@FinneousPJ Well spotted. I actually live near Oxford at the moment, but I move around quite a lot, so I thought London would better represent the UK as a whole.
Bonus points for anyone who can guess what my hometown is.
It's not a small obscure city, but not particularly well known outside Asia.
I can hardly picture a "small obscure city" in China. As far as I know, there are hardly any cities that have sub .5 million population.
I can hardly picture a "small obscure city" in China. As far as I know, there are hardly any cities that have sub .5 million population.
By "obscure", I meant unknown to the wider world. For example Xi'an is not as well known as Beijing, Shanghai and Hong Kong, but it does have some international renown because is the provincial capital of Shaanxi and associated with the Terracotta Army. In contrast, nearby Xianyang, also a city of over 5 million, is virtually unknown outside of China, even though it was technically the first capital of a united China.
Technically the Terracotta Army is in the countryside, so "the Terracotta Army is in Xi'an" is not strictly true. It was built when Xianyang was China's capital, but it got associated with Xi'an because the latter was larger and more important at the time of the discovery.
Staying in the same province, it is even less likely that anyone outside China will have heard of Baoji, a city of over 3 million. China simply has too many cities with million+ population. Even Chinese people don't know all of them.
If you did jump into your hole, how long would it take to fall through the earth to the other side?
Trick question? Cos even assuming there is no super-heated inner core that'd melt us, we'd still never reach the other side cos Earth's gravity would pull us towards the middle.
Heindrich Yes, it does, but you don't magically stop in the middle after being accelerated by the pull
Yes you would stop dead centre or even before. For there is no longer an up or down at that point and you will be pulled to either side of the tunnel.
Err, I don't think so. Here's what I think would happen:
Let's suppose for a moment that the earth is a perfect sphere, and the tunnel in question is dug directly through the center of the earth. Let's also neglect drag. The moment you fall into the tunnel , you would begin accelerating. You would continue to accelerate all the way until the moment you pass through the center. After that moment, you will begin to decelerate (but will continue moving in the same direction). You will reach zero velocity the moment you reach the end of the tunnel on the opposite side of the earth, at which point the whole process reverses itself. You oscillate between the 2 ends of the tunnel.
If we add back drag, a similar thing would happen, but you wouldn't make it all the way to the other end, and each trip through the earth you would make it less distance than before. In other words, you oscillations would be damped.
@deltago and @TJ_Hooker it'll depend on the acceleration * mass constant you have at the moment you reach the center. In the hypothetical situation that I jumped from 6 meters away from the center of the earth through a hole, I would only end 6 meters on the other side before reaching 0 speed and gong back again (considering I started at speed 0 too).
If you did jump into your hole, how long would it take to fall through the earth to the other side?
@FinneousPJ I've calculated from one side to the core, from the core to the other side. constDrag = 10m/s^2 (let's round it for my brain's sake...) initSpeed = 0m/s initKmToCenter = 12,742 / 2km = 6,371,000m initWeigth = 85kg initAcceleration = 0m/s^2 initEp = endEk 85kg * 10m/s^2 * 6,371,000m = 1/2 * 85kg * endSpeed^2 850n * 6,371,000m = 47,5kg * endSpeed^2 5,415,350,000nm = 47,5kg * endSpeed^2 5,415,350,000nm / 47,5kg = endSpeed^2 114,007,368.42105263158m^2/s^2 = endSpeed^2 !!2^ 114,007,368.42105263158m^2/s^2 = endSpeed 10,677.423304386346094m/s = endSpeed 6,371,000m / 10,677.423304386346094m/s = 596.67953759806048346s
initSpeed = 10,677.423304386346094m/s initWeigth = 85kg initEk + initEp = endEp 1/2 * 85kg * 10,677.423304386346094m/s + 85kg * (-10m/s^2) * 6,371,000m = 85kg * 10m/s^2 * -6,371,000m.... .... I think I did something wrong besides not taking out the mass/weight. I might do this tomorrow when I'm not so sleepy, lol.
I've calculated from one side to the core, from the core to the other side. constDrag = 10m/s^2 (let's round it for my brain's sake...) [...] initAcceleration = 0m/s^2
I think you've mixed these up. Drag is proportional to velocity, so your initial drag would be zero. Your initial acceleration however would be equal to standard gravitational acceleration, namely 9.80665 m/s^2 (which you rounded up to 10, which is not uncommon for rough calculations).
One of the things I like about this forum is that you never know where a particular thread will lead. A thread made for fun turned to SCIENCE! What's funny is that this is at least partially my fault...
However - as @Musigny also pointed out - your first mistake @CrevsDaak is assuming constant acceleration. The acceleration is 10 ms^-2 only at the start, and decreases as we near the center. Also, in your final calculation for time, you're also assuming constant velocity, which isn't true. The velocity is only "endSpeed" at the center, and thus you cannot simply solve for time from that.
