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More ways to get Braingle...

Balancing Broom

Science brain teasers require understanding of the physical or biological world and the laws that govern it.

 

Puzzle ID:#8270
Fun:**** (3.12)
Difficulty:** (1.65)
Category:Science
Submitted By:electronjohn*us****
Corrected By:scallio

 

 

 



If you balanced a broom horizontally on your finger, so that your finger was exactly on the broom's center of gravity, marked that spot and cut the broom in two, then you would have a long and a short piece. The long piece being most of the handle and the short piece being the bristle end and a small part of the handle. Now what will happen if you weigh both pieces? (pick all that apply)

A) The short piece will weigh more.
B) The long piece will weigh more.
C) Both will weigh the same.
D) Your mom will find out and hit you with both pieces!


Hint

Think about two kids on a see-saw. Where does the heavy kid have to sit to balance the see-saw with his smaller friend?
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Comments

jonko
Nov 04, 2002

The correct answer to this teaser is that both pieces have exactly the same mass ( weight ) since they balance perfectly at the centre of mass ( centre of gravity ) The short piece is made up of the bristles as well as the broom stick itself which has mass . The long piece has a longer broom stick but equal in mass to the other piece. The example of a big boy and a small one on a teeter totter is correct about torque but the mass of the teeter totter itself was not considered in the answer . The mass on either side of the teeter totter is exactly the same or else it would NOT balance in the first place . In fact this is what scientists call a balance as opposed to a scale that uses force of gravity to measure weight . A balance ( teeter totter ) measures mass ...both sides have the same mass .
electronjohn*us*
Nov 04, 2002

Sorry Jonko but you are wrong. I posted the correct answer. The best way to prove it to you is for you to run the experiment yourself. Use a pencil with a ball of clay stuck to one side to add some weight to it. Balance it, cut it, and weight both sides. You may want it buy a box of pencils so you can repeat the experiment enough times to change your mind. I got this question from a physics book. When I get the time I will post the explanation they had for why the short piece weighs more.
bluetwo*
Nov 08, 2002

sorry, gonna have to go with electronjohn here. the way center of mass works is that the greater the weight on one side of the fulcrum, the shorter the moment arm must be to balance (of course, the converse is then true). using the classic seesaw example, a 50lb child sitting farther from the fulcrum can balance out a 100lb child sitting closer to the fulcrum. The mass on each side is most assuredly NOT the same, yet they balance.
electronjohn*us*
Nov 08, 2002

Thanks Bluetwo. Here is what the book says about this problem.
The shorter part is heavier. The short part and the long handle balance because they exert equal and opposite torques about the point of support, not because they have equal weights. The center of gravity of the short part is closer to the point of support, so its weight (which may be assumed to be concentrated there) must be greater to provide the balancing torque. Think of two kids on a see-saw: for balance, the heavier kid must sit closer to the fulcrum.
-The book is "Mad About Physics" by Jargodzki & Potter and is very interesting. I recommend it to all that find this stuff fun.
electronjohn*us*
Nov 11, 2002

Well Jonko, you sounded so sure of yourself that I just did the torque experiment that I told you to do just to double check the results. I did not have a pencil around so I just used a 25cm long plastic rod with about a 3mm diameter (a plastic straw should work well also). I taped a metal washer on one end and carefully balanced this apparatus on a thin metal edge. I marked the center of gravity with a black sharpie and cut the plastic rod in two at that point taking great care to be as accurate as possible. After weighing both on the balance here in my lab I got the following results:

short end with washer= 6.28 grams
long end= 2.00 grams

Not even close. I could actually feel the difference of the two sides by holding them in my hands. Conclusion: Not only was the answer I posted correct (which was backed up by the physics book I noted earlier and three engineering co-workers of mine, two of which have a PhD in Physics) but it became clear that Jonko did not bother to conduct the torque experiment even though he said he did. For the sake of the USAs education system please stop teaching physics.
snaps*au*
Nov 14, 2002

This one has really messed with my head. I have to admit that I tried it with a couple of bits of scrap would and arrived at the same answer as electrojohn. I think the thing to think about is the moments/turning forces/torque/whatever-you-choose-to-call-it acting about the balance point. Let's say you balance a ruler at it's mid-point. On one side you place a 10 gram mass, 10cm away from the mid-point. On the other you place a 20 gram mass, 5cm away from the mid-point. Correct me if I'm wrong, but the ruler will still be balanced. What about the mass either side? On one side it would have a mass of half the ruler plus 10 grams, while on the other it would have a mass of half the ruler plus 20 grams.
electronjohn*us*
Nov 14, 2002

Snaps you got it! It does challenge our common sense beliefs of what we think will happen. But that is what I like about the problem. Don't worry about being initially fooled by the question; everyone I know was fooled at first. The important thing is to be about to use science and readjust our thinking to fit reality and not our belief of reality. Some people have more of a problem with that than others, including Physic Professors.
Lyceum_
Dec 04, 2002

Very cool!
mad_axeman
Dec 04, 2002

I think the example of kids on a see saw is misleading. Simply becasue the seesaw has its pivot point in the center of the apparatus. However, the broom example above does not have it's pivot point in the center. As far as I can tell, all the exaplanations given by ElectronJohn rely on the seesaw example. This seems to be a vital flaw in this example.

