Gs

Spaceship.

Spaceship.

Hum, I am an avid reader of science fiction, and there is something I've been wondering, in the same lines:

Let's imagine a spaceship in the shape of a cylinder, spinning on it's longitudinal axis. People live inside on the edge, and the spin gives them 1G. Now, I imagine that if they took a ladder to the center, they would experience decreasing Gs until they would float in the middle..

I assume that if they floated slowly back towards the edge, the air friction would give them back a spin and bring them back to the edge..?

Now, let's say the edges of the cylinder are open the the vacuum of space, no friction. Someone walking inside could jump up a few inches, but being spinning, they would fall back "down", maybe a very short distance from where they jumped.. But if they took the ladder to the center, then let go and floated back toward the edge, could they float a few feet from the ground as it passed beneath them?

Gil.
 
If you were to drop a feather or a canon ball from great height (but equal) which would hit the ground first?

The canon ball would hit first because it's terminal velocity is higher, but in a vacuum where there are no aerodynamic effects then both the feather and canon ball would hit the ground at the same time.

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The air friction of the air along the side of the cylinder will produce a rotating force that would result in everyone rotating, the closer to the edge of the cylinder the least rotation, those in the centre would rotate the fastest.

your analogy by the way is exactly how how our climate works. Little movement along the equater and large movements at the poles.

BTW Gil I like where you going with this. But I want to throw something out there as well.

We know that gravity increases as you approach the centre of the earth, what would the graivity force be at the centre of the earth?
 
Why is its terminal velocity is higher? or maybe I should re phrase what would hit the ground first, a 1cm round spherical shell or a 1cm lead solid sphere
 
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Jordan, I would have never guessed gravity increased towards the center of a planet! Maybe we'd find a tiny black hole there!

Ever heard of Dewey B. Larson's Reciprocal System of physical theory?

Gil.
 
If I understood Newton correctly, in a vacuum on earth, a 1000lb and a 1oz object of any shape, will fall at the same rate of acceleration. Now if they are moved to the moon, they will weigh less, but still fall at the same rate. There would be no falling at the 0G point between the earth and the moon…except for the gravity influence of the sun.
 
Here is one of the neatest thought experiments I know. It is the actual thought process that Galileo went through when figuring out that all bodies fall at the same rate, regardless of their weights (in the absence of air friction).

This elegant proof shows that all bodies fall at the same speed (i.e., accelarte at the same rate), inedpendent of their masses. To prove this statement, let us assume that actually heavier bodies fall faster than light ones. If this assumption leads us to a contradiction down the road, we will have shown that the original assumption must have been wrong and therefore cannot be true.

So let's start by imagining two balls of identical dimensions: one made of wood and the other of lead. The wooden ball is, of course a lot lighter than its leaden counter part. By our assumption (which we want to show is wrong), the heavier object should fall faster, i.e., the wooden ball should lag behind the lead one on their downward journey.

Before dropping, let's join the two balls by a short piece of lightweight string. So that they cannot really separate but are kept together by it.

Once we drop the assemblage, we expect the lead ball to be ahead since we think it will drop faster. The wood ball will lag behind and, because they are joined by the string, tend to slow down the lead ball. The net result is that the joined pair of balls ought to drop slower than the lead ball by itself.

However, you can look at the joined pair of balls as an object by itself, which is heavier than either of its constituents. After all, it has the combined weight of lead and wooden balls. Therefore the joined balls -- seen as an object as a whole -- should fall faster than either the lead or the wood ball taken by themselves.

And here you have it: looking at it one way the two balls should fall slower than the lead ball (because it is hampered by the wooden one), and looking at it another way, they should fall faster (because you can view it as an entire object comprised of two balls). This is a contradiction which can only be resolved if both balls fall at the same speed, regardless of their weight.

-- Chris.

P.S.: I know this is a bit beside Birdy's original question but I just had to sneak this little gem in. :)
 
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Nice comeback Gil!

But when does gravity stop?
 
Chris you didnt tell us whether the the individual all the combined balls falled faster. I am sure Galileo would have measured both.
 
Why is its terminal velocity is higher? or maybe I should re phrase what would hit the ground first, a 1cm round spherical shell or a 1cm lead solid sphere

Given the same size parachute, who would have the higher sink rate and hit the ground first, a heavy man or a light man?
Answer that and you have the answer to your question.

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I wish I knew, I'd be making more money! Maybe it doesn't stop until there is enough mass and energy there to trigger a reaction, not unlike fission, and wham! You get another big-bang and a new universe somewhere else.. Or maybe once the elasticity of space (if there is such a thing) is exceeded by mass, it breaks and all falls in a never ending gravity well.. I won't pretend to have a clue, especially before my morning coffee ;-) That "more gravity near the center" will sure bug me for a while...!