However - as Musigny also pointed out - your first mistake CrevsDaak is assuming constant acceleration. The acceleration is 10 ms^-2 only at the start, and decreases as we near the center. Also, in your final calculation for time, you're also assuming constant velocity, which isn't true. The velocity is only "endSpeed" at the center, and thus you cannot simply solve for time from that.
Yeah, now I realize I've done this as if it was on simple situation (eg a ball falling from a 2m heigth to the ground) and done many other errors too (weird that my mathematical calculations are OK...)
constDrag = 10m/s^2 (let's round it for my brain's sake...)
This is not a constant. Not even an approximate value in this case.
Having learnt physics in spanish I've supposed drag was the acceleration of an object going in a free fall due gravity (usually ~9.80 on most places (with surface/0 heigth) save the ecuador line and the poles), but I forgot it also changes with the change of the heigth (probably because it was 4am, same reason why I forgot calculating the loss of acceleration because of the air's friction).
Dislike the idea that I was lied to as a child and in fact the answer is South of New Zealand, in deep, deep water.
Well, I was always told I would end up in China… But ignore those, they are just people that were never given this task at school (yeah, when I was in 2nd year I think we did this on geography class).
Comments
My first guess was Xianyang though, but I was too far south.
More hints of @Heindrich home city:
It is the starting point of the Silk Road
It is home to The Terracotta Army
It's name means Western Peace. All according to Wikipedia.
Staying in the same province, it is even less likely that anyone outside China will have heard of Baoji, a city of over 3 million. China simply has too many cities with million+ population. Even Chinese people don't know all of them.
Hmmm
Too deep
Missed it by that much...glub...glub...glub...
If you did jump into your hole, how long would it take to fall through the earth to the other side?
supposedly
Let's suppose for a moment that the earth is a perfect sphere, and the tunnel in question is dug directly through the center of the earth. Let's also neglect drag. The moment you fall into the tunnel , you would begin accelerating. You would continue to accelerate all the way until the moment you pass through the center. After that moment, you will begin to decelerate (but will continue moving in the same direction). You will reach zero velocity the moment you reach the end of the tunnel on the opposite side of the earth, at which point the whole process reverses itself. You oscillate between the 2 ends of the tunnel.
If we add back drag, a similar thing would happen, but you wouldn't make it all the way to the other end, and each trip through the earth you would make it less distance than before. In other words, you oscillations would be damped.
Edit: http://science.howstuffworks.com/environmental/earth/geophysics/question373.htm
In the hypothetical situation that I jumped from 6 meters away from the center of the earth through a hole, I would only end 6 meters on the other side before reaching 0 speed and gong back again (considering I started at speed 0 too). @FinneousPJ I've calculated from one side to the core, from the core to the other side.
constDrag = 10m/s^2 (let's round it for my brain's sake...)
initSpeed = 0m/s
initKmToCenter = 12,742 / 2km = 6,371,000m
initWeigth = 85kg
initAcceleration = 0m/s^2
initEp = endEk
85kg * 10m/s^2 * 6,371,000m = 1/2 * 85kg * endSpeed^2
850n * 6,371,000m = 47,5kg * endSpeed^2
5,415,350,000nm = 47,5kg * endSpeed^2
5,415,350,000nm / 47,5kg = endSpeed^2
114,007,368.42105263158m^2/s^2 = endSpeed^2
!!2^ 114,007,368.42105263158m^2/s^2 = endSpeed
10,677.423304386346094m/s = endSpeed
6,371,000m / 10,677.423304386346094m/s = 596.67953759806048346s
initSpeed = 10,677.423304386346094m/s
initWeigth = 85kg
initEk + initEp = endEp
1/2 * 85kg * 10,677.423304386346094m/s + 85kg * (-10m/s^2) * 6,371,000m = 85kg * 10m/s^2 * -6,371,000m....
.... I think I did something wrong besides not taking out the mass/weight. I might do this tomorrow when I'm not so sleepy, lol.
If someone wants to still try don't open the link!
I think you have a problem with units here. You're equating force (mass x acceleration) with energy (1/2 x mass x velocity^2).Edit: derp, somehow missed where he multiplied by meters I see your sleepiness, and raise you drunkeness, haha. I guess we'll both come back to this in the morning.
However - as @Musigny also pointed out - your first mistake @CrevsDaak is assuming constant acceleration. The acceleration is 10 ms^-2 only at the start, and decreases as we near the center. Also, in your final calculation for time, you're also assuming constant velocity, which isn't true. The velocity is only "endSpeed" at the center, and thus you cannot simply solve for time from that.
Dislike the idea that I was lied to as a child and in fact the answer is South of New Zealand, in deep, deep water.
Well since you were a child the tetonic plates moved a couple hundred miles so you weren't lied to at all.