I could be wrong though.

However, everyone with any sense knows that the correct answer is indeed D. My mum would kill me for this!!!!
poppycat
Dec 04, 2002

I think you hit the nail on the head there. The see-saw analogy is false, because the pivot point does not change from the middle no matter what weight is added. This is a totally different situation that just appears superficially similar. No, I don't have a physics degree (though my hubby does), it's just obviously a different set up.
datra16**
Dec 04, 2002

well if snaps says that john is right, then he must be!!! interesting problem...
Gmoney-Gdog
Dec 04, 2002

great teaser! by the way, i got the answer right and i would have 2 agree with electronjohn's answer...
O_wise_one*
Dec 04, 2002

Ok, I'm new at this (I'm just a Freshman in HIgh school), but couldn't part of the answer have to deal with the density of the object? I'm not sure at all, or if this is even relevant, but take for example ice. If I walk across ice standing up, I could fall though, because all my weight is centered at one point, making it dense. But if I crawl across on all fours, my weight is more spread out, therefore less dense, and I would have a lesser chance of falling though. Such as the washer on the shorter sick, it is more dense, and its weight is more focused on one point (the washer). Whereas in the other stick the weight is eveny distributed.
Again, i am not sure if this is relevent to the preblem, but I think it may help.
(user deleted)
Dec 05, 2002

Don't worry, "O_wise_one". I'm a freshman, too, and all these older people are confusing me to death!!
Great teaser, "ElectronJohn". (even if the answer is controversial!)
Bobbrt**
Dec 05, 2002

The answer is by no means controversial. It is absolutely correct. If things worked the way Jonko describes, then you wouldn't be able to use a lever to lift a weight heavier than you, and two people on a see-saw would always have to be the exact same weight for the see-saw to work. I like to think that younger folks could learn a few things on this web site, but if you keep misleading them, Jonko, they'll just end up confused. Sorry to sound antagonistic, but there should be no confusion about this teaser. It's perfectly fine.
polaris
Dec 10, 2002

Nice teaser! The expererments carried out werent actually done with a broom, Does this effect the results? Maybe there is only one way to find out! and will a mop give the same results as the broom?
singcan*
Jan 23, 2003

How can you blance it on your finger? Wouldn't it fall off? I got the answer in the end, good one had me thinking...........lol
Piffle*
Feb 16, 2003

great teaser. i agree with the answer it gives. shorter piece would weigh more.
jimbo*au*
Feb 23, 2003

Certainly the original answer is correct. This may help. Replace the bristles with another handle equal in size to the original, fixed at right angles to the first handle. They have equal mass. The proponents of the equal mass theory would now require that the centre of balance was at the end of the first handle? No way! The moment of turning is equal to the product of the mass and the distance from the fulcrum. The mass of the first handle would act through its midpoint making the point of balance about one quarter of the handle length from the bristles(other handle). Thus on one side you would have 3/4 of a handle and on the other 1.25 handles. The shorter bit chopped off must be heavier!
gogogo1
May 29, 2003

This one messed with my mind a little but I got it in the end. The see-saw theory is false but the original answer is true.
If you didn't get it, then You just got outsmarted by a 12-year old, ME!
fishmedAus*
Jul 08, 2003

I got it right away, but do not have all the technical jargon. It just made sense that the portion that carried the bristles would be heavier as it has the greater mass, regardless of the length of the broom handle. If you take the bristles alone, in most cases, they will outweigh the handle anway.
tommo
Dec 05, 2003

This is interesting because it's one of those that shows that the general 'instinctive' perception of the human mind is not always the truth. Without knowledge of physics it seems that just the weight is the item to be balanced (this is just perception)
The true answer (which is the one given with the question) is explained by one of Sir Isaac Newton's Laws, the conservation of momentum. It's not just the size of the weight or force that's important but where it is. The moment is given by Force x distance.
electronjohn*us*
Dec 05, 2003

