| Physics riddle | |
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JavaGuy - Student  |
Two barrels of water, one frozen solid and the other at room temperature, start rolling at the same time from the same height on a ramp. Both are the exact same mass. Which one reaches the bottom first and why? _______________ My signature is only one line. You're welcome. |
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JavaGuy - Student 
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Ancient...I thought you said the ice barrel would reach the bottom first.  Anyway, Ancient hit on the correct principle: Moment of inertia (one-half eye omega-squared). The thing to remember is that both barrels have the exact same potential energy at the top because they have the same mass and start from the same height. As they roll to the bottom, potential energy is converted to kinetic energy. Because of the law of conservation of energy, if they had the same potential energy at the top, then they have the same potential energy at the bottom. So if they have the same potential energy at the bottom, they're going the same speed? No. Each barrel has two kinds of kinetic energy when it reaches the bottom, energy of translation and energy of rotation. Energy of translation is the energy of the whole barrel moving from one place to another. Energy of rotation is the energy of the barrel spinning around. If a barrel is flying through space and not turning, it has energy of translation but none of rotation. If a barrel is spinning in one place, it has energy of rotation but none of translation. If it is rolling down a ramp, it has a little of both, and the total of its energy of translation plus energy of rotation as it hits bottom has to be exactly equal to the potential engery (1/2mgh) that it had at the top of the ramp. To understand energy of rotation, think about an individual molecule inside the frozen barrel (it could be a molecule of water or a molecule of iron in the barrel itself). If the barrel makes one rotation per second, then that molecule is moving in a circle around the axis of the barrel at a speed of that circle's diamater per second. The individual molecule's kinetic energy is one-half its mass times the square of its velocity. Molecules close to the center travel around a smaller circle in the same amount of time and so move slower, have less energy. Molecules around the rim move the fastest and have the most energy. The barrel's total energy of rotation is the sum total of every molecule's kinetic energy with respect to its motion around the axis. Now when the ice barrel starts to roll, the ice, being solid, must roll exactly as fast as the barrel. The amount of energy that goes into rotational motion to achieve a given translational speed down the ramp is fixed. But when the water barrel starts to roll, inertia will cause the water to lag behind the barrel in rotational speed. Friction will cause the water to rotate, but it won't rotate as fast as the outside of the barrel, at least not when it first starts out, and thus it will require less energy to get it rolling the same speed as the frozen one. Since they both start out with the same potential energy, the water barrel will start rolling faster. _______________ My signature is only one line. You're welcome. |
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Gradius - Ex-Student 
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Man that's not what I mean I know why we need science. What I mean is that this is a RIDDLE, a JOKE, a GAME. It doesn't require this much thinking into. It's an answer of common sense. JavaGuy wasn't asking us out of his own curiosity. That's what I mean when I say you guys are thinking too far into this. It's a simple question with a simple answer that you don't really have to do math to figure out. _______________ - Proud padawan of Kueller. - We really are at the beginning of it all. The trick, of course, is to make sure we never find the end. - Bill Bryson, A Short History of Nearly Everything - <gen-e-sis-happy> Liek, you can train, liek, a n00b, but he'll just be a trained n00b... --> Wise words! - "daer SOE me likes your a company i am having your some money for letting me do stuff cos mes the best amd i do it all meself" - Slider |
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Ancient - Ex-Student 
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Quote: JavaGuy just tell us the answer please. Everyone's getting in way too deep with all this physics talk and they don't understand it's a very simple answer. Im sticking with mine still. The water barrel will reach bottom first because the ice barrel will get a slower start rolling. First, you have to understand that human intuition is not accurate at all, thats why we need science, we need laws to prove our hypothisis. If everyone prove and conclude things will there instinct, you wont be sitting in a chair that is that comfortable, you wont be sleeping in your bed without fear that it will collapse, you cannot ride any car or bus to school that safe, and you will never see any airplane in your life time, etc. You can see science everwhere, from small things to big things. They are all science and hypothesis that have been proven.  Hope that change you view point.P.S. if we all dont know what is density, everyone will think that ice will have a smaller mass than water _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! This comment was edited by Ancient on Apr 22 2004 05:34pm. |
