Unattractive Earth
Neglect the effect of rotation of the earth. Suppose the earth suddenly stops attracting objects placed near its surface. A person standing on the surface of the earth will...
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
What a load of rubbish. Has everyone forgotten the 30km/s orbital speed of the Earth w.r.t. the Sun? The person would start sliding slowly, until eventually completely detaching from the Earth.
For an extreme case, imagine a magnetized steel ball, and a much smaller magnetized steel rod. Assume they stick. Now, tie a string to the ball and start spinning it about a fixed axis of rotation. Now, using some electronic device or a signal, deactivate the magnetic field of both objects; are you trying to tell me that the rod will stay put?
Good luck, kid.
Log in to reply
John, I guess this is another one of those physics questions where you're supposed to assume a lot of unspoken things, such as, "Oh, by the way, the Earth is just hanging in space all by itself, besides not spinning". Then, yes, nothing happens to a person standing on it when the Earth's gravitational pull is shut off. Because nothing was moving in the first place.
However, as you've amply pointed out, in the real universe, the Earth is undergoing a complex gravitational freefall because of other gravitational bodies, like the moon, the sun, planets, the galaxy, etc. So, if just the Earth's gravitational pull is suddenly shut off, then it's exactly the same as if the Earth itself has disappeared, and the poor person is left to carry on this complex gravitational freefall through the universe. It's the suddenly massless Earth that will proceed on a straight line while the person goes off in a curved path, so that the correct answer is probably, "fly along a tangent to the Earth's surface", but in truth it's a bit complicated, depending on the person's complex freefall path, and where the person is on the Earth at the exact moment it has become massless.
But even that is making yet another unspoken assumption, and that is, it's ONLY the Earth that has lost its gravitational pull, i.e. behaves as if it has suddenly become massless, but meanwhile the person retains his own mass, along with other massive bodies still in the universe.
It's a complicated and interesting question. See my response to Abhineet Nayyar, regarding General Relativity.
Log in to reply
What if anyone starts walking or jumping? :D
What would happen to the atmosphere of the earth?
Log in to reply
@Soumo Mukherjee – It's be the same as what would happen with an astronaut on a really tiny asteroid, if he were to try to walk to jump. And that's going to involve yet another unspoken condition--will the Earth still retain its inertia?
The atmosphere will go where the person will be travelling. Of course, in a short time, it'll diffuse into space, because the molecules of the atmosphere aren't static.
Log in to reply
@Michael Mendrin – Yes...Moreover there is no gravity to attract the atmospheric gases and particles near the Earth's surface...and it might escape into the Space...Can this happen??
Alright so I didn't read much what of what was said below, but I agree with your point on "unspoken word." We are making lots of assumptions.
The way I interpreted this problem is via a conceptual classical problem, with the Earth being perfectly spherical and round, and it retaining its mass while simply losing its gravitational pull. In other words, we're really trying to determine the fate of a point mass as two types of important forces disappear (centripetal and gravitational).
In the "real" world, I cannot think of the possible consequences of losing gravity, but if we remain simplistic, it would depend on where you reside. If you're in a rainforest or your own house, you'll just be slammed into the nearest obstacle. But, in the problem's case, it's probably more like the desert.
And so, under all ideal conditions, I think my earlier solution will stand. That is, we assume the Earth keeps going 'round the sun. So probably first we will slide a bit, and then SLAM a bit, and then go off the tangent.
Log in to reply
@John M. – Tangential thought .....
What if all living creatures were spread out evenly over the surface of the Earth, (on boats where necessary), attached to each other by ropes. Then if the Earth were to simply disappear, the "web of life" that remains would continue to orbit the Sun, albeit at a different radius because our collective mass would be much less. We would have to create a spherical dome enveloping the Earth beforehand so as to keep some air to breathe, and perhaps allow for all the fresh water to remain as well. We should start preparing ..... Or perhaps we should take Newt Gingrich's advice and start colonizing the Moon and Mars. :)
First of all, there's no need to be rude!! Second of all, the Earth won't stop revolving around the Sun!!!!
@John Muradeli , Earth has stopped attracting us...But it is still moving around the Sun, with the same 30 Km/s...We would only fly off with that speed, if the Earth would stop revolving, but here it does not do that!!
Log in to reply
aren't you just forgetting that earth has stopped attracting objects, there are millions other stars and planets still attracting the person. with this sudden change, the potential energy of the body in the gravitational field will be hampered and the person wont just remain where he was. the rotation of the complete solar system, the galaxy and the expanding universe still apply forces and the most probable answer should be to fly along a tangent.
