Tilted Forum Project Discussion Community  

Go Back   Tilted Forum Project Discussion Community > Chatter > General Discussion


 
 
LinkBack Thread Tools
Old 04-22-2003, 08:29 AM   #1 (permalink)
Nobody Loves Me
 
Location: Irish In Madrid
Force of gravity?

Ok, so call me a freak but I was going up the escalator in a station this morn & i started thinking about gravity. It seems logical (to me) that climbing a moving stairs is more difficult than a static stairs - coz youre actually tarvelling faster/farther than you would on a nonmoving. SO,
1. Does the force of gravity increase when youre travelling upwards?
2. If im travelling straight up, how fast do I need to be going to double the force of gravity?
3. And at 45 degrees?
4. If im travelling on a train/lift/whatever at the speed of sound (Mach 1) and I start running towards the front of the train how fast am I travelling & is the force of gravity on me different to the force on said vehicle?
Magpie0001 is offline  
Old 04-22-2003, 09:33 AM   #2 (permalink)
Junkie
 
greytone's Avatar
 
The force of gravity is determined by your mass, the earth's mass, and the distance between the center of those two masses.

Your velocity does not affect the force of gravity. The fact that you may experiencing acceleration do to other forces, does not mean that the force of gravity has changed. The acceleration due to gravity is 32 feet per second per second. You would have to add a force that would cause the same acceleration in the same direction to cause the sensation of doubling the force of gravity. Keep in mind that force = mass x acceleration. So your mass would have to be known to calculate the force that would do this. When another force is applied at 45 degrees to perpendicular, exactly on half of the force would be added to gravity. The other half would be the horizontal component.

I don't remember the exact formulas, but there is a dusty thought in the back of my brain that the force of gravity is inversley proportional to the square of the distance. This would mean that you would have to dig down 3/4 of the way to the center of the earth to experience a doubling in gravity. Of course you could just apply weights, as that would be easier, and a whole lot cooler.
__________________
I was there to see beautiful naked women. So was everybody else. It's a common failing.
Robert A Heinlein in "They Do It With Mirrors"

Last edited by greytone; 04-22-2003 at 09:37 AM..
greytone is offline  
Old 04-22-2003, 09:50 AM   #3 (permalink)
Transfer Agent
 
troit's Avatar
 
Location: NYC
Hold on everyone -- Rogue will be by in a few minutes...
__________________
I've yet to dephile myself...
troit is offline  
Old 04-22-2003, 10:07 AM   #4 (permalink)
Here
 
World's King's Avatar
 
Location: Denver City Denver
This just sailed way over my head... Boobs anyone?
__________________
heavy is the head that wears the crown
World's King is offline  
Old 04-22-2003, 10:14 AM   #5 (permalink)
Tilted
 
Gravity is assumed to act from the centre of the planet so digging down wouldn't effect it in the wya of equations but thinking logically it should have some effect on it.

If you going upwards at a constant speed you'l notice no differences from gravity (unless your travelling so fast that the earth is no longer effecting you) [again i say you'll not notice, if say you were an atomic clock instead of an TFP poster you might notice there's a change in g at altitude].

As you go upwards you are gaining potential energy faster BUT the floor is going up and that's providing the power.

if you were accelaerating upwards at 9.9081 m/s^2 your weight would be twice as much (although your mass is constant).

If travelling at 45 degrees upwards you'd need to accelating at root (9.9801^2 + 9.9801^2) which is 14.11m/s^2.

The gravity constants are from my head so may be wrong but are in the right ball park for figures. Hope this helps somewhatt.

I always liked to imagine a hole through the centre of the earth that you could jump through and experience simple harmonic motion, but then again I don't get to sleep alot and have time on my hands! Hope this helped.

Insom
__________________
Insomniac
Insomniac(uk) is offline  
Old 04-22-2003, 10:23 AM   #6 (permalink)
Upright
 
The force of gravity by classical physics (which are good enough for this discussion) can be calculated as

F = G * (m1 * m2) / r^3, where F is the force we're looking for, G is the gravitational constant, m1 and m2 are the two masses in question, and r is the distance between the two.