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Gradius - Ex-Student
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JavaGuy just tell us the answer please. Everyone's getting in way too deep with all this physics talk and they don't understand it's a very simple answer. Im sticking with mine still. The water barrel will reach bottom first because the ice barrel will get a slower start rolling. _______________ - Proud padawan of Kueller. - We really are at the beginning of it all. The trick, of course, is to make sure we never find the end. - Bill Bryson, A Short History of Nearly Everything - <gen-e-sis-happy> Liek, you can train, liek, a n00b, but he'll just be a trained n00b... --> Wise words! - "daer SOE me likes your a company i am having your some money for letting me do stuff cos mes the best amd i do it all meself" - Slider |
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Ancient - Ex-Student
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Quote: Umm... what if the barrel with the liquid is missing its top.   The result will be a lot more complex to figure out, since the barrel without water "empty barrel" will excatly satisfy the equation of inertia for a "Hoop", recall my post eariler, the KE<t> will become even lesser than the KE<t> with water in it. But the problem is, the mass of that empty barrel will not equal to the mass of the iced barrel. THerefore, it will involve a lot more physics and calculas calulation to figure that out, which i wont do it here. _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! |
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Xipkell - Student |
Umm... what if the barrel with the liquid is missing its top. |
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Ancient - Ex-Student
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Quote: Hey what about one of the unique properties of water, think about the frozen tundra where I live. Frozen is the key word. All our 10,000+ lakes, rivers, and streams are nice and solid with ICE for half the year. Now that is funny because well how can ice float? Is that because ice is lighter than water. Hmmmmmm...... ps I live in Minnesnowta! OK, how can ice float on water? IT IS NOT BECAUSE ICE IS LIGHTER IN MASS! BUT INSTEAD, ICE HAS LOWER DENSITY THAN WATER. These kinds of things concerning about density is very basic topic in science. P.S. if you never learn physics before, why bother to argue? _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! This comment was edited by Ancient on Apr 22 2004 04:29pm. |
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_cmad_ - Ex-Student 
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things float cuz their density is less than the water density. d_water = m_water / V_water = 1 (about 1 anyway) so if something has big volume, at least greater than the mass then it can float _______________ Your friends of today, are your enemies of tomorrow. |
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Ancient - Ex-Student
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Quote: you know ancient, it's sometimes impossible to understand if you are agreeing with someone or not  3th, i am saying that it dosent matter if the water inside the barrel sloshes or not. The ice barrel will still go down there faster _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! |
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Bubu - Hubbub 
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koushka things float not because they are lighter than water. think about a big fat oil tanker. heavy, right? floats, right? i can't wait for the answer to this _______________ make install -not war This comment was edited by Bubu on Apr 22 2004 04:16pm. |
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koushka - Student 
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Hey what about one of the unique properties of water, think about the frozen tundra where I live. Frozen is the key word. All our 10,000+ lakes, rivers, and streams are nice and solid with ICE for half the year. Now that is funny because well how can ice float? Is that because ice is lighter than water. Hmmmmmm...... ps I live in Minnesnowta! _______________ Faithful Padawan of {SKX}Dark Blade My profile pic is luke skywalker
This comment was edited by koushka on Apr 22 2004 02:35pm. |
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3th - Retired 
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you know ancient, it's sometimes impossible to understand if you are agreeing with someone or not _______________ this is the internet, be serious damn it! This comment was edited by 3th on Apr 22 2004 09:38am. |
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Garos - Student 
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I thought they'd hit at the same time tooooo |
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Ancient - Ex-Student 
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Quote:
