Gravity physics

[DerwenArtos12]

my dad and I were working on a cabinet today. Ov course using a square and a level to make sure it woudl sit level wehre we are putting it, which is not level ground. I realized that the "level" is straight. but with the curvature and roundness of the earth if you got a long enough level that is perfectly level to the ground for the full length of the level it would not be straight. I managed to get him to finally understand that. The we started discussing the fact that thing that are supposedly level like the concrete slab that a house is on. IF it were perfectly level at all points it would not be flat. But as they use very long 4x4 boards to make it flat. Now, thinking in perfect physics not real life actual earth physics, if you extende this perfectly striaght line out for thousands of miles you would ge a definate grade going out from the earth. I think that if you placed a ball on the end of this many mile surface, assuming there is no friction as there is in perfect physics, it would rill to the origin as it is closer to the center of the earth. He thinks that as the surcase is level from and origin and is completely flat the ball will just it there and not roll at all. Any light you could shed on this woudl be great.

BTW: I posted theis here in hopes of avoiding too many fluff responses.

 

[jagec]

If I'm understanding your description correctly, than what you predicted is correct, the ball would come to a rest at the point (in your infinite slab) closest to the earth (at the origin).

 

[Geniere]

Yes - If you placed a long, level rigid plank accross the north pole, a ball would roll to the pole. If the plank was extremly flexible, it would bend to conform to the ground. The plank would appear only to be level at the point of contact. At the extremities, a long, rigid plank would not "read" level, the bubble would float to indicate the ends of the plank were high. Sighting along a string and a weight tied to the plank would point to the center of the Earth.

 

[DerwenArtos12]

Thank you guys.

 

[DrPizza]

Of course, if you want the ball to come to rest at the center/origin, you have to have some resistance, otherwise it would roll back and forth endlessly. And, since you have resistance, I doubt it would come to rest at the exact center/origin.

 

[beansbaxter]

If the one end of your line starts out level, and projects out straight, perpendicular to the radius of the earth, the line will be 1 foot away from the earth in a mere 1.225 miles.

sure it would roll to the point where it is closest to earth. the obvious way of looking at it is that it is on a slope relative to the earth, so it will roll same as it would roll down any other sloped surface. if he needs a more mathematical explanation, realize that any object wants to sit at the lowest place possible, and the lowest means the closest to the earth, so given zero friction of course it will roll (well, slide actually) to the point of the surface closest to the earth.

Perhaps you should start a campaign to rename the "level" to the "perpendicular" .. .you may be more comfortable knowing that the center of you house, or surface you are "leveling" is infact not level, but "perpendicular" to an axis you have drawn to the center of the earth.... . from that point (your "leveling point" or where the "bubble" is) you can be assured that as long as you work outwards from your established "perpendicular" you can be assured that things are "level" or in reality the same plane as your established starting point...

you are correct in stating that if you were to check for level at one point of a foundation and then check, say 30' farther down, that it would not be level but instead be curved.

 

[Mday]

This may sound like just talk with no real value in terms of real life. But that is not the case.

If you consider that anything level on the planet is affected by the gravity, then there is nothing truly flat that can be created with respect to the earth. In modern window and glass production, float glass using molten glass on a pool of molten tin does not create perfectly flat glass panels. The panels have the same curvature as the earth. Sure, this curvature is nearly flat and windows are windows. But what happens when you're creating a LARGE lens that's a few hundred feet in diameter?

Then there are also maritime simulations. You know those large boats? They design and build smaller models and use them in small pools first (very VERY long pools). If you want to simulate a moving boat, you will have to tow the boat on a rail. Guess what? If the rail is flat (really flat), it won't work. The rail must have the same curvature as the water's surface, which is the curvature of the earth. If not, the boat will start rising above the water as you move along as if the rail was a tangent (it's a line parallel to an actual tangent drawn to the water's curvature).

 

[buleyb]

just because common practice leads to curved objects doesn't mean you couldn't create a flat object tangent to the earth's curvature. For the sake of theory, its possible.

 

[beansbaxter]

Don't they grind and polish those lenses until they are within the scientists exacting standards?
I know somewhere I saw where they had to do that them to get them near perfect as they needed. (taking up to a year or more?)

I'm pretty sure that their method could fix "your problem".

 

[grant2]

I always imagine "what if the earth was a cube?"

It would be really neat to climb to the 8 corners because they would get steeper and steeper.

And i guess there would be 6 oceans, one on each side.

 

[DrPizza]

It seems to me that some of you are getting a little bit carried away with the idea of these calculations. You're achieving incredible precision on a small scale by generalizing the Earth as a perfect sphere. As I look at the curvature of the Earth out my classroom window, I notice that after about 3 hundred yards, it curves sharply uphill. Also, as far as gravity goes, gravity isn't constant across the surface of the earth. Nor is it constant across the surface of the ocean.

If you were to build your 1 mile long ramp , and position it so that the center of the ramp was parallel to the gravitational field at the point where the center of the ramp was, I'm not 100% positive that a frictionless ball placed on one end of the frictionless ramp would necessarily roll toward the center. What if the end of the ramp was against the base of a cliff?

 

[Smilin]

Yes you are right, your dad is wrong.

Draw a big circle on paper and then put a square around it, touching on all four sides.

Each side is your board.

Now draw a big X touching each corner of the square. These lines represent the direction gravity will pull you. Now if you place a ball bearing or something at the corner of the square you'll see gravity doesn't pull at a right angle to the surface. It pulls to one side. Hence the ball will roll. It's nothing to do with the strength of gravity (try drawing the square inside the circle instead to think about that one).