So, answering your questions:
1. because the force is inversely proportional to the cube of the distance, gravity actually decreases as you go away from Earth.

2. Well, you can put another force on yourself, double that of gravity. I won't go into that, though, as I doubt that's what you're talking about.

3. the "angle" won't make a difference, the distance between the two bodies will.

4. You'd be travelling at a speed of however fast you were running plus the speed of the train. As I assume the train is on the Earth, then the distance between you and Earth's center of mass won't change, so gravity will remain constant.
Gravity will be ever so slightly stronger on the train because it has more mass than you; however, the difference is neglible. Gravity is a force at work on astronomically large bodies, on smaller bodies it is far too weak.
PKoi is offline  
Old 04-22-2003, 10:41 AM   #7 (permalink)
Insane
 
Ouch, my head hurts!!!
Unknown Poster is offline  
Old 04-22-2003, 10:44 AM   #8 (permalink)
Invisible
 
yournamehere's Avatar
 
Location: tentative, at best
In $1 words (I hope):

First of all, walking on an escalator is not harder than walking on stairs, because your speed <i>relative to</i> the two is the same.

1. The force of gravity always remains constant, regardless of the direction you are traveling. Sometimes it works in your favor (going down), sometimes not (going up). But it never changes.
2. You cannot realistically double the force of gravity, however, if you were accelerating UP at 32' per second squared, you would experience the <i>feeling</i> of double that of normal gravity.
3. At 45 degrees, it's still pulling you down at 32' per second squared. it's easier to walk at 45 degrees compared to straight up because for every foot uphill you walk, you also walk a foot horizontally. However, in order to travel the same distance vertically, walking at 45 degrees requires you to walk twice as far (total distance) That's the give-and-take. Think of using a board as a ramp up to something - the more gentle the slope, the longer the board you'll need, and the more steps you'll need to take to reach your destination.
4. If you are traveling on a train and start running, your speed is the sum of the train's speed plus your speed (or <i>minus</i> your speed - if you run from front to back). The force of gravity is still constant.

As <b>greytone</b> accurately pointed out, the <i>actual</i> force of gravity is 32 feet per second per second (or 9.8 meters per second per second)<i>at sea level</i> (and at the equator, I think). Naturally, this force actually changes relative to your distance to the center of the earth. However, for all practical purposes, I think it's safe to assume it's a constant. Most of us will never vary that distance by more than 8 miles or so, and considering the distance to the center of the earth is close to 15,000 miles, that's not much of a difference.

There - that's not as accurate or eloquent as <b>greytone</b> put it, but I hope it helps clarify some things.
__________________
If you want to avoid 95% of internet spelling errors:
"If your ridiculous pants are too loose, you're definitely going to lose them. Tell your two loser friends over there that they're going to lose theirs, too."
It won't hurt your fashion sense, either.
yournamehere is offline  
Old 04-22-2003, 11:59 AM   #9 (permalink)
Insane
 
*Escalator= Moving stairs.

Urm, consider your relative velocity wrt to the moving escalator* when you are standing on it still. Zero. When you move, you exert about as much force as you would on a "normal" staircase of identical charecteristics.Therefore to answer you pointwise:

1. Gravitational force decrease with distance.

Consider g aka acceleration due to gravity. It depends upon mass(kg) of Earth(M) and the radius(R)(unit is meter) of the planet and the formula is g=((MG)/R^(2))=~9.8m/s^(2) roughly. G is the universal constant of Gravity and its value is 6.67*10^(-11) Nm^(2)kg^(-2)

Therefore the gravitational force(F) has unit Newton and is calculated by the formula F=mg where m(small) is the mass(kg) of the object(you) and g the acceleration due to gravity.

Note that the g is independent of the mass of the object. Of course, the object(you) also exert gravitational force on the Earth but considering the difference in the scale it's negligible and can be safely ignored. Or don't ignore it. Whatever floats your boat.

