This Crazy Physics Trick Makes Gravity Easy! 

So, those two clones in space... if they were completely without motion, is there any movement they could make to start moving? Basically if you were still in space is there any arm or leg movement that could get you moving?

@@jamesweeks9583 No. They can twist and contort their bodies, but the best they'll ever be able to do is turn. The only way their _center of mass_ will ever move is from an external force (a force from outside them)... like the gravity exerted by the other clone. Without that external force, they're stuck in place forever. Other examples of external forces would be some kind of rocket pack or simply throwing something opposite the direction you want to move.

Did you mean to pin this comment? Also, Einstein's General Relativity says that it's not possible to distinguish what you call "apparent weight" from just "weight".

@@jamesweeks9583 They could throw their clothes away, or maybe spit (or other forms of ejection of bodily waste)

@@Alexagrigorieff I did. RU-vid has been randomly _unpinning_ my comments. I don't know why. It's happened on several other videos over the last couple days.

You have the crazy “attention” to details… Nick has the crazy details.

I laughed as he kept throwing clones in holes.

6371 km in 20 minutes of acceleration means a top speed of 40250 km per hour, or 25000 mph You can bet he's on fire

The clone in the hole burnt to ash. So I guess that was the ash hole clone.

@@AlleyKatt I know that guy sucks

You are a wonderful person. Anton Petrov says so.

42.

What if the tunnel isn't straight but is a cycloid?

@@johnclark8359 then you have to say "Weeee!" the whole time. State law.

@@johnclark8359 I think you're asking if the trip time is still the same. I only know one very blunt approach to that question, and it's not a very good one, so hopefully a more mathy person can do the real work. That doesn't mean we can't have fun. According to one video I just looked up, the arc length of a cycloid is equal to eight times its radius. So to make things more fun, let's say we're not even limited to a cycloid that is entirely underground. So we increase its radius so much that its path takes us away from the surface of Earth and then hopefully back. I guess at that point our tunnel is more of a pipe. Two facts arise from this: 1. If the tunnel leads away from the surface of the planet, gravity will not compel us to move in the correct direction from our starting point. 2. If there is no limit to the radius, there is no limit to the length of the tunnel, since it's just 8 times the radius. So that's the distance, right? Or maybe two of those are the distance, since we have to get back to our starting point. What happens if we take "distance equals rate multiplied by time", plug a really really high number in for distance, and hold time at 40 minutes? Eventually, your average speed would be greater than the speed of light. But even before that, your peak speed reaches the speed of light. Since that can't happen, it must not be true that my really long tunnel you weren't asking about anyway could get you to the other side in just 40 minutes. At least not if you're being observed by someone who is standing on the surface of Earth watching this happen. But perhaps you, the traveler, would observe the trip to only take 40 minutes. Relativity and stuff. Maybe that's the 40 minute figure. It's for the traveler. Unlikely, though, as my really long pipe takes you super far from Earth for a while, and it's a highly eccentric orbit, meaning at some point you're out really far and barely moving at all. It would be hard to make up for that.

😂

@Phoenix I think it's reasonable to assume that air resistance is not part of this theoretical exercise. Because the other issue is, unless it's a diameter tunnel (straight line through the core), gravity is going to pull the falling body against the wall of the tunnel, and we'd have to factor in the friction from that. Plus, he's using the same model for the Earth tunnel as for bodies in the vacuum of space.

@Phoenix maybe if you're tossed imperfectly down a tunnel that goes straight though the core. But if the tunnel is off-center, you'd roll instead. It would feel like the tunnel is at an incline, because from a flatworld perspective, it is. That means your acceleration due to gravity would be attenuated by your moment of inertia.

@Phoenix another point for "no air resistance". It only holds us back.

@Phoenix I can see the argument for that, but at the same time, does anyone really ever want to have a discussion on semantics? It seems like one of those things that a conversation _accidentally_ turns into, with no one actually intending it to happen. All we'd have to say is that the tunnel is frictionless and evacuated of all air, and other gasses and perfectly sealed off from any other materials that may turn into gasses at low enough pressure, and it's a physics problem again.

I also use computers to do my calculations. Elsie, Sally, Gladis and Mavis have been doing it for many years! They also make a good cup of tea and bake nice cakes.

@@crouchingtigerhiddenadam1352 Who are they?

It's a really easy one to solve, actually. You can just write d²r/dt² as v•dv/dr (where v = dr/dt) and then solve for v wrt r. Once you do that, you have a 1st order differential equation for r wrt t, and it's easily solvable by simply seperating the variables.

