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 Okay, I lied, science question today.
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| Author | Topic: Okay, I lied, science question today. | ||
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Guru 
Posts: 2952 |
If you were to throw a pebble into hole from one side of the earth to the other, directly through the center. What would be the period, max velocity and what would the ocillation look like? (what kind of wave) 10 points extra credit     | ||
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Amateur Bodybuilder 
Posts: 120 |
I hope for the love of Jesus the other hole doesn't happen to be a toilet that someone is taking a shit on. That would be a mighty unpleasant surprise. | ||
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Guru
Posts: 2952 |
Hint, the velocity at either end of the hole through the earth would be zero. | ||
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Amateur Bodybuilder
Posts: 120 |
So are you saying that the pebble will not go up someones ass? Seriously though, would it just stop in the middle or burn off? | ||
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Guru
Posts: 2952 |
that is what I am asking you. Hint, neglect the temperature at the center of the earth and max velocity would be at the center of the earth. Why? | ||
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Amateur Bodybuilder
Posts: 117 |
the pebble would be at zero velocity at the exact center of the earth. Assuming the pebble is a perfect sphere, the exact center of the pebble would arrive at the exact center of the earth then stop because there can be no other forces of gravity to pull the pebble towards the center, it is already at the center, therefore it will be at a total standstill. ------------------ | ||
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Guru
Posts: 2952 |
Nope. Aren't you my PhD in Astronomy? Hint it oscillates, what is that period? | ||
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Pro Bodybuilder 
Posts: 424 |
{edited} I actually have no idea. They don't teach physics at my school.  [This message has been edited by Frackal (edited October 04, 2000).] | ||
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Pro Bodybuilder
Posts: 450 |
I THINK IT WOULD REACH THE CENTER STOP AND THEN COME OUT THE WAY IT CAME IN,WHAT THE HELL DOES ocillation MEAN?I THINK IT WOULD START LOSING SPEED THE FUTHER IT GOT THROUGH.NEVER WENT TO COLLEGE SO I'M GUESSING. | ||
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Novice 
Posts: 4 |
DIFFICULT question for a bodybuilding forum! I had this question in an astrodynamics course once, but of course have forgotten the answer. I did use the all-mighty Law of Universal Gravitation and determined that the pebble will start accelerating at g (9.8 m/s) at the surface-its acceleration will decrease to zero approximating 20% down toward the center, turn negative, where its velocity will then hit zero and the pebble will start going toward the surface. The same thing will then happen in reverse-the acceleration will hit zero again, velocity decreases and turns negative which means the pebble will start moving downward again. The period is sinusoidal, but would have to use some calculus to get that, I think. Of course this could never be proven experimentally, so this is only a theory. | ||
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Amateur Bodybuilder
Posts: 117 |
I guess im a pretty good bullshitter then.  ------------------ | ||
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Pro Bodybuilder
Posts: 450 |
MDGUY THATS BASICALLY WHAT I SAID BEFORE YOU BUT WITHOUT ALL THE SCIENTIC STUFF.GOOD JOB IF YOUR RIGHT.I HOPE I'M CLOSE THEN I WOULD FEEL BETTER ABOUT MYSELF FOR NOT GOING TO COLLEGE. | ||
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Pro Bodybuilder
Posts: 450 |
AS FOR THE EXTRA CREDIT ? I CALLED THE DAMN SCHOOL AND THEY DON'T EVEN KNOW.IS IT SOMETHING DUMB LIKE SHINGLES OR THE SKY. | ||
