The “ordinary” equation for gravitional potential energy they teach kids is
PE = g m h
(Acceleration due to gravity, e.g., 9.81 m/sec^2 at the Earth’s surface. Mass. Height.)
But this is an approximation and is only when the “marble” has low mass compared to the mass of the Earth and is the difference in PE between 1000ft and the Earth’s surface. The approximation doesn’t work for heavy objects. E.g., at two Earth masses.
The comparison of delta PE between the Earth’s surface and 1000 ft up doesn’t matter here. The marble isn’t going to stop when it hits the Earth’s surface. It’s going to keep on going! So that extra 1000 feet affects low end digits. Not the big picture.
And, as to the big picture. It’s going to be heavily overexposed to say the least! The biggest flash of light you ever saw is nothing compared to what happens.
Exactly. I’ve clearly stated what I’m asking, and I’m pretty sure everyone understands the question.
In my scenario, I am a being of God like powers and I make the rules. The rules are to erase the gravitational effects of the marble, and to see what happens when I throw that marble to the ground. The weight could be 10 earths… it doesn’t matter, the weight is arbitrary… it just has to be a huge amount in a tiny object… like a marble… a marble that will never explode or change shape.
I’m interested in which is the most likely scenario - will the marble easily pass through whatever it touches without fuss, or will there be an explosion of epic proportions, even if the marble remains intact…
I think it would punch through the earth like a bullet fired at a watermelon. Yeah, it’s only going 150 mph, or around that, but what could possibly stop it? It pushes right through dirt and rock, as easily as if moving through air.
There’s some friction as it passes through, so it won’t go all the way out again, but fall back toward the center of the earth, oscillating until it stops, right in the center.
Having no gravitational effect, that’s pretty much the end of the story.
And now we are back to “What does god wish it do do” because he is remanipulating everything by divine intervention.
Everything that should be happening is given the answer “No i suppress that”
When this divinely intervened object lands on the earth, since it has no forces of its own
now becomes part of the mass of earth, unless you are going to intervene on that too?
Because now we have earth with an earthX2 weight lump on one side, and earth is probably going to disassociate with itself in an attempt to redistribute the mass.
I mean how many real effects are we going to eradicate here?
Not really, because it still has Mass
And earth does have gravitational effect, and if you stick this in the earth, since it has been robbed of its own effects, it’s going to become part of earths.
Also the pressure and energy of earthX2 trying to push through earth if probably going to be enough to get a reaction from something, that is if earth with now over 2/3 it’s mass sitting all in one non central place is not going to react kindly to it.
And if you magically get said marble into the center of the iron core, you have another problem.
Now you have EarthX3, what happens when earthX1 suddenly becomes earthX3?
This is an incorrect way to frame the question and attempting to consider the problem in these terms doesn’t work.
The Earth isn’t going to act like a solid object for this problem. It’s sort of going to act like a swimming pool full of ping pong balls (SPPPB).
If you put a watermelon in front of a speeding train, the watermelon explodes, but if you dropped a bowling ball into an SPPPB you would only get a displacement of the balls around the bowling ball as it falls though the balls until it hits the bottom.
Your magic marble isn’t going to notice anything in its path. The difference between air and solid metal would be insignificant for something that dense. It simply would do through whatever you put there.
Nothing could cause an explosion.
The friction of the Earth would be insignificant but it would still act like a pendulum because of the effect of Earth’s gravity on it (assuming the magic marble acts like a one-way receiver of gravity).
Once it passes through the center of the Earth, gravity would start to slow it down until it reached the same distance from the center as the initial condition, it would come to a stop and then go back through.
Given enough eons of time, friction would eventually stop it.
I’d just like to point out, you know, to stop further confusion… there is no God here, just me typing on a keyboard. Nothing else to eradicate…
Thanks for your thoughts. I always assumed the marble would act like a bullet from a high powered rifle passing through solid rock and iron like it would through wet paper… although my understanding of physics is basic and I have no idea whether that would do anything to the atoms it touches other than simply ‘nothing to see here, passing through, don’t mind me’.
Now this may seem a stupid question, but is there not a weight that would negate this pendulum effect once the marble passes through the centre of the earth?
Basically what I’m now asking is, what would cause the marble to just keep going and totally escape the earths atmosphere?
What if instead of being dropped as in the original scenario, it was projected like a missile or bullet so it had all this extra force behind it?
I know that’s a childlike question to those who study this stuff, but if you don’t ask, you don’t learn!
