mjrpes wrote:Does this asymptotic graph hold as the object passes through the surface and heads to the centre?
It would against a different axis (the graph would switch to a different section on a cartesian coordinate system)...but when I was discussing that I wasn't referring to one object passing directly through the center of gravity of another. In that case, distance would be 0, which would lead to an incalculable answer, as you can't divide by 0.
Ok jules - here is the answer, from a PhD in physics, about the whole "is zero net force the same as no force..." and a few other things...
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(BODY OF EMAIL)
Hi Eric,
This is not a simple question to answer, as you have discovered.
Neglecting pressure (assuming the ball was in a vacuum shaft for
instance) and neglecting the fact that the ball has a measurable size
(i.e. we don't worry that half the ball is on one side of the center,
and half the ball is on the other) then:
According to Newton, we would say that the forces acting on the ball are balanced, and so the net force adds up to zero. Newton would not say that there are no forces on the ball.
According to Einstein, there is NO difference between a balance of
forces and no force whatsoever (except on the smallest scales where the laws of quantum mechanics rule.) So according to Einstein, any of your statements are fair to say.
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So, balanced forces and no forces are both the same thing. I say no net force, you say no force, and the bottom line is there is no real difference between the two, according to Einstein.
I wasn't asking him about that...I just was asking about whether balanced gravitational force is the same thing as no force.
I'll ask him the other one...but please paraphrase it for me here (he is a college professor, and I don't want to bug him with having to sift through extra info - so the more direct a question you can give me the better.)
I think I know what you are getting at, but please restate the question in a stand-alone fashion and I'll get it to him.
If a ball is being tugged by two ropes from opposite directions with equal force (ropes are connected to opposite ends of ball), the net force is zero. Yet the ball experiences a stress force - we understand this when we see the ball as comprising of parts. The rope is only connected to the edge of the ball, so there is a tension force since the other elements of the ball are not being pulled by the rope directly.
In the case of a ball suspended between two large masses, the two gravitational forces cancel out. The question at hand is whether a tension force is similarly experienced.
My intuition is that there is no tension force, since gravity acts upon all the "parts" of the ball simultaneously.
If this is so, then there is a major difference between the two scenarios (rope vs. gravity).
Got the answer back from the physicist. The ball will experience tension.
I PMd you the whole explanation.
But one way to think about it came to my mind as I read your idea.
You said that there will be no tension, because gravity acts on all 'parts' of the ball at once...
True, it does act on all 'points' - but only at the center of the ball will these forces be in equilibrium. Take a point X near the left edge of the ball. That point will experience a greater gravitational force from the object on the left than it will from the object on the right since it is closer to that point. These forces will not be in equilibrium....so there will be tension.
Yea - if the ball was a point it would be a moot issue. The dimple analysis works too, as in a few posts back, since the left and right side of the ball would be on different angled dimples, and only the centre would be in that perfectly flat region.
So - if you were in the centre of a really really large planet, i'm assuming you'd probably be ripped apart by the gravitational forces around you?
Jules - I really recommend that you read a couple books - here they are:
"Before the Beginning" by Sir Martin Rees
"The Fabric of the Cosmos" by Brian Greene
Both will touch on some of the things we've discussed and are great reads.
As for the center of the planet -
Tidal forces might rip you apart. The coriolis effect would also have to be factored in.
Did the PhD's answer make sense and address the question at hand?
Also - another good book that I am reading right now - "Scientists Confront Creationism"
edited by Laurie R. Godfrey
Unrelated to this discussion, but still a collection of great essays.
Put them on your 'to be read' list.
yea his answer made sense - as you go from the centre of the ball toward its end, the relative force of gravity from the planet nearer that end, gets greater and greater, resulting in a tidal force.
scary shit, gravity is...
tx for the recommendations.
i've heard of coriolis force but don't really know what it is. Will look it up.
[xeno]Julios wrote:yea his answer made sense - as you go from the centre of the ball toward its end, the relative force of gravity from the planet nearer that end, gets greater and greater, resulting in a tidal force.
scary shit, gravity is...
tx for the recommendations.
i've heard of coriolis force but don't really know what it is. Will look it up.
This thread's been educational
It was funny, because I emailed him this morning, then went to the gym, and in the middle of a set of preacher curls the tidal force thing suddenly hit me out of the blue...the relative gravitional forces are only all balanced if we view the ball as a point, which it is not. Thus, there will be tension from tidal forces. It was an epiphany during a workout, probably caused by the endorphins helping me think clearer. heh.
[xeno]Julios wrote:
So - if you were in the centre of a really really large planet, i'm assuming you'd probably be ripped apart by the gravitational forces around you?
actually, come to think of it, since the ball is so small compared to the size of the planet, the differential forces would be practically negligible insofar as dangerous stress is concerned.