Log in to reply
@Ansh Bhatt – I would request you to read the question again @Ansh Bhatt , It states that earth has stopped attracting objects near the surface...So, that doesn't account to the hampering to the potential fields of the stars and the planets!
Log in to reply
@A Former Brilliant Member – keep two magnets together. they attract each other. now replace one of it with a piece of iron. the magnet will still attract it. though the earth has stopped attracting the person, the sun, for example, has not stopped attracting the person. think over it keeping this perspective in mind
Log in to reply
@Ansh Bhatt – I know...what you are saying is that, since the sun attracts the man towards it..the man should fly, right??
Log in to reply
@A Former Brilliant Member – thats what.....in fact all of us are correct in our own ways....now the question which arises: what should really happen? because it is possible that all of us are wrong and the solution is something totally different.
Log in to reply
@Ansh Bhatt – but look...even if the sun attracts the man...he is still moving with a speed of 30km/s...and thus the centripetal force might balance his motion!! And hence, the man must stay!!!
Log in to reply
@A Former Brilliant Member – the thing is it 'might' balance. it 'might' not. now it is a question on which we can debate tirelessly
Log in to reply
@Ansh Bhatt – no...it will surely balance... See, when the Earth and man is moving with a speed of 30km/s...then the entire system is bound to the Sun, and down not flow off...After the gravity turns off, the man and Earth will still move with the speed of 30km/s...and this velocity is the same as the initial velocity. So, the man will surely stay in the orbit around Sun, stuck to the Earth's surface. Remember, the centrifugal and gravitational forces are independent of the mass of the object!!
Abhineet, but, actually, no. If the Earth suddenly became massless, it will stop orbiting the sun and start on a straight path with uniform velocity. Well, even that supposes YET another unspoken condition--would the suddenly massless Earth still obey the laws of General Relativity, or no?
This sound like what happens when attorneys battle in court, doesn't it?
Log in to reply
@Michael Mendrin – Haha...Yea..But i don't think, the question assumes Earth to turn massless...What i think is that we just assume the Earth's gravity near the surface to decrease to zero, due to a hypothetical alien phenomena...What if we think of it this way...?
Log in to reply
@A Former Brilliant Member – I think poor Albert Einstein would be spinning in his grave at the idea of Earth's gravity "near the surface decreasing to zero". How would one warp spacetime to produce this effect? Making a wormhole would be much easier.
Log in to reply
@Michael Mendrin – Hehehe!:D:D Poor Einstein..Lmao
Yeah sorry about that I never intended to be rude :p All those politics getting to my head lately.
Also, I don't feel like this is pure science fiction. The problem unnecessarily assumes the unrealistic condition that the entire Earth's gravity will be "turned off"; instead, we could simply assume that a person has worn an anti-gravity suit and pressed the on button. There, that's not as controversial.
Okay, I have gone through your comments once more. And now I agree with you.
The only reason why we would not slide could be explained by friction. In your simplified model of "bigger ball and smaller rod", when the big ball gets de-magnetized the small rod will have a sliding tendency. This tendency would be opposed by the friction between the small rod and the big ball.
But how much is the friction? How much is the force due to sliding tendency? Is the latter greater than the former? The sliding tendency can overcome the maximum static friction. And the rod would slide "until eventually completely detaching from the Earth." Still we need more data and more analysis to confidently say that.
And I think we should add a separate option "(E) not sufficient information" as the correct answer.
0_o
We need to answer under the assumption that effect of rotation of earth is negligible. Will then inertia be the answer?
That's why the assumption "Neglect the effect of rotation of the earth" is stated at the very beginning :)
Nice solution.
Log in to reply
Yea!:) Had it been not mentioned, we would have flown right off...hehe
Log in to reply
Me be like : "A mountain in labor and a mouse be result."
Log in to reply
@Soumo Mukherjee – Actually, I find this subject interesting. It may be muddled and infuriating, but it does pose the kind of "what-ifs" questions that sometimes do lead to interesting physics. Look up Mach's principle, as a related example.
Log in to reply
@Michael Mendrin – Can earth really lose its gravitation. It is billions year old, has there been no change in its gravitation.
I cannot understand this line "local inertial frames are determined by the large scale distribution of matter" A frame is inertial or non inertial is determined by applicability of Newton's law right?
It's nice that you find it interesting. I want to discuss more things.
Log in to reply
@Soumo Mukherjee – This reminds me of the time a meteorite expert showed, in a microscope, an inclusion in a sliced meteorite which contained water and a bubble--which was about 4.5 billion years old. Think about that--a tiny bit of water and a bubble, unchanged in 4.5 billion years. Just because something is really old doesn't necessarily mean it's aged. That's almost like wondering if the Earth can get tired of "being round like a ball".
