why doesn't gravity break everything?

Factual Questions
1

i have a bucket on a piece of plywood. don’t know why, but i voice told me to build it in the center of my living room the other day, suspended over two ladders. it just stands there, haunting me and taunting me. more than the mashed potato mountain ever did. i can’t shut my eyes without knowing that the plywood/bucket structure is looking at me with its mocking glare. i’ve tried sleeping in the dryer, but the fabric softener sheets make me ill.

why doesn’t the bucket crash through the plywood? the closer to the earth the bucket gets, the stronger it feels gravity’s tug. gravity pulls the bucket constantly, and the bucket at soem point will sink a bit closer to the ground than it was before. the force of gravity should then pull the bucket even harder, which causes the bucket to go lower, which causes gravity to pull harder, which causes teh bucket to sink even lower, which causes gravity to— the horror, the horror!

the only thing i can think to stop the gradual neverending procession of increasing gravity is the elasticity of the board itself. but that would mean that a strained chemical bond is stronger than a non-strained one. and that seems counterintuitive.

oh well, back to the looking at the bucket… my god, it’s full of stars!

2

Because the force of gravity is a heck of a lot weaker than the electrochemical forces holding the atoms together in the plywood.

Lithium is an old treatment but still effective.

3

yeah, but the trust of the question has to do with the chain reaction of the the gravitational attraction, not with strength of the force of gravity. basically, if the gradation of attraction happens as i set it out in the OP, then the force of gravity (quickly or not) would build up to the point that it overcame electrostatic attraction in the plywood,

unless the electrostatic forces bcome stronger the more they are stressed.

which may or may not be true, but i’m assuming that they don’t.

4

Nope. Specifically:

This is not true. Look up “Zeno’s Paradox” for more information.

5

rotfl… whatever you were on when you built this “plywood/bucket structure”, pass some over here.

6

This bucket is on Earth, right? Not Jupiter or some neutron star?
What you are discribing sounds kinda like speghetification. Where you get really really stretched out while going into a black hole because of the great gravitational difference between your feet and your head.

Anyway, gravity is pulling down on your bucket with enough force to make the plywood bend. Granted, gravity is a little- no make that miniscual - bit stronger there, but not strong enough to bend the board further. So the board stays put.

I know what you are thinking though. “The board should move a very-tiny-bit more, since a very-tiny-bit stronger force is now pulling on it.” “And now, after it moved a down a little more, gravity should be stronger and pull it closer. . .”

When the wood starts drooping, some of its atoms are being pulled further apart (the outside of the U shape)and others are being crunched together (the inside of the U shape). The crunched atoms are naturally repelling eachother, trying to pushing the board straight again, and therefore back up. Also, the bond in the atoms being stretched is pulling them back. These forces are much stronger than the force gravity is exerting. So the board will stretch to a point an then stop. Even though some microscopically stronger gravity is pulling on it.

. . . I think

7

Gravity does indeed get stronger the closer you get to it’s source. So why doesn’t a runaway gravitational attraction bring the bucket down? Because the gravity isn’t getting stronger that rapidly.

The earth is a sphere approximately 8000 miles in diameter; so the earth’s gravity behaves (to a first approximation) as if it were located in a point 4000 miles away in the earth’s center.

Let’s say that the earth’s center is 253,440,000 inches away from the bucket (sorry I don’t have metric equivalents handy). If the bucket’s weight causes the boards to sag half an inch, the bucket is now 1/507,880,000 closer to the earth’s center of gravity. The resulting increase in gravity is trivial.

8

Assuming the OP is serious:

You can analyze the question by assuming that the bucket sits on the plywood, the Earth attracts the bucket and the plywood deflects, moving the bucket towards the center of the Earth. Then the gravitational attraction of the Earth is stronger, so the bucket moves a tiny bit closer to the center of the Earth, again slightly increasing the force on the bucket, … and so on infinitely.

But you should not assume that the sum of this infinite series of deflections is enough to break the plywood, or even noticably increase the deflection of the plywood.

You can do it more easily by successive approximations. Calculate the force ignoring the deflection of the plywood. Calculate the deflection of the plywood. Recalculate the force at the new distance. Recalculate the deflection of the plywood under the new total force. Repeat until the answer doesn’t change any more.

The Earth masses about 5.97610[sup]24[/sup] kg. Let’s start with the bucket at the Earth’s equatorial radius, about 6378 km, plus one meter, or 6378.001 km. Let’s assume your bucket is pretty heavy, 10 kg (about 22 pounds). The universal gravitational constant G is 6.67210[sup]-17[/sup] Newton km[sup]2[/sup] per kg[sup]2[/sup]. So the force between the Earth and the bucket is:

F = G*m[sub]1[/sub]*m[sub]2[/sub]/r[sup]2[/sup]

F = 6.672*10[sup]-17[/sup]5.97610[sup]24[/sup]*10/(6378.001)[sup]2[/sup]

F = 98.0161095301043366351828082911877 Newtons.

(yes, I know that not all those figures are significant).