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Novice
Posts: 4 |
Osicllation means that is moves back and forth and repeats its movement over and over again. You don't need a college degree to know stuff-if you took physics in high school you could understand why the pebble does what it does. I forgot the extra credit, but knowing how goofy most engineers are, I would guess old slide rules. | ||
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Amateur Bodybuilder
Posts: 66 |
This one's not that hard... it was an old AP Physics problem that I did in high school. The key is to use the conservation of energy theorem. At the point of release, KE = 0 and U = a value... at the center of the Earth U = 0 and KE = the original value of U. Normally we'd just use U = mgh, but since "m" and "g" are changing as the pebble falls, we'd have to resort to using Calculus. The total Work to get the pebble from the release point down to the center of the Earth would be equal to the kinetic energy of the pebble at the center of the Earth. (1/2)(m)(v^2) = work done to get pebble from top of Earth to center. Work is equal to the integral of Force with respect to distance. Force = - (G)(m1)(m2) / (r^2) where G = universal gravitational constant, m1 = mass of the pebble, m2 = mass of the Earth, r = distance from pebble to center of the Earth. F = -(6.67 x 10^-11) x (mass of pebble) x (mass of Earth) / r^2. The problem is, the mass of the Earth keeps changing as the pebble falls (it doesn't LITERALLY change... but you fellow physicists know what I mean). The "mass" of the Earth beneath the pebble can be determined at any point with the function m2 = (4/3)(pi)(density of Earth)(distance from pebble to center of the Earth, cubed) m2 = (4/3)(pi)(density)(r^3) so... (m1 = mass of the pebble) F = -(6.67 x 10^-11)(m1)(4/3)(pi)(density of the Earth)(r^3) all divided by r^2 Simplified... F = -(6.67 x 10^-11)(m1)(4/3)(3.1415926535)(5515 kilograms per cubic meter)(r) Now we can integrate! Work = Integral [F] dr Work = -((1.54 x 10^-6) * m1) * Integral [r] dr evaluated from R (radius of Earth) to zero. Work = -((1.54 x 10^-6) * m1) * [(r^2)/2)] evaluated from 6.38 x 10^6 to zero Work = -((1.54 x 10^-6) * m1) * (2.03522 x 10^13) Work = -(31342388 * m1) I'm getting tired of using m1... let's just assume that we tossed a big barbell plate down there, ok? m1 = 20.45kg. Work = -(640951834.6) Joules Well, if it took -640951834.6 Joules of work to get the barbell plate from the dropping point to the center of the Earth, then that means that the barbell plate had 640951834.6 Joules of potential energy when we dropped it! (1/2)(20.45)(v^2) = 640951834.6 Joules v^2 = 62684776 v = 7917.37 meters per second. The barbell plate is travelling at about 7,917.37 meters per second (17,710 miles per hour!) the instant it reaches the center of the Earth. Simple physics tells us that it would now begin to slow down and eventually reach a velocity of 0 meters per second once it came out the other end of the Earth. To answer your second question, chesty, the maximum velocity would be 7,917.37 m/s. The period is the time that it takes for the barbell plate to fall through the Earth, come out the other side, and then fall back down and whack us in the face. This can be solved with a simple (yeah right) integral, or we can just use the equation for the period of a pendulum (because the barbell plate will begin to experience simple harmonic motion). T = 2(pi) * square root of (l/g) l = r g = (4/3)(pi)(G)(5510)(r) l/g = 1 / (4/3)(3.1415926535)(6.67 x 10^-11)(5510) T = 2(pi) * square root of (649582) T = 2(pi) * 805.97 T = 5064.06 seconds. It takes the barbell plate about an hour and 24 minutes to fall down, through the center of the Earth, come out the other side, then fall back down, through the center of the Earth, and smack us in the face. It takes the barbell plate about 20 minutes to fall to the center of the Earth, for those who care. In regards to the oscillation... well... simple harmonic motion... sinusoidal wave...