Mach's principle was one of the things that led to the formulation of General Relativity, which holds that certain attributes of local bodies cannot be independent of the universe at large. That is to say, if the universe were to simply disappear, then certain physical properties of a local body will vanish as well. Einstein understood the implications of Mach's conjecture, and formulation his connection between gravitation and curved spacetime, which was a major departure from the older Newtonian interpretation of gravity.
Nevertheless, some scenarios of the universe in the far future paints a picture of a cosmos where even spacetime breaks down, so in that context, yes, finally it's possible that Earth (if it was still around) would its gravitational pull, along with a lot of other physical attributes. This is fairly far-fetched stuff, and cosmologists and theoretical physicists are still arguing about the ultimate fate of the universe.
Log in to reply
@Michael Mendrin – Speaking of mass - i've watched a video not too long ago by veritasium, in which he states that most of an object's mass is derived from its energy, not the higgs field (i think ~99%). I gave it thought, and conjectured that it has to do with net momentum. Why? Well, I know very little of quantum chromodynamo, but of what i know, I know about force-transmitting particles, quarks, bosons, and the other soup. So, I thought, you know, just like with mass particles, say, billiard balls, if a particle is made of those other, massless particles, and if those massless particles (say photons) transmit force (EM), then they must interact with the other particles. In this case, newton's third law kicks in and now their interactions have the same effect as on macro scale; and hence, momentum. So say two quarks of an atom meet one quark of another atom in a 1D simulation; assume they move the same speed; the one with two quarks "wins" and thus the "net" momentum (or energy) is toward the two quarks' direction. Now if we assume there's many, many quarks, and they move way faster, they tend to get their way much more than an atom with one quark that moves slow. hence, the other system has way more ... tendency to get its way, or, resistance resistanceness, or, inertia , or, MASS . its cause of individual velocities and total energy count (energy as ... somehow purely determined from their motion? maybe they get some instantaneous mass from the higgs field?)
Dunno. I have way more to learn. I don't even know nuclear physics. I'm like 22 weeks behind in my virutal high school work (physics & statistics), so I gotta catch up, FAST.
So, was I close? Probably not. Anyway, hope I didn't waste your time with my poorly written machinations.
Cheers!
Log in to reply
@John M. – How about if you took a peek at some of the actual quantum field theory math explaining the Higgs mechanism? This is merely an introductory text.
Masses and the Higgs Mechanism
It's pretty well thought out, and trusted enough for CERN to have spent many billions of dollars to confirm the existence of the Higgs boson. If some other, far much simpler theory explained mass, well, CERN would have found out by now that they've wasted all those billions on a theory that didn't work. It's kind of like how some people still insist that spacetime can't be warped, as predicted by General Relativity, while in the meantime heavily relying on GPS used by their smartphones. If General Relativity wasn't true, then GPS today would be way off, and Google maps would be putting smartphone users in the all the wrong places.
Log in to reply
@Michael Mendrin – So, no?
Alright I'll look into it. Thanks! (and yeah I know all about relativity research, and how they spent 2 billion $$$ digging a hole and filling it back in. What a bunch of baboons US Congress)
Log in to reply
@John M. – CERN isn't exactly "relativity research", although a couple of relativity projects, LIGO and Gravity Probe B, did cost between them about a billion. I am a strong believer in the value of high end physics projects, because in the long run, they pay for themselves many times over.
Our current US Congress is busy cutting off funds for science projects--and that's a shame. The US military is spending over $600B a year, and Congress wants to increase it--while cutting back science. I remember a time when it wasn't like that, but things have changed.
Log in to reply
@Michael Mendrin – $600B?!? That's cute.
Recently they've ordered some sort of plane that costs $400B alone. Dunno if it's a God-plane or some crap, but I'm sure it's not going to win all wars or end all conflicts.
When I was in HMC, I was in the House of Intelligence, and so I had to research the Department of Defense. They allocate BILLIONS by day to developing weaponry. Now, I don't know what they define as "military budget," but I'm sure it does not fully factor in the war spending. It's probably a couple figures more.
Either way, Military spending tops 30-50% each year, whereas science remains <3%. Absolutely ridiculous. And yet watch all the scientific advancements. Imagine if we could direct all that money into science?
That would be a catastrophe.
Log in to reply
@John M. – It's the Lockheed Martin F-35 fighter jet program that you're referring to. which is expected to have a total cost of about $1.5T. Yes, that's right, T, not B. And it DOESN'T EVEN WORK!
