Free falling
From: dick greenhaus
Date: 11 Jul 05 - 06:00 PM

Does anyone recall the classic suggestion for using computers as an aid to education? Well, you take a desktop and a laptop and toss them off the roof at the same time and see which hits the ground first.

Subject: RE: BS: Free falling
From: robomatic
Date: 11 Jul 05 - 10:56 PM

Sorcha's comment about the Board of Education in Kansas stole my thunder, but as an approximation that is understood to be an approximation, I don't think it's a horrible horrible thing, after all, that equation won't deal realistically with a skydiver at all, whose situation is more determined by his/her position in the air stream as he/she reaches terminal velocity, which means acceleration is zero due to a balance between acceleration due to gravity and wind resistance.

Amos, making the 'g' constant of gravity equivalent to acceleration is a relatively recent development known as Einstein's general theory of relativity.

Subject: RE: BS: Free falling
From: Amos
Date: 12 Jul 05 - 09:53 AM

Robo:

Not clear what point you are making. It seems pretty Newtonian to me that gravity is an accelerative force which speeds bodies up in free-fall at about 9.8 m/s^2. But what do I know? How did they calculate it prior to EInsteins theory?


A

Subject: RE: BS: Free falling
From: TheBigPinkLad
Date: 12 Jul 05 - 12:06 PM

Got it.
So when I tune my guitar to "A" equal to 454 hz at the 5th fret instead of 440hz, I can tell the others, "I'm not out of tune, I'm just fine in Victoria, Australia."

I'll give you an A for sarcasm, but evidently you have not got it, Mark. The answer arrived at in a school exam has nothing to do with (e.g.) bungee jumping. Its purpose it to find out how well the student can perform the mathematics. So if they are presented with a given, they will be required to use it. It would be the same if they had told to assume the value to be 20m per second, or 90m per second, or any arbitrary value at all.

If student grew up to be scientists and used anything but the true value in calculating the landing of a space shuttle, however, they would indeed be out of tune.

Subject: RE: BS: Free falling
From: Paul Burke
Date: 12 Jul 05 - 12:14 PM

Local G in China varies by as much as 2% north to south.

According to my table(*) of local gs (not G, that's the universal gravitational constant), at the equator it's about 9.78 metres per square second, at the N pole it's about 9.83. That makes the range about 0.5%

They also give a very useful equation for deriving G at any latitude:

for latitude L (degrees I think, they don't say) and height h metres

g = 9.80616 - 0.025928 co2L + .000069 cos(sq)2L - 0.000003h

I bet you're glad you know that- all of you, write it down and keep it in your purse, you never know when you'll need it!

If I'm doing ball-park calculations, I use 10, the result is only about 2% out, and if you're talking about free fall remember you're not in a vacuum.

(8)R>M>Tennent, Science Data Book, Oliver & Boyd 1978.

Subject: RE: BS: Free falling
From: Amos
Date: 12 Jul 05 - 12:24 PM

In fact, now that we are planting robots on Mars, they will need to be able to calculate using any given g value depending on the planet they are deploying on.

For your entertainment, the percentage of your weight as it reads at sea-level on Earth, as it would appear using the same scale on other planets:

Mercury 37.8%
Venus    90.7%
Moon    16.6%
Mars    37.7%
Jupiter 253.3%
Saturn   106.4%
URanus    88.9%
NEptune   112.5%
Pluto    6.7%
Io (moon of Jupiter) 18.35%
Europa ( " "       ) 13.35%
Ganymede ( "   " ) 14.48%
Callisto ( " " ) 12.64%

SOL 2707.2%

Basics:

We often use the terms "mass" and "weight" interchangeably in our daily speech, but to an astronomer or a physicist they are completely different things. The mass of a body is a measure of how much matter it contains. An object with mass has a quality called inertia. If you shake an object like a stone in your hand, you would notice that it takes a push to get it moving, and another push to stop it again. If the stone is at rest, it wants to remain at rest. Once you've got it moving, it wants to stay moving. This quality or "sluggishness" of matter is its inertia. Mass is a measure of how much inertia an object displays.

Weight is an entirely different thing. Every object in the universe with mass attracts every other object with mass. The amount of attraction depends on the size of the masses and how far apart they are. For everyday-sized objects, this gravitational pull is vanishingly small, but the pull between a very large object, like the Earth, and another object, like you, can be easily measured. How? All you have to do is stand on a scale. Scales measure the force of attraction between you and the Earth. This force of attraction between you and the Earth (or any other planet) is called your weight. Weight is proportional to mass, but not the same thing.

Amos

Subject: RE: BS: Free falling
From: Amos
Date: 12 Jul 05 - 02:59 PM

Azizi:

I goofed the math in that explanation; after two seconds, the speed will be 2 times 9.8 or 19.6, not 10.16 as I wrote above. Thanks for the catch, gnu!


A

Subject: RE: BS: Free falling
From: Azizi
Date: 12 Jul 05 - 05:01 PM

Amos, I assure you I caught your mistake before gnu did.

You guys are too much for me.

LOL!!

Subject: RE: BS: Free falling
From: Grab
Date: 12 Jul 05 - 05:48 PM

Exam questions should have a list of constants for this reason. A couple of questions though: do students have to memorise the exact value; and do they have to do all calculations longhand on paper? If the answer to either is "yes", then this makes sense. If both are "no", then this is bloody stupid.

FWIW, most primary- and early-secondary-school books represent pi as 22/7. It's close enough for that kind of stuff, even if it's not 100% right. So redefining constants to "something convenient for the sums" is not an entirely new concept for school exercises.

Please also bear in mind that all these school exercises start with a zillion caveats like no air resistance/frictionless pulley/non-stretchable string/perfectly elastic collision/perfectly inelastic collision/point mass/infinitely strong beam/etc. In other words you'd better know that it's only ever approximate to the real world anyway!

Graham.

Subject: RE: BS: Free falling
From: Shanghaiceltic
Date: 13 Jul 05 - 12:33 AM

Re Paul Burkes equation. It is totally correct but ignores the effect of purely local effects such as masses of iron, oil or coal bearing rocks. Mountains too have an effect.

So when someone uses a piston gauge to do precise measurements they call in the services of someone who uses a gravitometer to measure the local G to a reasonable degree of uncertainty. That figure is then used to correct the piston guage readings.

By the way a vibrating string can be affected by local G but to a very small degree. The frequency of vibration is proportional to the square root of the stiffness of the string (k) over the mass of the string. As mass is subject to gravity you can blame your out of tune guitar, banjo, mando, fiddle, zither, dulcimer on the local G ;)

Subject: RE: BS: Free falling
From: Amos
Date: 13 Jul 05 - 01:23 AM

I always knew gravity sucked, SC; but I didn't realize that was why my tuning sucked as well!! I feel SO much better!! :D


A