-Warik | ||
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Amateur Bodybuilder
Posts: 74 |
Warik: <Applause....> That brought back some very bad memories of college physics. Stop it. ------------------ | ||
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Amateur Bodybuilder
Posts: 66 |
quote:
-Warik | ||
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Amateur Bodybuilder
Posts: 117 |
He already did, Warik, please explain to us how time travel, either forward or back, is possible either in theory or in practice. ------------------ | ||
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Amateur Bodybuilder
Posts: 66 |
Well, I can't "explain" it since it's all theory/speculation... but here are my thoughts. Forward: Possible? Yes. Probable for human beings at this point in time? No... Time travel forward in time is caused by an object (person) travelling at close to the speed of light for a given period of time. Unfortunately, accelerating to the speed of light for a human being would take a very long time in order to avoid killing the human being from high G-forces. (Imagine sitting in a Dodge Viper and flooring it... now imagine that force on you x 1000000000... you'd turn into chunky salsa). Then, to slow down it would take an equally long time to keep the human being from being turned into chunky salsa. Also, very funny things start happening to matter as it approaches the speed of light, things that would not allow a human to survive. Time travel forward in time is clearly possible; however, it is not feasible for humanity at this point. In addition, it'd be pretty useless, too. =(
Some physicists say "yes," others say "no," others say "maybe" - I say "no, period." Paradox - (n) self-contradictory proposition. We all know that paradoxes are those fun "what if" statements. "What if you went back in time and killed yourself... what would happen? Cause if you killed yourself then you wouldn't be able to go back in time and kill yourself. etc..." If a paradox were to occur, what would happen? That is irrelevant because paradoxes cannot occur. They are fun to think about, but I don't think we'll see any of them happening. As such, time travel backwards in time can't be possible simply because the universe won't allow it in order to keep this "kill yourself" paradox from taking place. Now, we can look INTO the past, but we can't "go" there. We can look into the past because of the fact that light takes time to travel. When we observe the Andromeda Galaxy, we are looking 2 million years into the past. Can we actually go to the Andromeda Galaxy 2 million years in the past? Nope... There are my beliefs on time travel. Besides, if time travel backwards in time were possible (and if humanity lived long enough to discover technology enabling it to travel backwards in time), don't you think they would have used it to improve us (and in turn, them)? Imagine if someone went back in time to the 1700s and taught us how to create and use the internal combustion engine. Imagine where we'd be today! Imagine where THEY would be today! (Wait a minute... if we already had internal combustion technology in the 1700s, then why would they go back to the 1700s to teach it to us? But if they didn't go back into the 1700s to teach it to us, we would never have it! Oh no! Paradox!) See? Can't happen. Time travel is fun... | ||
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Amateur Bodybuilder
Posts: 190 |
i'm guessing that the extra credit is a trick question since it's purdue university, not purdue college. | ||
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Pro Bodybuilder
Posts: 575 |
It would melt.....be come a part of MOLTEN HOT MAGMA baby | ||
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Elite Bodybuilder 
Posts: 684 |
The two objects big ball with lil ol ball inside would eventually "stick" together somewhere along the path of decent due to their mutual intertia created by their occilation "LOOK AT ME I'm SPINNIN!" WOO HOO kind of thing. Purdue U has Iron Plates from Boilers on the roof as shingles... Just a wild geuss all the way around! ------------------ | ||
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Amateur Bodybuilder
Posts: 66 |
That can't be, WODIN. Assuming that the little ball and the Earth are the only objects in the universe, the little ball would HAVE to continue oscillating or it would violate the law of conservation of energy. When you first let go of the ball, it has a potential energy of *a big number* Joules. Because of that fact, there must ALWAYS be *a big number* Joules of energy in the Earth-ball system at all times or else the law of conservation of energy would be violated. "Stick together" = No motion = No energy = Law is broken... This problem is cool... Here's another question for you all, what would the graph of Force vs. Time look like? How would you graph a function with Force on the Y-axis and Time on the X-axis? What would this function look like....... and WHY? -Warik | ||
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Amateur Bodybuilder
Posts: 120 |
f(t) = k * sin(T*t) | ||
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Guru
Posts: 2952 |
Warik gets a 100%, the extra credit is copper or more poignetly bird shit. Very good Warik, I got more will see how ya do next round. |
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posted October 04, 2000 08:16 PM
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