Work is defined as Force*Distance and the units is Joule so the actual work you'll be doing in this case would be (mg)(h2-h1) where hn is your difference in initial and final height, m is your mass and g the acceleration due to gravity. Now....the value of g decreases with increase in R, so actually you'll be doing less work when climbing the same distance on a already high situated escalator rather than a "ground level" staricase. But all this is codswallop because the difference in R is negligible, nor is the centre of mass properly defined.

TO the point, there is this thing called power[unit Watt]. Power=Work/Time. Therefore, the power exerted by you would be more if you are trying to cover the same distance(vertical component, obviously) in shorter period of time. May be you try to climb faster while on escalators? I know I do. All things equal, escalators will help conserve your fat more than the regular stairs. If only because you'll be covering the same distance in shorter time. So take the "static" stairs and stay healthy.



2. Double the force of Gravity? And that too while going straight up?! Gravitational Force between two mass bodies is calculated with F= ((GMm)/R^(2)). And since you are already going up and increasing the distance, and since you cannot possibly influence the Mass(M) of the Earth, and G is G, what we can do is increase your mass dramatically, all the while ensuring that as you go up more mass is addded! Maybe we could teleport lots of Ice-cream to you...

Haha, I am so funny.

In case you were trying to refer to acceleration due to gravity aka g as experienced by your body, while travelling vertically, all you would have to do is build an apparatus like a rocket/plane that can provide you with 2g acceleration vertical. The initial speed would be zero, obviously, and after that it would keep increasing wrt time. So either with known rate of acceleration we can calculate speed at t seconds after launch/take-off, or if you want x speed at y distance than we can calculate the rate of acceleration. This is dealing purely with vertical component ie 2d.



3. You haven't specified in what axis you want to feel this 2g force. If it's the net of the horizontal and vertical in 3d, then it can be easily calculated through trignometric formula though because of my lame HTML skills I cannot elaborate more here. However, you can easily experience this much g's on Earth surface itself 2d. Any car that brakes from 100 kmph to 0 within 1.4 seconds. F1 cars with carbon-fibre brakes regularly hit more g's(momentarily, and decreasing) at the end of long straights followed by slow corners.



4. Relative velocity. And depends on the point of observation. As a point object, and certainly if mass is taken into consideration, all your running stunts are pretty much ignorable and "your" speed will be taken as the speed of train(x kmph). Relatively, however, your body is at rest (inertia) and if you start running(y kmph) towards front you will momentarily be covering more distance per unit time(x+y kmph) compared to other pax(x kmph) and are "faster"(by y kmph) than the train, to someone viewing this whole scene from a staionary platform from the outside. That is, until you run out of room and head back to your seat. So you'll arrive at the same time as the rest of the pax.


Gravity, as you know by now, applies to mass. For all theorotical physics problems, we take a point mass(hypothetical), where all the mass of an object is centered, and then calculate. So, your mass is irrelevant, what matters is the total mass and how it's distributed to make sense from an engineering point of view. Because you are travelling at the same speed as your vehicle, your and your vehicle's mass is combined in calculations. But as soon as you jump out, you'll be taken as a seperate point mass and studied as you form a nice trajectory and come to rest. Strictly, the force of gravity is affected only by the variables mentioned in te formula. Draw your conclusions.


EDIT: Improved Formatting. Relatively speaking.
__________________
Make me Mad.
Make me Sad.
Make me feel Alright.

Last edited by oane; 04-22-2003 at 12:04 PM..
oane is offline  
Old 04-22-2003, 12:03 PM   #10 (permalink)
Insane
 
You don't say so

Quote:
Originally posted by greytone
The acceleration due to gravity is 32 feet per second per second.
In civilized world, it is called 9.8 meters per second
__________________
Make me Mad.
Make me Sad.
Make me feel Alright.
oane is offline  
Old 04-22-2003, 12:29 PM   #11 (permalink)
Invisible
 
yournamehere's Avatar
 
Location: tentative, at best
Re: You don't say so

Quote:
Originally posted by oane
In civilized world, it is called 9.8 meters per second
Not to split hairs, <b>oane</b>, but 9.8 meters per second would be a velocity.

