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Gregorian Donating Member (1000+ posts) Send PM | Profile | Ignore Fri Nov-24-06 09:40 PM
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64. Without actually pulling out a calculator...
Edited on Fri Nov-24-06 10:24 PM by Gregorian
1 No matter what you do, circumference is just the ratio of 2(pi)radius. When you do the math, it's surprising how big a change in radius that small addition makes.



Argh! I screwed up the last two.

Number two shows that I didn't understand Achimede's principal. Since the steel is heavier than water, it'll sink. But in the boat, since it's heavier than water, it would be able to displace more than it's own volume, due to the geometry of the boat. That is because the boat floats due to the fact that it incorporates enough air to make the entire structure lighter than the water that it displaces. Sheesh. It's been way too long since I've had to actually think about something other than George!

There's no way the third problem is a fixed leash. That's much too complex for just doing in one's head.


2 You haven't changed the mass in the swimming pool, whether the scrap iron is in the boat or in the pool. That's not really a good answer. It has more to do with the fact that it displaces as much water in the boat as out of the boat because it's more dense than water.

3 This is a good one. A 100 foot rope give the cow a 50 foot radius of grazing. Since the silo is also a 50 foot radius, it effectively cuts the cow's grazing area in half. Wrong. I just realized I didn't see this correctly.