Now, plywood is actually a pretty complex material, and a sheet of plywood is more like a plate than a beam, so neither you nor I want to get into a real calculation. Let’s assume a pretty soft piece of plywood that deflects 25 mm (about one inch) under a force of 100 Newtons (a weight of about 22 pounds), so the deflection at 98.0161095301043366351828082911877 Newtons is 24.5040273825260841587957020727969 mm. (It’s not really linear, but this is close enough). So the distance between the two bodies is now:

r = 6378.001 km - 0.0000245040273825260841587957020727969 km = 6378.0009754959726174739158412043 km

Now re-run the calculation:

F = 6.672*10[sup]-17[/sup]5.97610[sup]24[/sup]*10/(6378.0009754959726174739158412043)[sup]2[/sup]

F = 98.0161102832523670904061621040281 Newtons

In one step, the force changed by 0.00000077 percent!

You are welcome to try another step or two if you wish; the change at the second step will be much smaller. You may have a hard time finding a calculator or program that will carry the number of digits you’ll need to see any change at all in the next step.

The change in force on the plywood due to the bucket moving closer to the center of the Earth (when the plywood deflects) would be difficult to measure with very sensitive instruments.

9

I’ll add the chemical side to this. The board is held together by a heck of a lot of chemical bonds. An individual bond in a lot of ways acts as a spring–at least with near it’s resting length (ok, technically there is no “resting length”, so sue me). The more you stretch or compress it, the more force it generates back towards equilibrium. Stretch it too far, and it will snap. It takes a heck of a lot to get just one to snap (relatively speaking, of course) in a decently stable system, which wood is. Now imagine millions of different molecules, all held together by these bonds, and held to other ones by similar bonds. The more you stretch it, the more it resists.
Of course, the breaking point varies from substance to substance, but the basic principle is the same.

10

okay, so the answer as i should explain it to the ladders/bucket/plywood confab is that:

  1. sure, your bucket is moving down, but hardly any. but i still don’t understand how, in an ‘infinite series of deflections’, even a miniscule amount of movement won’t add up.

it may think it has won, until i whip out number

  1. the bonds actually are stronger when they are stretched a bit. because they are trying to maintain equilibrium. take that, l/b/p confab! now if i could find someway to get the houseplants to stop singing “Sailing” by Christopher Cross.
11

Think of the following series: 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + … and so on infinitely. No matter how many terms you add onto that series, the result will never be greater than two: The series falls of rapidly enough to be finite, even with an infinite number of terms. Basically, when you add each new term, you’re going half of the remaining distance to two. A similar effect is at work in your bucket example, except that there, the sucessive terms fall off even more rapidly, so the net result is still finite.

12

jb, you ever play football (American)? At least ever watch it? The distance penalized for holding 1 yard away from the endzone is “Half the Distance to the Goal Line”. So now the ball goes .5 yards from the endzone. Another flag? .25 yards from the endzone. The team could have a million penalties and the ball would never reach the endzone.
SO gravity could pull with in infinately smaller increments and still never move it anywhere.

13

If I understand this OP correctly, it might be simpler to analyze if we held the bucket up with an unbreakable spring hanging from the ceiling, rather than a sheet of plywood. As the bucket drops down, the spring stretches - same basic principle, but easier to perform stress analyses.

Hang the bucket on the spring and very slowly let it down (to avoid bouncing) until the spring eventually supports the weight. Or, as the OP questions, will it ever?

The bucket will stop going down when the forces on it are in balance. This is when the gravitational force (downwards) exactly balances the returning force on the spring (upwards).

If the bucket’s weight is considered constant, then it seems clear that, eventually, the spring will become stretched enough to match it. The farther the bucket falls, the harder the spring pulls back - eventually they will be in balance. Remember, we’re assuming that this spring can support an infinite weight without just breaking.

What if the bucket’s weight really does increase appreciably the more it drops? Well, then it becomes something of a race. If the bucket’s weight increases faster (with distance) than the force by the spring does, than the bucket will never be stopped. If the spring’s restoring force increases faster, then the bucket’s going to halt at some location - the one where they are the same. Recall, the bucket has a head start - at zero deflection, the spring force is zero, but the gravitational force is not.

If the spring has a 5 lb/ft spring constant, then after stretching by 1 foot it will be pulling up with a force of 5 pounds. If the bucket weighed 1 pound to start out with, it’s weight would have had to increased to more than 5 pounds in that 1-foot drop in height if it were to “beat” the spring. While there are situations in which that’s possible, it doesn’t go up anywhere near that fast on the surface of Mother Earth.

It would take in unbelievably weak spring to have the gravity gradient be “bigger” than the spring constant.

A sheet of plywood works more or less like a spring in this sense: the farther it deflects, the harder it pushes up on the bucket. Most sheets of plywood increase their restoring force (with deflection) much faster than gravity increases.

14

Chronos, that reminds me of a bad joke.

A mathemetician was brought into a hotel room with a gorgeous woman on the bed, nude. He was given a chair, and told to sit at the opposite wall, and every 5 minutes, he could move half the distance to the woman. The poor man ran out of the room crying. “I’ll never get there!”

A physicist was brought into the same room and told the rules, and he promptly sat down in the chair and began timing. “But you’ll never get there!” “I’ll get close enough for all intents and purposes!” he retorted.

–Tim

15

Especially that 5 in the middle there. :slight_smile:

16

I heard the same joke except that the frustrated one was a “scientist” and the other one was an “engineer”.

17

If jb’s horror were true, then all matter in the universe would collapse down into black holes.

18

not only that, but the bucket would have fallen by now. not to mention that we’d have a lot more funny clips of gerry ford tumbling ass over teakettle.

i know its wrong. i’m just wasn’t sure how.