9.8 meters per second <b>squared</b> is acceleration.

I know you meant that.
__________________
If you want to avoid 95% of internet spelling errors:
"If your ridiculous pants are too loose, you're definitely going to lose them. Tell your two loser friends over there that they're going to lose theirs, too."
It won't hurt your fashion sense, either.
yournamehere is offline  
Old 04-22-2003, 01:41 PM   #12 (permalink)
Insane
 
Re: Re: You don't say so

Quote:
Originally posted by yournamehere
Not to split hairs, <b>oane</b>, but 9.8 meters per second would be a velocity.

9.8 meters per second <b>squared</b> is acceleration.

I know you meant that.
Damn! Yeah, you are right...heh.
__________________
Make me Mad.
Make me Sad.
Make me feel Alright.
oane is offline  
Old 04-22-2003, 03:06 PM   #13 (permalink)
Crazy
 
Location: Doesn't matter - you wouldn't want to be here
http://www.curtin.edu.au/curtin/dept/phys-sci/gravity/
nine is offline  
Old 04-22-2003, 04:51 PM   #14 (permalink)
Junkie
 
greytone's Avatar
 
Quote:
Originally posted by troit
Hold on everyone -- Rogue will be by in a few minutes...
I know he will, I was just trying to beat him to it for once.

As for the units, I just could not remember the value in m/s/s. I knew it was 9 point something, but I had not used it in many years. I think in metric at work (except temperature and usually body weight) and the old English system at play.
greytone is offline  
Old 04-22-2003, 05:46 PM   #15 (permalink)
Loser
 
Location: TN
I think I actually understand this now! I've been wondering about that train problem, too. Thank you, tfp.
pickledaddy is offline  
Old 04-22-2003, 06:32 PM   #16 (permalink)
There's someone in my head, but its not me
 
Zotz's Avatar
 
In layman's terms.......gravity sucks
Zotz is offline  
Old 04-22-2003, 06:58 PM   #17 (permalink)
Tilted
 
Location: 213
"escalators are great because they won't break down... they just become stairs"
-- Mitch Hedburg (Comedian)
Gatecrasher is offline  
Old 04-22-2003, 07:17 PM   #18 (permalink)
Psycho
 
TheDave87's Avatar
 
Location: The Amish Wastelands of Ohio
Heres something i always wondered about gravity... if you have a hole that goes straight through the planet, much like when you core an apple... and you jump into this hole. Do you get stuck in the center of the planet? Do you get ripped to shreds? all this is assuming that the immense heat does not effect you.
__________________
Honk if you've never seen an uzi fired from a car window!
TheDave87 is offline  
Old 04-22-2003, 09:58 PM   #19 (permalink)
Invisible
 
yournamehere's Avatar
 
Location: tentative, at best
Quote:
Originally posted by TheDave87
. . . . all this is assuming that the immense heat does not affect you.
That's a pretty dangerous assumption.

But - and please correct me if I'm wrong (Ha - like no one would!), I believe that, also assuming you don't bump up against the sides of the holes, and neglecting air friction (and air pressure), you would appear at the opposite end of the hole (upside down, of course), with the top of your head at ground level, then start your descent again, where you would appear again at your point of origin - feet at ground level. But of course, although Physics 101 may let us neglect air friction, the real world doesn't, so each "ascent" up the hole from the center would get shorter, and yes, eventually, your body would be stuck at the earth's center, burnt and compressed into a tiny, unrecognizable, dense cinder.

Of course - that's all theory - if you've got the shovel and the time, go for it.
__________________
If you want to avoid 95% of internet spelling errors:
"If your ridiculous pants are too loose, you're definitely going to lose them. Tell your two loser friends over there that they're going to lose theirs, too."
It won't hurt your fashion sense, either.