@@TheReligiousAtheists the thing is that is just a trick. You have to solve a similar d.e. before to know to use it(unless you are a genius). Computers don't need to do the same.

@@noether9447 It's actually a pretty standard trick in solving higher order DEs. The harmonic oscillator equation comes by solving a similar DE using the same trick, so it should be pretty well-known to a professional physicist like Nick

CG Account so deepthought was right!

It should be 42 on all the planets.

Hitchhikers guide to Galaxy

@@hit3894 Finally! Thanks for all the fish!

Pangalatic gargleblaster anyone?

Happy to help 😊

Flow and current have such similar behaviour because they are described by the same piece of mathematics. Statistics.

@@noether9447 I think it's the other way around the physical phenomenon of current on a macro scale is the same as flow on a macro scale and because of that described by the same mathematics. Supper zoom 😉 to microscopic level though and the behavior of an electron in a wire is very different than the behavior of a molecule in a pipe. For example electrons don't experience turbulence, so the analogy flow and current only works on macro level.

@@noether9447 Don't forget Traffic :-)

@@noether9447 Flow and current have such similar behavior because they both amount to the same underlying phenomenon: electrostatic repulsion.

dependant on mathematics but has systems that are mathematically impossible! We do ok at describing things and making predictions but we cant explain nothing and have no clue whats going on! :D

I've often said 'you want to find the easiest way to do something? Get a lazy person'

@@adreanmarantz2103 "I choose a lazy person to do a hard job. Because a lazy person will find an easy way to do it." - Bill Gates

If a hole is drilled through the earth which on its own is impossible ,, objects or mass cannot pass through it period dumb guy .

Yup😊

@@8600esemusa speak English buddy

Eddie Van Halen got famous by using harmonic motion.

Simple harmonic oskalator. Often studied as a free-body.

😆

I knew that But I wrote it because I have seen it on the Internet Don't believe me, Google It

Seriously Nick😒 Why didn't you heart my comment? I think you should make a hearty clone for that one

How do you know though? They're clones after all :P

Newton was the man!

NEXT PLEASE

It was bugging me too. But I guess it works if you ignore any friction when you bump into the tunnel walls & slide along them? The counterintuitive thing is that if you dig a straight tunnel parallel to a tangent to Earth's circumference, it looks as if every point was "level" - but "down" is always pointing to center of Earth - so the "straight" tunnel is actually "sloping inward", like a valley (in terms of gravity). You'd still fall/roll/slide through.

I didn't get your question

Yes. We're ignoring friction in the shorter tunnels.

Imagine a train on a frictionless track. In fact, people have proposed designs for just such a method of travel. Look up "gravity train" on Wikipedia.

Just bring some rollerblades

@@lionel4685 ... creating a warp bubble and falling on a downslope of gravity in the direction you are traveling. Light has the fastest speed within spacetime, but what if you bent spacetime itself? Hmm. What is your out-of-the-box thinking? That was the question at the end of this Science Asylum video.

Uncontrolled crash = ablative lithobraking -Kerbal Space Program

That's just a coincidence of what our planet's properties happen to be, and how we define the minute. Try this calculation with data for a different planet, and you'll get a completely different number. This isn't like the fine structure constant, where it is a very specific rational number that shows up in a surprising place, in a way that is independent from any physical object we inherited, or any manmade unit definition.

@@carultch Please watch (or read) H2G2 : "The HitchHiker Guide to the Galaxy."

I worked for 12 hours straight yesterday trying to get this video finished by today. Thanks for appreciating the work.

@@ScienceAsylum How do you explain human levitation and the observed levitation of ufos where there appears to be no prop wash? There are some good, believable youtube videos on human levitation. Then there's Crookes et al 19th century account of human levitation.

@@peterfred445 I can levitate for a brief moment, but I required a lot of beans to be consumed.

@@peterfred445 Given that they traveled thru space to get here, one would assume they got technology we don't, so anything we say would be just speculation. Maybe they're using the same kind of space warping that could be used for faster-than-light interstellar travel; maybe we're not seeing them, but a side-effect of their cloaking technology; maybe they were not really there in the first place and our memories and recording devices have been tampered with; maybe it's just rockets but using dark matter as propellant etc. There is no way to know without actually studying an alien craft directly.

If you know "how much more there is to learn on any given subject," then you are in fact smarter now 👍

@@ScienceAsylum Good point!

Thx

It's a mix between After Effects and Python. Like anything, it took a lot of practice. I've been making videos for 7 years and I was making animations for my university physics teaching before that.

Those two portions of the Earth are different masses, but they’re also different distances from the clone. The bigger part is farther away by just the right amount for the forces to be the same.