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  -Any Mensa DUers? 3 math/physics problems for your consideration: karlrschneider  Nov-24-06 08:06 PM   #0 
  - You're posting during a geometry exam, aren't you?  dicksteele   Nov-24-06 08:10 PM   #1 
  - No. in the classic case... the attachment point at the silo  lapfog_1   Nov-24-06 08:19 PM   #7 
  - As the problem was posed  canetoad   Nov-24-06 08:29 PM   #20 
  - Yes, I neglected to mention that, sorry!  karlrschneider   Nov-24-06 08:30 PM   #21 
  - Im in MENSA  FARAFIELD   Nov-24-06 08:33 PM   #24 
     - No offense, I assure you, I just find these to be fun games for some who  karlrschneider   Nov-24-06 08:38 PM   #31 
     - Sounds like the "dumbing down" of MENSA, still an IQ of 144 is not  whistle   Nov-24-06 08:45 PM   #39 
     - I could be in MENSA but I never needed to  Nobody   Nov-26-06 12:23 PM   #101 
  - #2 - stays the same  Viva_La_Revolution   Nov-24-06 08:11 PM   #2 
  - i don't think this is correct  unblock   Nov-24-06 08:26 PM   #18 
  - Yes, you're right! Think Archimedes!  karlrschneider   Nov-24-06 08:32 PM   # 
  - For #2, there isn't quite enough information in the problem.  Tesha   Nov-27-06 07:00 AM   #132 
  - ack! I didn't take into account the weight of the metal vs. the wt of the water  Viva_La_Revolution   Nov-24-06 08:33 PM   #25 
  - No it is about displacement  Toots   Nov-25-06 07:27 AM   #87 
     - Sorry Toots, I didn't read your reply before making mine. n/t  greyhound1966   Nov-26-06 11:34 AM   #94 
  - The mass of the metal while in the boat causes the boat to displace  greyhound1966   Nov-26-06 11:33 AM   #93 
  - Nope. Something that floats displaces a volume of water equal to  karlrschneider   Nov-26-06 11:50 AM   #96 
     - But only if you assume that the scrap metal does not itself float, as someone  greyhound1966   Nov-26-06 12:48 PM   #104 
        - Yes that's true but one wouldn't ordinarily find water-tight hollow scrap  karlrschneider   Nov-26-06 12:54 PM   #108 
           - Thanks, partial credit got me summa cum laude...  greyhound1966   Nov-26-06 01:19 PM   #110 
  - Wouldn't the scrap in the boat also push some air in the boat below the water's surface level?  Bucky   Nov-26-06 01:21 PM   #112 
  - #1 is a bit more than 3 feet high...nt  SidDithers   Nov-24-06 08:12 PM   #3 
  - nah... that can't be right  Viva_La_Revolution   Nov-24-06 08:15 PM   #5 
  - Isn't it about 1.59 feet high?  Boojatta   Nov-24-06 08:21 PM   #9 
  - Yeah, you're right, I buggered it up...  SidDithers   Nov-24-06 08:27 PM   #19 
  - Yes, it turns out to be 5/pi feet  karlrschneider   Nov-24-06 08:33 PM   #27 
  - Don't understand this question. If you have 132,000,000 (25,000 * 5280) feet of wire  greyhound1966   Nov-26-06 11:47 AM   #95 
     - You got it...  SidDithers   Nov-26-06 12:21 PM   #100 
  - heh-what am I missing on #3?  nam78_two   Nov-24-06 08:14 PM   #4 
  - Number three is just the area of a 200 ft. diameter circle  A Simple Game   Nov-24-06 08:18 PM   #6 
  - Yeah agreed on 2 and 3  nam78_two   Nov-24-06 08:22 PM   #12 
  - You fogot that the point at which the rope is thethered varies by 50 feet...  StraightDope   Nov-24-06 08:22 PM   #13 
  - Yes, the rope starts wrapping around the silo once the cow gets  karlrschneider   Nov-24-06 08:39 PM   #34 
     - It would be sort of like the affect of gravity on an orbiting object around a  whistle   Nov-24-06 08:50 PM   #43 
     - That changes things considerably...  StraightDope   Nov-25-06 03:11 PM   #90 
  - The radius of the rope changes as the cow wraps around the silo  tridim   Nov-24-06 08:26 PM   #17 
  - Exactly. That's why it's a hard problem, it's a doulbe involute  karlrschneider   Nov-24-06 08:42 PM   #35 
     - It also has to be assumed the rope is attached at graze ht.  Mr_Spock   Nov-24-06 11:29 PM   #84 
  - Actually, no. On #3 I forgot to mention the rope is firmly attached  karlrschneider   Nov-24-06 08:35 PM   #28 
  - It's the difference of circles. 1) is an easy version of finding dD/dC  BlooInBloo   Nov-24-06 08:22 PM   #11 