Quote: That's what I thought too orion, but how is the water going to behave when its rolling down. Is it possible it could slosh around thus changing its center of gravity and that effects its speed? I don't know if it will or not. i would think that buzz is kinda onto the answer here. i would say the frozen one reaches the bottom first because there's additional internal friction with the one with liquid water in it. so i would disagree with KWSN on that issue, i think the one with water in would get a slower start. (that shifting center of gravity might have something to do with it too, i dunno.) and that's my final answer. i could always be wrong though It doesnt matter, since the water in the barrel must distributed more unevenly than the iced barrel. And unevenly distribution will bring more inertia than even distribution, AND MORE INERTIA WILL LEAD TO MORE KE<rot> AND MORE KE<rot> WILL LEAD TO LESS KE<t>. FINALLY MORE KE<t> will lead to faster velocity. THEREFORE, the iced barrel will get down there faster, nomatter what...situation buzz has discribed _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! This comment was edited by Ancient on Apr 22 2004 07:06am. |
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Ancient - Ex-Student
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WHAT A GREAT QUESTION!!! ok, first of all I prefer the ICE BARREL will get to the bottom first. My explaination to this is that the therom of rotational moments of inertia has addressed the equation: {KE<rot>=(1/2)IW^2} which shows us that the rotational kinetic energy(KE<rot> ) depends on the moment of inertia(I), and also the anglar velocity(W). OK, now since both barrels have the same mass and the same "roll down path", anglar velocity(W) should be exactly the same. However, inertia(I) will be difference as the "shape change". What do i mean "shape change"?? Well, remember when you roll the room temperture water barrel down, the water wont be evenly distributed inside the barrel, and the water molecule will kind of spread out among the inner surface of the barrel(centriptial force). Thus, it will form a shape looks like a cylindrical shell or hoop {inertia equation for hoop: I=MR^2}, although is true that if we dont have enough "W", there will not have much water molecules stick to the inner wall, still they will have an inertia(I)greater than the "ice barrel". For the ice barrel you can expect that it will form a Solid cylinder shape, for a solid cylinder shape, we can conclude that inertia equation must be equal to I=(1/2)MR^2, mass evenly distributed. So, because R(radius) and M(mass) are exactly the same, we can conclude that Inertia of Solid cylinder is smaller than inertia of a hoop. NOW, we have understand that I<i> (abb.for inertia of the iced barrel) is smaller than I<w> (abb. for inertia of the water barrel) for a factor of "1/2". WE CAN CONCLUDE THAT ROTATIONAL KINETIC ENERGY FOR ICED BARREL IS ALSO SMALLER THAN THAT OF THE WATER BARREL. Why? lets us refer back to the equation i have mentioned eariler: KE<rot>=(1/2)IW^2, we can see that as "I" increase, the rotational kinetic energy increase, and KE<rot> is direct proprotional to "I". Therefore, KE<rot> of the iced barrel will consume less energy and left more energy to the KE<t>(translational kinetic energy, which is the KE that dominate the movment speed), we can see that from the law of conservation of energy:{PE<g>=KE<rot>+KE<t>} Since, PE (gravitational potential energy) ARE THE SAME IN BOTH SITUATION, if the iced barrel have a smaller KE<rot>, it must have a greater KE<t> compare to the water barrel. AND FINALLY WE CAN CONCLUDE THAT THE SPEED OF THE ICED BARREL IS FASTER DUE TO LESS ENERGY CONSUME OF KE<rot> AND THE SPEED OF THE WATER BARREL IS SLOWER DUE TO MORE ENERGY CONSUME OF KE<rot>.So, the iced barrel will get to the bottom first and water barrel will get to the bottom next. P.S. i used an hour to write this, plz read it more carefully before you ask or point out i am wrong. ALSO, FOR THE EQUATION OF THE LAW OF INERIA, WE HAVE TO USE INTEGRAL CALCULUS TO EXPALN AND I AM SRY THAT MY CALCULUS IS NOT THAT GOOD AND COULDNT EXPLAIN IT REALLY WELL IN HERE. _______________ -THE ONE WITH THE "STAFF" -BROTHER TO FROSTY -Admitted to University of California, San Diego(UCSD). YAY! This comment was edited by Ancient on Apr 22 2004 07:08am. |
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3th - Retired
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Quote: That's what I thought too orion, but how is the water going to behave when its rolling down. Is it possible it could slosh around thus changing its center of gravity and that effects its speed? I don't know if it will or not. i would think that buzz is kinda onto the answer here. i would say the frozen one reaches the bottom first because there's additional internal friction with the one with liquid water in it. so i would disagree with KWSN on that issue, i think the one with water in would get a slower start. (that shifting center of gravity might have something to do with it too, i dunno.) and that's my final answer. i could always be wrong though _______________ this is the internet, be serious damn it! |
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Gradius - Ex-Student 