 

[jagec]

Originally posted by: DrPizza
If you were to build your 1 mile long ramp , and position it so that the center of the ramp was parallel to the gravitational field at the point where the center of the ramp was, I'm not 100% positive that a frictionless ball placed on one end of the frictionless ramp would necessarily roll toward the center. What if the end of the ramp was against the base of a cliff?

he said "thousands of miles long".

While due to the effects you mentioned (non-constant gravity, etc), the ball wouldn't rest exactly on the origin, if you have a 5000 mile board the ball will be darn close to the center by the time it stops rolling.

 

[zephyrprime]

it would roll.

By the way, the twin towers were tall enough that the they were measurably not perfectly parallel to each other by about ~11cm or something like that.

 

[beansbaxter]

it is level if the customer/foreman thinks its level and the check clears

 

[beansbaxter]

Originally posted by: grant2
I always imagine "what if the earth was a cube?"

It would be really neat to climb to the 8 corners because they would get steeper and steeper.

And i guess there would be 6 oceans, one on each side.

WOW!

 

[beansbaxter]

absolutely true about gravity not being perfectly equal. all mass generates gravity (yes, i know that statement in itself isnt correctly phrased), so a mountain or a valley etc will all affect the results. but we're talking about a generic quastion so we have to assume perfectly generic parameters, which is a smooth, round sphere. i used the radius at the equator in calculating it which of course is only accurate when placing your board on the equator. but given that we were assuming a frictionless surface, i kinda took the other assumptions to be fair game as to your example of putting the high end off the board next to the base of, say everest, it may infact no roll due to the direction of gravity being slightly shifted there. if it's enough tho, i'm not sure. everest may be pretty massive, but it's pretty puny compared to the earth as a whole.

 

[DrPizza]

Originally posted by: beansbaxter
absolutely true about gravity not being perfectly equal. all mass generates gravity (yes, i know that statement in itself isnt correctly phrased), so a mountain or a valley etc will all affect the results. but we're talking about a generic quastion so we have to assume perfectly generic parameters, which is a smooth, round sphere. i used the radius at the equator in calculating it which of course is only accurate when placing your board on the equator. but given that we were assuming a frictionless surface, i kinda took the other assumptions to be fair game as to your example of putting the high end off the board next to the base of, say everest, it may infact no roll due to the direction of gravity being slightly shifted there. if it's enough tho, i'm not sure. everest may be pretty massive, but it's pretty puny compared to the earth as a whole.

Wait a second. If we assume a frictionless surface, the ball will NOT roll. It will slide.

I did a quick (rough, and possibly has an error, since I didn't draw much of a diagram) calculation for the force on a 100kg ball 1.0 kilometers away from the point where the "ramp" is perpendicular to the direction of earth's gravity (assuming a perfectly spherical earth, etc). Using 6350 km as the radius of the earth, I calculated a force of .15 Newtons parallel to the "ramp"
980Newtons * sin(arctan(1km/6350km)

Of course, my method of calculation isn't perfect, since it neglects the greater distance from the center of the earth. Nonetheless, the difference is far far less than the precision of my acceleration 9.80 m/s^2
The actual weight would be .9999999752*the original weight.

Assuming a spherical Mount Everest, mass 5x10^10 kg (googled it), and that the distance from the center to be approximately3 km (a guess), using Gm1m2/r^2, I calculated a force of around 40 Newtons??.
oh sh!t. I forgot to change it to meters. Damn it!
make that 3.7 x 10^-5 Newtons.

Mountain isn't enough to stop it if it's frictionless. However, if it's frictionless, as I said above, it won't roll, it'll slide.

Well, I was almost about to calculate the velocity of the ball as it passed the center of the ramp, but I'm done procrastinating something else now.

 

[beansbaxter]

If the surface of the board is always equidistant from the center of the earth i.e., (yielding a curved board) the ball just sits, of course. Given that the center of the gravitational force lies at the center of the mass, and that the mass is a true sphere, the force vector goes to that center. But if the board is flat, the ends of the board become relatively "uphill" from the center of mass (and "pull") and the ball rolls to the center where the board contacts the sphere (earth).

The turn & slip indicator in an airplane (that little curved glass tube with the black ball in it) is a very simple and precise indicator of this. When that ball is at the low point of the curved tube, all is right with the world. Roll the airplane off level while keeping the nose on a point and that little ball always stays "down" with great sensitivity.

 

[beansbaxter]

Actually, have you not considered unified field theory, wherein the very fabric of the universe distorts around 'pools' of mass. So nothing is ever truly 'level'.

 

[jmagg]

Interesting concept.
As a builder, I will now need to begin footings in the middle, and work out to the ends, to achieve a truely level end product. Simplistic yes, but will prove to be interesting construction field fodder.

 

[josphII]

you are both wrong. if the system is truely frictionless the ball would oscilate back and forth

 

[Smilin]

Originally posted by: josphII
you are both wrong. if the system is truely frictionless the ball would oscilate back and forth

true

 

[DrPizza]

Originally posted by: Smilin

Originally posted by: josphII
you are both wrong. if the system is truely frictionless the ball would oscilate back and forth

true

yes, and without rolling.

 

[Basse]

Originally posted by: beansbaxter
The turn & slip indicator in an airplane (that little curved glass tube with the black ball in it) is a very simple and precise indicator of this. When that ball is at the low point of the curved tube, all is right with the world. Roll the airplane off level while keeping the nose on a point and that little ball always stays "down" with great sensitivity.

Speaking of airplanes, a different view on this topic.
Say your in a Concorde that can go halfway round the world without refueling. If you wanted to stay @ 80,000 feet the whole trip, you would have to keep the rudder at a constant slight downward position. Otherwise the altitude would increase as you go. (I have deliberately kept gravity out of the example).