If you want to learn something, why not give up on marbles that follow only magic rules that you have invented? It’s perfectly reasonable (and informative) to discuss an outlandish hypothetical, but why not let it follow the real laws of physics? That would be pretty much Randall Munroe’s “What If?” series.
The two are not mutually exclusive. It’s perfectly acceptable to dissect and isolate something within a scenario as a means to understand and learn about something.
It’s like the question ‘what would happen if I was in a car that travelled faster than the speed of light, how would the headlights behave, what would it look like etc?’
We know cars don’t go that fast. We know the human body can’t handle those speeds either. What is the car made of? How would the person be protected? What about turning corners and the G force it would exert on the body?
All that can be made totally irrelevant by ignoring it and saying ‘meh, just say all that wasn’t an issue’. Ok, so if I was in a car that…
I watched a scene from a show the other day where some characters were running away from an explosion. As is always the case, they got far enough away to only get thrown 20 feet through the air, but aside from some minor cuts and bruises, were totally fine.
Now in reality, a force powerful enough to propel you like that would kill you, and shatter your bones in the process - like bomb blasts tend to do.
But we accept it. The shockwave can rip your jacket, ruffle the hair and send you 20 foot in the air… but not cause harm to the body… ok, whatever, it advances the plot and that’s that.
I’m sure there are many people who will watch a superhero movie and say ‘no no no, that wouldn’t happen like that…’ but sometimes you just have to let it slide.
Sure, but the person doing the “dissect and isolate” part should be an expert in the field, who understands how to do that in a way that grants insight, rather than nonsense such as:
There is no possible meaningful answer to this question. The hypothetical itself is based on fundamental misconceptions about the laws of physics.
To give you an analogy, suppose a young child asked you “Do dogs lay bigger eggs than chickens?”, do you think that the most productive outcome would be for you to just “let it slide” and attempt to answer the question?
Umm, ever seen a meteor? Many of these are grains of sand. They heat up the air in front of them causing a glow seen from far off. Larger ones can heat up enough to explode. This magic 2EarthM marble would produce an astonishing “meteor trail” as it passed thru the Earth. The energy disappointed would be mind bending. That energy would definitely create something a person standing very far off, like a well sheltered spot on Mars, would describe as an explosion.
There would most definitely be a non-trivial amount of “friction”. Pushing the marble-width tube of mass out of the way is what’s going to flare off most of the potential energy.
There would need to be a sideways component of motion. In the OP, the marble is dropped straight down, so it can only “orbit” straight down and back up again.
(A straight line of this sort is a “degenerate” orbit, an “ellipse” where the eccentricity is 1.)
We spend a lot of time here discussing physics of superpowers! What if you had Superman’s strength? What if you could teleport like Nightcrawler? Jolly fun!
Yes, but the “fun” format for this is when we first have at least some expertise in basic physical principles; this knowledge allows us to create a hypothetical where we suspend some isolated element of physics in a way that doesn’t immediately break everything; then we try to explore what might happen if all the rest of physics then proceeded much as usual. Akin, as I’ve said, to Randall Munroe’s hugely entertaining “What If?” series.
But you need some knowledge of physics to do this. Otherwise it results in “ok, I don’t know physics, but what if you just had a powerful enough spaceship that you went faster than light, what would it look like?”. Which is just tedious.
Similarly, I’m not sure that discussing magic is a useful (or fun) way to teach (say) high school kids the basic principles of physics.
Well, for me, the most interesting aspect is whether inertial and gravitational mass must be identical. Einstein said yes, and gave really good reasons for it, but there are still unanswered questions.
So, for instance, it’s valid to explore thought-experiments regarding anti-gravity.
re “magic,” it’s another useful way to explore some ideas.
Example: suppose you could magically tag every molecule of water in a liter. You pour the liter into the ocean and wait 100 years. Now you go to a beach, anywhere on earth, and fill a liter-jar with seawater. How many of the magically-identified molecules will be in the jar?
Answer: If there are 3.345 * 10^25 water molecules in a liter, and around 1.2 * 10^21 liters in the sea, then there are something like 10,000 magical molecules in the jar.
It’s a way of promoting the correct kind of thinking regarding physical measurements.
(Is it really so very, very different from Euclid positing perfectly straight lines?)
I would not describe this as “magic”. This is normal physics. It’s just that it’s a thought experiment rather than a practical experiment, to grant insight into how mind-bogglingly small molecules really are.
On smaller scales, we really could do such an experiment using radioactive isotopes.
