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Post by Deleted on Jan 23, 2014 9:27:26 GMT -5
Sounds good to me!
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Lizard King
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Post by Lizard King on Jan 23, 2014 9:28:08 GMT -5
It's not though. It's accelerating under gravity.
When you accelerate a car, you feel yourself pushed back in your seat. You're part of the 'system' of the car, but distinct from the car. Inertia tends to keep you at rest; the motive force is acting on the car around you, not on you directly, so inertia has to be overcome (by the normal force of the seat in your back) before you move.
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Virgil Showlion
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Post by Virgil Showlion on Jan 23, 2014 9:30:48 GMT -5
Phoenix is correct with his explanation of #3. The short end of the broom will be heavier. An an analogy, think of a balanced see-saw with a fat kid sitting close to the fulcrum across from a skinny kid sitting further away from the fulcrum. As for Beer's guess on problem #2... she might be right, or she might not be. Do any others dare present a theory to challenge hers? ETA: I see that phoenix has also presented a theory: that the cork will float more slowly to the top. Does any third party wish to challenge both of these physicists?
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Post by Deleted on Jan 23, 2014 9:33:10 GMT -5
I am sure there will be a line soon....
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Virgil Showlion
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Post by Virgil Showlion on Jan 23, 2014 9:39:32 GMT -5
I am sure there will be a line soon.... Are you insinuating that our board isn't overwhelmingly patronized by lovers of physics? Tsk. My good woman, even the thought of such a thing...
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Post by Deleted on Jan 23, 2014 9:41:11 GMT -5
Who knew that one day I'd actually be using the stuff I learned in my HS Physics class in REAL LIFE?!?!?
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Lizard King
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Post by Lizard King on Jan 23, 2014 9:46:24 GMT -5
Oh, I think it is. *pats Virgil on the head*
Captain Selective Quote strikes again!
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Virgil Showlion
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Post by Virgil Showlion on Jan 23, 2014 9:46:58 GMT -5
Who knew that one day I'd actually be using the stuff I learned in my HS Physics class in REAL LIFE?!?!? Technically a brainteaser challenge isn't "real life" application of physics knowledge. But that time you hauled both your toilet and a filing cabinet at the same time by balancing them perfectly across your furniture dolly certainly qualifies.
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Lizard King
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Post by Lizard King on Jan 23, 2014 9:49:50 GMT -5
I've had another think about the inertia on the cork.
At the instant that the pail and cork are simultaneously released, inertia is acting on the whole system, but the net force acting on the pail and water is downward. By contrast, the net force on the cork - due to buoyancy - is upward. Its relative motion upward, relative to the descending pail, will therefore be faster than in a pail at rest.
Accordingly, I totally reverse my earlier answer by using the exact same reasoning.
If anybody mentions planes and treadmills, I will hit them with the short end of an unevenly-bisected broom.
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Virgil Showlion
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Post by Virgil Showlion on Jan 23, 2014 9:56:49 GMT -5
Ah, the "Republicans on RomneyCare" gambit. A classic. We'll leave the floor open for other contenders.
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Lizard King
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Post by Lizard King on Jan 23, 2014 10:01:51 GMT -5
I have a new suggestion. Upon examining the pail at the conclusion of its descent, you realize that you forgot to put the cork in at all. Deciding the whole thing was a waste of time, you meditate on the rigorous splendor of the presented solution to problem 3 and go about your daily business a contended and corkless individual.
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Virgil Showlion
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Post by Virgil Showlion on Jan 23, 2014 10:12:51 GMT -5
I have a new suggestion. Upon examining the pail at the conclusion of its descent, you realize that you forgot to put the cork in at all. Deciding the whole thing was a waste of time, you meditate on the rigorous splendor of the presented solution to problem 3 and go about your daily business a contended and corkless individual. The implications are obvious: you could improve your day by putting a cork in it.
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Lizard King
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Post by Lizard King on Feb 4, 2014 10:48:21 GMT -5
Yeah, that's right, I bumped it. I want closure.
Also, here's a cute little problem, a little late for the Superbowl. The Broncos, bless 'em, demonstrated that it's possible to score 2 points both for a safety and for a touchdown conversion; but suppose the only possible scoring increments were 3 for a field goal, 6 for a touchdown, and 7 for a converted touchdown...
A) What would be the highest score no team could achieve, even given infinitely long to achieve it?
B) More generally, if the only possible scoring increments were (blah) for a field goal and (snore) for a converted touchdown, what would be the highest score no team could achieve?
["The highest score no team could achieve" implies that every conceivable score higher than that one can be achieved in the increments identified in the question.]
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spartan7886
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Post by spartan7886 on Feb 4, 2014 13:28:33 GMT -5
A) 11
B) Assuming neither blah nor snore is a multiple of the other, (blah)*(score)-(score)-(blah)
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Lizard King
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Post by Lizard King on Feb 4, 2014 13:35:34 GMT -5
Nicely done, Spartan. You're quite right, blah and snore do have to be coprime for that general formula to hold.