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You guys are taking this way too far it's supposed to be a simple answer that's right under your nose...hence the name "riddle." Anyways, I know the answer is the barrel that's not frozen. I just don't know why. My best guess, because the frozen barrel would get a slower start rolling down the ramp. _______________ - Proud padawan of Kueller. - We really are at the beginning of it all. The trick, of course, is to make sure we never find the end. - Bill Bryson, A Short History of Nearly Everything - <gen-e-sis-happy> Liek, you can train, liek, a n00b, but he'll just be a trained n00b... --> Wise words! - "daer SOE me likes your a company i am having your some money for letting me do stuff cos mes the best amd i do it all meself" - Slider This comment was edited by Gradius on Apr 22 2004 05:24am. |
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JavaGuy - Student 
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For clarity: The two barrels are exactly identical in all respects except for one's being frozen sold and the other room temperature. For the sake of simplicity let us assume that there's just enough air inside the barrel to give the water room to expand when it freezes (air compresses rather easily under such conditions) without deforming the barrel. (An aside: If the barrel did expand, it would not change the answer to the riddle.) _______________ My signature is only one line. You're welcome. |
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BlueDragon - Ex-Student 
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it says that the two barrels have the same mass, so the same number of molecules. When it freezes, it creates crystal-shaped bonds and expands, meaning that the volume will rise. It will have the same number of molecules, but will appear to be bigger than the same amount of molecules of water. _______________ -BlueDragon This comment was edited by BlueDragon on Apr 22 2004 01:21am. |
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tarpman - The Tarped Avenger 
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But where does it say the two barrels are the same volume? _______________ Saving the world, one kilobyte at a time. |
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BlueDragon - Ex-Student
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When water freezes, it expands, and since both are the same mass, there has to be less volume of water in the water barrel than the ice. Then it can slosh around and slow down once it starts rolling. The other one is solid, and therefore doesn't slosh around, and just roll down faster and faster without any interruptions at a constant acceleration, so my bets on the ice barrel. _______________ -BlueDragon This comment was edited by BlueDragon on Apr 22 2004 12:01am. |
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Orion - Retired 
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well if the barrel is full to the top, can the water splash around? and i think it could buzz, the moving water could add some forward force to teh barrel if i am thinking about this right. _______________ When a Man lies he murder's some part of the world. These are the pale deaths which men misscall there lives. All this I cannot bear to witness any longer. Cannot the kingdom of salvation take me home? -Cliff Burton Owner of Smily's 1900th comment | <Lady_Catherine> i love your sexy white socks! | (Lady_Catherine) i adore u! | (Lady_Catherine) onion (Lady_Catherine) i lub u This comment was edited by Orion on Apr 21 2004 11:35pm. |
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Buzz - Student 
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That's what I thought too orion, but how is the water going to behave when its rolling down. Is it possible it could slosh around thus changing its center of gravity and that effects its speed? I don't know if it will or not. _______________ When you are going through Hell, keep going. -Sir Winston Churchill. Those who seek power and control of others, no matter the level, no matter the intentions, should never be given it. |
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Orion - Retired
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well the ice is still water, and the water/ice forms to the shape of the object it is in and they should be teh same mass, and based on the princple that everything falls at 9.8m/s2 they both should hit at the same time. _______________ When a Man lies he murder's some part of the world. These are the pale deaths which men misscall there lives. All this I cannot bear to witness any longer. Cannot the kingdom of salvation take me home? -Cliff Burton Owner of Smily's 1900th comment | <Lady_Catherine> i love your sexy white socks! | (Lady_Catherine) i adore u! | (Lady_Catherine) onion (Lady_Catherine) i lub u |
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Buzz - Student
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hmmmm, well the barrel with the water in it would be a little smaller than the one full of ice. I don't know which one would finish first though. _______________ When you are going through Hell, keep going. -Sir Winston Churchill. Those who seek power and control of others, no matter the level, no matter the intentions, should never be given it. |
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