Last edited by yournamehere; 04-23-2003 at 06:23 AM..
yournamehere is offline  
Old 04-22-2003, 10:30 PM   #20 (permalink)
Winter is Coming
 
Frosstbyte's Avatar
 
Location: The North
You know, it's nice to see some people paid attention in physics. I know I didn't. Way too much time spent talking and making bad jokes. Oh well, I did ok and it was a damn good time.
Frosstbyte is offline  
Old 04-22-2003, 10:46 PM   #21 (permalink)
Loser
 
Quote:
Originally posted by troit
Hold on everyone -- Rogue will be by in a few minutes...
Nah, I think you all pretty much got the info down.

Now, here's the REAL question.

WHY does gravity act that way?


BTW, besides all your explanations of gravity.
You forgot to say to the questioner why they are "feeling"
a change in "pull".

The change you might "feel" when you are going faster (accelerating),
or going slower (decelerating)
is because you are changing your velocity in respect to the laws of inertia.

This means as you go faster, you "feel" a pull.
And as you go slower, you "feel" a push.
And this "feeling" can exist when you change your direction too.

This is why you are "feeling" pushed & pulled all different types of ways on a roller coaster.
It's not gravity changing, the pull is always constant (at least on that small scale)
Gravity only affects the energy or work needed to move you back up, but the coaster is taking care of this.
Notice that on your ride the hills are getting smaller and smaller.
That's because of the loss of energy through friction,
it doesn't have as much to get up the next hill.

However, let's say you were on the same roller coaster,
but now it's up on the non-gravity space-station and the first car is pulling at a constant rate.
Even though there is no gravity & no acceleration you would still feel all the twists and turns, etc. that you felt on Earth.
Why?
Because as you change direction you are changing your relation in Space with Inertia.

Some all this "Centrifigal Force"
But this is NOT really a "force"
This is an illusion, an effect.
Because your body wants to continue in a straight line ALWAYS.
But the car you are within is pulling you left & right, etc.
And then you "feel" the pull in the opposing direction.
Giving the illusion of a force or "gravity".

Last edited by rogue49; 04-22-2003 at 11:22 PM..
rogue49 is offline  
Old 04-23-2003, 07:16 AM   #22 (permalink)
Loser
 
Aww, did I scare everyone away?

Well, someone once said,
"Don't talk physics in public"
rogue49 is offline  
Old 04-23-2003, 07:40 AM   #23 (permalink)
not your typical god-fearing junkie
 
Location: State of Confusion
Quote:
Originally posted by Gatecrasher
"escalators are great because they won't break down... they just become stairs"
-- Mitch Hedburg (Comedian)
"Sorry for the convenience"

I love mitch hedburg
__________________
the light that burns twice as bright
burns half as long

and you have burned so very, very brightly
YzermanS19 is offline  
Old 04-23-2003, 07:52 AM   #24 (permalink)
Tilted
 
Location: US, East Coast. Blah.
All I heard was "LA LA LA LA LA Boobs Anyone?"

In all seriousness, has anyone ever entertained the thought that walking is just a form of controlled falling?
SpoilSport is offline  
Old 04-23-2003, 08:13 AM   #25 (permalink)
Pup no More
 
Loup's Avatar
 
Location: Voted the Best
World's King:

Yes please
__________________
"If you cannot lift the load off another's back, do not walk away. Try to lighten it."
~ Frank Tyger
Loup is offline  
Old 04-23-2003, 08:16 AM   #26 (permalink)
Insane
 
Quote:
Originally posted by SpoilSport
In all seriousness, has anyone ever entertained the thought that walking is just a form of controlled falling?
Urm, I thought this was a known fact that didn't need stating. You are always falling thanks to g.
__________________
Make me Mad.
Make me Sad.
Make me feel Alright.
oane is offline  
Old 04-23-2003, 08:27 AM   #27 (permalink)
Right Now
 
Location: Home
Re: You don't say so

Quote:
Originally posted by oane
In civilized world, it is called 9.8 meters per second
You mean 9.8 meters per second squared. Meters per second is just a velocity. ;-)

Rogue, I think we need to come closer to a unified theory before we can explain "why" gravity does what it does. I personally have no clue. As a Kant fan, I just observe my surroundings and hope they don'tchange laws tomorrow. :-)