One of the saddest times I can remember was when Congress back in 1993 killed the SSC project. Suddenly, in one fell swoop, America fell right off its position as the world leader in high energy physics. The projected cost was about $5B--which is about what CERN subsequently spent to discover the Higgs boson. Many of the top physicists followed the project to CERN, and America was never the same again. The torch has been passed on.
Log in to reply
@Michael Mendrin – WHAAAT?!?!?!?!?!??!?!?!?!?
you're lying.
proof?
DUDE! 1.5T??? WHAT IS IT SUPPOSED TO DO, GO THROUGH WORMHOLES AND WARP REALITY?? ? SHOOT ANTIMATTER AND ABSORB NUKES??
Okay, US, okay.
okay...
on is a fish
@John M. – It has been a long time since you have conducted any discussion. Like this one : "Time" .
When you get some free time from AP and studies, plz start one. It's fun and enlightening (if I can make out what is being said) to have John Muradeli, Brian Charlesworth and Michael Mendrin debate on topics
The community would love it
:)
@Michael Mendrin – We were discussing about friction yesterday. What would happen if friction and gravity both decide to abandon us. Will then mankind perish?. Hollywood should make a movie on this. Sequel to "2012" :)
Log in to reply
@Soumo Mukherjee – I think this time the arks would simply keep on going into empty space, and nobody would hug any more at the end because you need friction for that.
@Soumo Mukherjee – before they decide to abandon us man would have progressed enough to create artificial gravity and friction :p
Log in to reply
@Ansh Bhatt – This should go into the climax of the movie I am talking about.
Log in to reply
@Soumo Mukherjee – Hahaha...Why dont you make one @Math Philic ?? Lol
@Michael Mendrin – What would happen to atomic structure if subatomic particles suddenly became massless? I realize that the electroweak and strong forces dominate at the atomic level, but I can't help but think that turning off gravity would have some effect. And I'm not even sure what the concept of "substance without mass" really means. Does pure energy, (e.g., photons), have substance?
Log in to reply
@Brian Charlesworth – You know, i asked these questions to my physics teacher...And he told me about Einstein's complete formula for E=mc^2 which includes momentum as well, and that is what relates pure energy, example photons,with substantial qualities...What do you think? Moreover, at the subatomic level the effect of gravity can be debated, although i feel its absence would not have a significant effect..
Log in to reply
@A Former Brilliant Member – Good point. When a system with mass absorbs a photon with energy E its mass increases by an amount c 2 E , so a photon is in essence "potential mass". Along with the fact that a photon has momentum h ν , I guess that the notion of "substance without mass" does have some meaning.
Without the concept of mass, though, E = m c 2 would no longer have relevance. In a universe with only electromagnetic, weak and strong forces, I don't think atoms (and humans) would start flying into pieces, but celestial bodies would no longer be "bound" to one another through gravity. Scary thought. :O
@Brian Charlesworth – A number of particles are massless, like photons. gauge bosons, and, theoretically, gluons. It simply means they're unaffected by the Higgs field.
One of the greatest unresolved problems in theoretical physics is finding a way to reconcile General Relativity with Quantum Field Theory, which the Standard Model is based on. For instance, in General Relativity, gravity is caused by curved spacetime, but some models in Quantum Field Theory (including String Theory) proposes that the carrier of the gravitational force is the graviton, which is also supposed to be massless. But so far, its existence is still hypothetical and never observationally confirmed.
The idea that we either have "things that have substance" or "forms of pure energy which have no substance" now belongs to simplified science fiction for laymen. It seems intuitive and appealing, but the real mathematical apparatus behind modern particle theory is much more convoluted than that.
Log in to reply
@Michael Mendrin – Thanks for setting me straight. I should have known that my binary thought process was flawed. As you've said often before, we should be taking cues from the mathematical findings no matter how (initially) unintuitive they may be.
I have read a number of the posts hear I may have missed this but everyone seams to be ignoring the fact that the earth is rotating on its axis as well as traveling around the sun.
If I am standing on one of the poles I have no angular momentum, however If I am standing at the equator I have plenty of angular momentum. Earths gravity is constantly pulling object sitting on the earth towards earth center of mass. Without the gravitational pull all of the object sitting on the earth would stop the constant angular acceleration. Any object not on the pole would just continue to move in the direction it was moving when the gravitational pull was removed. That would mean that most object would immediately leave the earth surface and fly off in a straight path tangent to the earth surface, in the direction that they where moving do to the rotation of the earth on its axis. So relative to the earths position most object would now be moving away from the earth tangent to the earths surface.
Well, this question can be answered in a word: INERTIA! An object tends to stay in it's natural state unless an external force is applied on it. Since, in this case, there is no external force, as the force due to rotation is neglected, then, we will stay standing up as we were, before the gravity switched itself 'OFF' .