     - yeah  nam78_two   Nov-24-06 08:24 PM   #15 
  - #3 isn't that bad...  StraightDope   Nov-24-06 08:21 PM   #8 
  - ahh but  Little Wing   Nov-25-06 02:04 PM   #89 
  - I win!  stonecoldsober   Nov-24-06 08:22 PM   #10 
  - good answers and here is more information I need.  uppityperson   Nov-24-06 10:05 PM   #69 
  - I'm busy trying to find a wire that long. Be back to you later.....  Lastlaughin08   Nov-24-06 08:23 PM   #14 
  - Uhhh.  jayctravis   Nov-24-06 08:24 PM   #16 
  - Beware relying on your intuition unless it is well-developed in the subject area.  Boojatta   Nov-24-06 08:36 PM   #29 
  - The question makes no sense...  jayctravis   Nov-24-06 08:49 PM   #42 
     - Well, I did say "if it was evely supported above the ground..."  karlrschneider   Nov-24-06 08:53 PM   #44 
  - I agree on all points  toshirajo   Nov-24-06 08:39 PM   #33 
     - Welcome to DU! Unfortunately you missed all 3.  karlrschneider   Nov-24-06 08:44 PM   #37 
        - Thanx Karl  toshirajo   Nov-24-06 09:06 PM   #52 
  - #2 - water level drops  unblock   Nov-24-06 08:31 PM   #22 
  - Does it matter if the scrap metal happens to be in the shape of a boat's hull? :)  BlooInBloo   Nov-24-06 08:38 PM   #32 
  - It might.  karlrschneider   Nov-24-06 08:45 PM   #38 
     - who? moi? lolol!  BlooInBloo   Nov-24-06 08:47 PM   #41 
  - Exactly!  karlrschneider   Nov-24-06 08:42 PM   #36 
     - Wait, wait, wait, by your logic...  BrotherBuzz   Nov-24-06 10:58 PM   #80 
        - It sure would! Not much though.  karlrschneider   Nov-26-06 12:52 PM   #106 
  - Ok karl... quit teasing  Viva_La_Revolution   Nov-24-06 08:32 PM   #23 
  - I used to be a Mensa  Blue_In_AK   Nov-24-06 08:33 PM   #26 
  - For #1  joe_sixpack   Nov-24-06 08:37 PM   #30 
  - Very close! 10 extra points to 'show your work'  karlrschneider   Nov-24-06 08:46 PM   #40 
  - 1 & 2  selfdestructive   Nov-26-06 12:10 PM   #98 
  - Right on #2, 1 is actually about 19 inches...  karlrschneider   Nov-26-06 12:49 PM   #105 
  - Hope this helps with #1.  aggiesal   Nov-27-06 12:35 AM   #130 
  - #3 results in an ovoid, assuming the cow can walk both  bleever   Nov-24-06 08:53 PM   #45 
  - I probably should have left that one out, it actually is a very difficult  karlrschneider   Nov-24-06 08:59 PM   #48 
  - Answers  boolean   Nov-24-06 08:54 PM   #46 
  - Are you thinking of it as a constrained maximization problem? lol  BlooInBloo   Nov-24-06 08:55 PM   #47 
  - No  boolean   Nov-24-06 09:06 PM   #51 
     - Yup - just said the same in a more jackass way...  BlooInBloo   Nov-24-06 09:11 PM   #56 
  - You got #1 exactly. The shape on #2 doesn't matter as long as it sinks  karlrschneider   Nov-24-06 09:01 PM   #50 
  - ah - I see the problem with 3 - the poverty of available paths on the "silo side"...  BlooInBloo   Nov-24-06 09:09 PM   #53 
  - What if....  boolean   Nov-24-06 09:10 PM   #55 
  - The boat wouldn't float in the first place!  karlrschneider   Nov-24-06 09:39 PM   #63 
  - I believe that if the scrap iron was in the shape of sphere or cylinder  heidler1   Nov-24-06 11:02 PM   #81 
  - excellent point on #2  porkrind   Nov-24-06 09:38 PM   #62 
     - Okay you got me. If I ever pose this again I will carefully specify  karlrschneider   Nov-24-06 09:43 PM   #66 
  - and now for the REAL answers:  antifaschits   Nov-24-06 09:00 PM   #49 
  - Well, there you go  toshirajo   Nov-24-06 09:12 PM   #57 
     - we already have faith based physicks, geology, and genetics.  antifaschits   Nov-24-06 09:21 PM   #58 
  - Small boat in a swimming pool with all that scrap would sink before you  spacelady   Nov-24-06 09:09 PM   #54 
  - In #3, consider the point where the rope is attached  bleever   Nov-24-06 09:23 PM   #59 
  - The shape of the grazing area looks a bit like round-bottom heart with a big hole in it..  TahitiNut   Nov-24-06 11:04 PM   #82 
  - Tricky!  porkrind   Nov-24-06 09:28 PM   #60 
  - oops, I assumed the rope was fixed at one point on the silo  porkrind   Nov-24-06 09:32 PM   #61 
     - Nice! That #3 took me hours when I first saw it years ago!  karlrschneider   Nov-24-06 09:41 PM   #65 