Sorry about taking this thread somewhere else Birdy!

Chris, that's a great story about Galileo, thanks!

Gil.
 
It will probably depend on whether the heavy man is rotound or not
 
I assume that if they floated slowly back towards the edge, the air friction would give them back a spin and bring them back to the edge..?Gil.

The aerodynamic effects of any air friction would be weak on the floating persons mass and would not be able to accelerate them rapidly enough to match the velocity of the cylinders inside surface before they made contact. The result would be a "crash".

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Gravitional force at the centre of the earth is zero. Gravity is simply the force between two bodies propotional to the mass and distance of those bodies. At the centre of the earth there is equal amount of mass in all directions so the gravity is zero. The accelaration towards the centre of earth decreases. The 9.8 m/s/s we use is actually at the surface of the earth it would be slightly less and decreases as you move towards space.

If you were to approach earth from space you would experience an increase in gravity as you approach until you are within the 100km (or there abouts) when you are reach 9.8 m/s/s. Remember the Earth is 6000km radius.
 
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Alan even though the difference mass of the air and mass of the human are great, over time if the rotation is constant the air will accerate the greater mass to the point that both will rotate at the same velocity, less aerodynamic drag. Even if they do crash
 
That thought experiment was neat Chris! I never heard that one before.

Any mass has gravity. If we placed those same lead and wood balls inside a hollow metal sphere and moved them into deep space, they would float to the center of this sphere. The lead ball would float to the center and the wood ball would snuggle in beside it. If we placed a large mass outside the sphere, the balls would then gravitate to that mass…..as I view it ;).
 
Gravity cancels out for all points inside a hollow spherical shell. There is no tendency for objects within to move to the center.
Quoting from http://www.physicsforums.com/archive/index.php/t-121120.html
This can be shown by adapting the integral form of Gauss's Law replacing the magnetic field with the gravitational field. If you are not yet familiar with vector calculus in order to use Gauss's Law directly, then you can simply think about it this way. In the exact middle of the hollow shell, there will be a gravitational pull from every point on the shell, but each point will have a different direction. In fact, for every point with a gravitational pull in one direction, there is a point on the exact opposite side of the ball with the same amount of pull but in the opposite direction.

As you move from the middle to some other point inside the ball, you move closer to one edge of the ball than the other, and thus the forces from one side become stronger than the other. However, there is a competing change, as you move towards one side of the ball the amount of material behind you gets large, as you get closer to the material in front of you, these two competing changes will tend to cancel each other. What Gauss's Law beautifully proves, and what you may not guess intuitively, is that these two competing changes actually cancel each other exactly. Thus there is no net gravitational force anywhere inside the hollow spherical shell.
External masses would attract the balls and the sphere at equal rates and the balls would not move relative to the walls of the sphere if they were at rest to begin with.
 
I heard of Gauss….but not this law. Hmm….my commonsense view doesn't seem to agree with this guy's law…although it does tend to possibly sound somewhat reasonable. If you agree with him Al (good to read ya)….I yield…..except for the exterior mass, because that gravity should also act on the balls inside the spherical shell....being gravity does not attact the same as magnetic forces, I think ;).
 
with regard to Terminal Velocity it is a variable that changes with the medium and the size body that is moving through it towards the object or mass exerting the attraction.

During project Excelsior in 1959 Captain Joseph Kittinger USAF free-fell for 4 minutes and 36 seconds from a height of 102800' It took 13 minutes and 45 seconds. During the descent, Kittinger had a variable TV and reached a top speed of 614 mph before this reduced in the lower increasingly denser atmosphere.

In normal lower range skydiving in a stable face to earth position in the early days we had a TV of about 120mph though in the track this velocity increased. Later suits slowed this down to extend freefall time.

In a vacuum as someone has already pointed out everything falls at the same rate, and in steady state velocity, my guess, 1G
 
Alan even though the difference mass of the air and mass of the human are great, over time if the rotation is constant the air will accerate the greater mass to the point that both will rotate at the same velocity, less aerodynamic drag. Even if they do crash

This would only be true IF there were a force allowing the person to hover above the inside surface of the rotating cylinder and allow the aerodynamic forces, over time, to accelerate that person to matching speed. This force would also be needed to allow the person to take on a curved trajectory to match the curvature of the cylinder, a rope attached to a frictionless bearing located at the cylinders center would suffice.

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