Last edited by Peetster; 04-23-2003 at 08:31 AM..
Peetster is offline  
Old 04-23-2003, 08:59 AM   #28 (permalink)
Everything's better with bacon
 
SaltPork's Avatar
 
Location: In your local grocer's freezer.
must...fight...knowledge....must.....fight....it......AAAAGGGGHHHHH!!!!!!! I'M LEARNING!!!!!!!!!!!!!!!!! NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
__________________
It was like that when I got here....I swear.
SaltPork is offline  
Old 04-23-2003, 04:30 PM   #29 (permalink)
Loser
 
Re: Re: You don't say so

Quote:
Originally posted by Peetster
You mean 9.8 meters per second squared. Meters per second is just a velocity. ;-)

Rogue, I think we need to come closer to a unified theory before we can explain "why" gravity does what it does. I personally have no clue. As a Kant fan, I just observe my surroundings and hope they donít change laws tomorrow. :-)
Actually, we don't need to come even close to a unified theory to explain this.

First, gravity is explained pretty much by Einstein's General Theory of Relativity
which states that ANY mass "warps" the Space-Time surrounding it.

Kind of like a bowling ball in the middle of a rubber mat.

And if we pretend "we" are a marble moving at a certain rate near this mat,
we can see the effects of gravity.

If you are moving at a fast enough rate, in comparison of the warping caused by the ball,
then the path will curve and then escape area of the warp.

If you are moving at a constant rate in comparison but not fast enough to escape the area,
the marble will start circling the ball at a certain distance or "orbit"

If you are moving too slowly in comparison,
the marble will curve "fall" to the edge of the ball and come to rest against it.
This is why we stand on the Earth
We are constantly falling toward the middle, but the Earth holds us with its substance.

BTW, by this very definition, I doubt Gravity will ever "fit" into a Unified Theory
with the other 3 forces (Strong, Weak, and Electro-Magnetism)
Because with this significant description we see Gravity is not a force,
it is an effect, an illusionary "force" caused by the warping of Space-Time.
It can be used as a force in certain calculations but it's not actually one.

Thus the Unified Theory as they are now defining it will fail,
Until they change their conceptual viewpoints.

Last edited by rogue49; 04-24-2003 at 08:52 AM..
rogue49 is offline  
Old 04-23-2003, 06:41 PM   #30 (permalink)
Fledgling Dead Head
 
krwlz's Avatar
 
Location: Clarkson U.
just want to add, strictly physics wise, yes more work is done by you climbing a moving stair, however not by you. By the equation, more work is done because you moved the same distance in less time.
krwlz is offline  
Old 04-24-2003, 02:09 AM   #31 (permalink)
Conspiracy Realist
 
Sun Tzu's Avatar
 
Location: The Event Horizon
If Nibiru ever comes by again is it possible for the Earth to stop rotating briefly?
__________________
To confine our attention to terrestrial matters would be to limit the human spirit.- Stephen Hawking
Sun Tzu is offline  
Old 04-24-2003, 02:29 AM   #32 (permalink)
Crazy
 
Location: Arizona
I've actually thought about this myself. Very interesting to think about when you don't have much to do! It had kept me busy for hours on end.
__________________
"So I was sitting in my cubicle today, and I realized, ever since I started working, every single day of my life has been worse than the day before it. So that means that every single day that you see me, that's on the worst day of my life." -Peter Gibbons, Office Space
zizdog69 is offline  
Old 04-24-2003, 08:53 AM   #33 (permalink)
Loser
 
Quote:
Originally posted by Sun Tzu
If Nibiru ever comes by again is it possible for the Earth to stop rotating briefly?
Wha?
rogue49 is offline  
 

Tags
force, gravity

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On



All times are GMT -8. The time now is 12:45 PM.

Tilted Forum Project

Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2022, vBulletin Solutions, Inc.
Search Engine Optimization by vBSEO 3.6.0 PL2
© 2002-2012 Tilted Forum Project

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360