        - Wouldn't be the the worst Ponder This question I've ever seen....  BlooInBloo   Nov-24-06 09:44 PM   #67 
        - Thanks for the fun thread!  porkrind   Nov-24-06 09:58 PM   #68 
  - Without actually pulling out a calculator...  Gregorian   Nov-24-06 09:40 PM   #64 
  - #3 - 49,090 +/-  alittlelark   Nov-24-06 10:17 PM   #70 
  - I Would Expect Any Teenage Schoolchild To Be AbleTo Answer Each Of Those  ThomWV   Nov-24-06 10:24 PM   #71 
  - #2 - 19" (w/in 1% ) above the surace.  alittlelark   Nov-24-06 10:24 PM   #72 
  - #2 goes down  alittlelark   Nov-24-06 10:26 PM   #73 
  - Do you have any more problems?  alittlelark   Nov-24-06 10:33 PM   #74 
  - Along the lines of (3). Citation after solution/give up - fair warning - it's a bit harder...  BlooInBloo   Nov-24-06 10:45 PM   #75 
     - I'd like to see the elementary solution.  Gregorian   Nov-24-06 10:51 PM   #77 
     - elementary != easy. just means doesn't use concepts beyond typical high school...  BlooInBloo   Nov-24-06 10:53 PM   #78 
     - Yes. Please.  Gregorian   Nov-24-06 10:57 PM   #79 
     - The tether attached to the silo does not say it is fixed  alittlelark   Nov-24-06 11:12 PM   #83 
     - Do you mean the 'elementary' solution is an approximate one  muriel_volestrangler   Nov-25-06 07:08 AM   #86 
        - A solution gets the right answer by definition...  BlooInBloo   Nov-25-06 01:59 PM   #88 
           - In that case, I'll give up  muriel_volestrangler   Nov-25-06 03:27 PM   #91 
              - :)  Gregorian   Nov-26-06 11:10 AM   #92 
                 - I found a fairly simple integral that should calculate  BrewerJohn   Nov-26-06 12:44 PM   #103 
                    - Haha.  Gregorian   Nov-26-06 01:41 PM   #115 
  - #3 is the area of the silo  ChaoticSilly   Nov-24-06 10:47 PM   #76 
  - 1,2,3  Mr_Spock   Nov-24-06 11:42 PM   #85 
  - #2 is Down  stepnw1f   Nov-26-06 12:06 PM   #97 
  - 1 & 2  selfdestructive   Nov-26-06 12:10 PM   #99 
  - Geometry & simple algebra solution to #1:  karlrschneider   Nov-26-06 12:26 PM   #102 
  - *shakes fist*  selfdestructive   Nov-26-06 01:01 PM   #109 
  - Right, another way...  IMModerate   Nov-26-06 01:41 PM   #114 
     - Very good!  karlrschneider   Nov-26-06 02:27 PM   #118 
        - I think you mean...  IMModerate   Nov-26-06 03:25 PM   #119 
           - Well, there are actually 2 involutes  karlrschneider   Nov-26-06 03:47 PM   #121 
  - #3 is the rope fixed to a single point on the silo? If so, how far above the ground is  greyhound1966   Nov-26-06 12:52 PM   #107 
  - I think it is really indicative that this thread has generated so many  greyhound1966   Nov-26-06 01:20 PM   #111 
  - I wish I could join Mensa, but I am very stopid  Bucky   Nov-26-06 01:24 PM   #113 
     - In other words, you're a "moran".  StraightDope   Nov-26-06 02:00 PM   #116 
  - let's just say  selfdestructive   Nov-26-06 02:04 PM   #117 
  - Question 1: 23.097744 nanometers  Cookie wookie   Nov-26-06 03:44 PM   #120 
  - Question 2. Stays the same  Cookie wookie   Nov-26-06 03:49 PM   #122 
  - Ha! You forgot the water displaced by the air in the boat.  Bucky   Nov-26-06 08:57 PM   #126 
     - well, I'm not a Mensa, but what the hey  Cookie wookie   Nov-27-06 10:08 PM   #134 
  - I've never joined Mensa, but I'll try.  porphyrian   Nov-26-06 04:00 PM   #123 
  - Here's what I settled on as a solution to (3)  BrewerJohn   Nov-26-06 05:18 PM   #124 
  - You have the right approach but your region 3 is actually part of region 2!  karlrschneider   Nov-26-06 11:42 PM   #128 
     - Uh, if the cow can go there, I need to calculate it, no?  BrewerJohn   Nov-27-06 12:02 AM   #129 
        - Okay I see what you're saying but my solution considered all area alements  karlrschneider   Nov-27-06 01:06 AM   #131 
  - Here's the approach to answering #3  Gregorian   Nov-26-06 08:53 PM   #125 
  - I think my solution reduces to Wolfram's  BrewerJohn   Nov-26-06 10:06 PM   #127 
  - I'm not going to try to answer the first one.  Sentinel Chicken   Nov-27-06 07:35 AM   #133 
 

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