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Virgil Showlion
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Post by Virgil Showlion on Feb 4, 2014 16:59:52 GMT -5
Coprimality is the correct condition, but it's a stronger condition than B) in #726. For example, the formula fails for the pair 6, 9 even though 6 doesn't divide 9 and 9 doesn't divide 6. As for the cork problem, we had three contenders: @beerwench - cork will float to top at normal rate Lizard King (v1.0) - cork floats to the top at less than normal rate Lizard King (v2.0) - cork floats to the top at greater than normal rate And the winner is *drumroll*: Nobody. The cork actually stays at the bottom of the bucket. It doesn't float at all. This is because buoyancy is a function of the static forces induced by gravity. Under the effects of gravity, water is heavier than the cork and hence induces an upward force. But for a pail in freefall, the whole system is uniformly accelerating at g. The components in the pail (the water and the cork) exert no net buoyancy forces since both are completely weightless in the accelerating frame. If this doesn't make conceptual sense to you, consider an opposite case where you start by holding a brick at the very top of a bucket of water and then simultaneously drop the bucket and the brick. Both will accelerate downward uniformly at g. The brick will not sink into the water until the bucket hits the ground.
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Peace Of Mind
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Post by Peace Of Mind on Feb 4, 2014 17:04:10 GMT -5
I have no idea what any of you are saying. I think that means I win! Yay me!!
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Lizard King
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Post by Lizard King on Feb 4, 2014 17:04:14 GMT -5
Thanks
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Lizard King
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Post by Lizard King on Feb 4, 2014 17:05:41 GMT -5
I have no idea what any of you are saying. I think that means I win! Yay me!! I like this attitude. We should play cards some time.
I know a fun game called Mao. Only two rules:
1) All Jokers are the Nine of Diamonds;
2) I'm not allowed to tell you any more rules.
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Peace Of Mind
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Post by Peace Of Mind on Feb 4, 2014 17:06:59 GMT -5
Then what are the 9 of Diamonds going to be? Go fish!
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wyouser
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Post by wyouser on Feb 4, 2014 17:14:44 GMT -5
However, if one were to add Wiley Coyote, a bucket and a brick both built by ACME, with water provided by Looney Tunes , would that not alter any laws of physics? You might drop them simultaneously but it's anybody's guess who or what hits te desert floor first.
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Lizard King
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Post by Lizard King on Feb 4, 2014 17:15:33 GMT -5
I think we can safely assume that Wile E. would pause, feel around the air, determine there was no solid ground there, and gulp, before beginning his descent. After that it's a crapshoot.
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Virgil Showlion
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Post by Virgil Showlion on Feb 4, 2014 17:16:36 GMT -5
I have no idea what any of you are saying. I think that means I win! Yay me!! You won the very day you declared snow leopards to be foul, abominable beasties. Or maybe that was Iggy. At any rate, one of you is a winner.
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Virgil Showlion
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Post by Virgil Showlion on Feb 4, 2014 17:19:22 GMT -5
I have no idea what any of you are saying. I think that means I win! Yay me!! I like this attitude. We should play cards some time.
I know a fun game called Mao. Only two rules:
1) All Jokers are the Nine of Diamonds;
2) I'm not allowed to tell you any more rules.
You have to vote for the game to see what's in it, eh? Seems... somehow... familiar.
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Peace Of Mind
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Post by Peace Of Mind on Feb 4, 2014 17:20:58 GMT -5
I have no idea what any of you are saying. I think that means I win! Yay me!! You won the very day you declared snow leopards to be foul, abominable beasties. At any rate, you is a winner. Fixed! I would never be so stupid or a sell out to ever declare that. Now put down the booze and weed and snap out of it! Me: WINNER and I get to pet the kitty!
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ken a.k.a OMK
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Post by ken a.k.a OMK on Feb 4, 2014 17:24:27 GMT -5
I'd like to play strip poker with POM.
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Peace Of Mind
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Post by Peace Of Mind on Feb 4, 2014 17:25:26 GMT -5
I'd like to play strip poker with POM. Wouldn't I have to be wearing clothes to play that game?
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ken a.k.a OMK
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Post by ken a.k.a OMK on Feb 4, 2014 17:27:20 GMT -5
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ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ
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Post by ՏՇԾԵԵʅՏɧ_LԹՏՏʅҼ on Feb 4, 2014 17:30:21 GMT -5
Only at the beginning of the game, POM - you can always throw your hand.
(I think Virgil needs to "dumb-down" these BTOTD's for the rest of us mere mortals.
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Peace Of Mind
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Post by Peace Of Mind on Feb 4, 2014 17:47:40 GMT -5
Ok - I'm ready to play poker now! One eyed Jacks are wild. And Virgil - no touching the, ummmm, kitties!
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