Very insightful comment Tommo. It even helped me understand the problem better and I posted it in the first place, although I am not a physics genious or anything. Thanks for posting.
electronjohn*us*
Dec 05, 2003

uh, I mean "genius". Guess I am not a spelling genius either.
bluetwo*
Dec 05, 2003

thanks for the explanation, tommo. for all those saying that the see-saw example is inherently false due to the length of see-saw extending out past the lighter child, you are misguided. the whole key (as i, and now tommo, pointed out) is the concept of the MOMENT. in each example given, the moment arm is much shorter for the side with the lower mass, which is necessary to offset the longer moment and greater mass on the other side of the fulcrum (or balancing point). it does NOT matter (in the see-saw example) that the fulcrum does not move, because the moment arm is changing.
hip2b2Aza*
Dec 08, 2003

Sorry, but you are all wrong. If you cut the broom in HALF, both pieces will be of equal length, irrespective of where you made a mark. Therefore neither the longer or shorter piece will be heavier, but the half with the bristles.
goldenguide
Dec 11, 2003

Thats right, Mark, tell them!!
electronjohn*us*
Dec 11, 2003

Hip2b2, What part of this do you not understand?
"If you balanced a broom horizontally on your finger, so that your finger was exactly on the broom's center of gravity, marked that spot and cut the broom in half then you would have a long and a short piece."

The teaser clearly states that after you cut the broom you have a long and a short piece, which make sense since you were suppose to cut it at its center of gravity. Cutting in half only means cutting it in two. No where did I state "equal halves" or how they were equal (e.g. equal in length, equal in mass, equal in value, etc.). But nice try at being clever.
Bobbrt**
Dec 12, 2003

Awful lot of comments for a teaser that has absolutely nothing wrong with it, wouldn't you say? By the way, Electronjohn, on a couple of occasions I've had to explain to a submitter why their science teaser was rejected. When this happens I always refer them to this teaser. It is an absolutely perfect example of a science teaser in my opinion: the answer can be explained using technical wording about torque and moments, but it can also be reasoned out by someone who knows little about those things. It plays on your "scientific intuition" without requiring too much education.
electronjohn*us*
Dec 12, 2003

Thanks Bobbrt!
curtiss82**
Dec 24, 2003

I am a physics genius and I agree that the problem is correct the way it was stated.
liltunalol
Dec 30, 2003

oy vey! electronjohn, you really like to prove things, eh? this really got me thinking and i actually DID try it... and you're right, the shorter side IS heavier!! wow... interesting! and i love your sense of humore
liltunalol
Dec 30, 2003

oy vey! electronjohn, you really like to prove things, eh? this really got me thinking and i actually DID try it... and you're right, the shorter side IS heavier!! wow... interesting! and i love your sense of humore
dhang*
Dec 05, 2004

only I can say is... NYE!!!
great!
TiggrAus*
Dec 05, 2004

electronjohn I have absolutely no clue why everybody is making such a big fuss over an answer that I knew was correct as soon as I looked at it. When I was in 8th grade my friend ws failing physics and he came to a guy (me) who never had a physics class in his life to save his tail. He also had me doing all of his English homework, and I got him an A in that. It's an answer that is simply one based on common sense so people...don't be so extra analytical about this answer.
I_am_the_Omega***
Dec 05, 2004

Argggghhhh shame on me.. i only got it half right.... I picked C and D

Lol, then when I was reading your explanation, my brain tricked me (yep, it does that.. ), and I thought you'd said the longer piece was shorter. And then when I started thinking about the physics of it, I was like *wait a second! the shorter piece needs to be heavier!*

Of course, I went back and checked and that's what you'd said >.
maddieisacocker
Dec 05, 2004

hate it. it's so stupid just kidding but i dont get it
BastetA*
Dec 05, 2004

I got the answer wrong because I wrongly assumed both pieces would have to be of equal weight to balance. If I had thought about the hint, I would have realized this was not the case. Take the seesaw analogy. If you cut the seesaw in half, the half with the heavy kid would weigh more even though both kids were in balance. I can't believe I didn't see that, Duh! (This is why I was an English major).

I loved this teaser!
heyishme3
Dec 05, 2004

that was the easiest one ive heard
Chelsie*
Dec 06, 2004

THE ANSWER IS "D"!!
mcgrawactor1
Dec 06, 2004

Very intriguing. I was wrong when I surmised that it would be even because of balance, but after I read the explanation, it made more sense. I am not mathmatically inclined at all, so these kinds of riddles/problems are fun for me and expand my brain power.
mcgrawactor1
Dec 06, 2004

I am adding another comment cuz I went back and read all the comments & I think it is so funny that everyone is so jacked over this one; a sure sign that it is a success. Bravo, Maestro!!
ElectronJohn*us*
Dec 06, 2004

Thanks Mcgrawactor1 and everyone else that liked this one. For everyone rereading the earlier posts I just want you all to know that Jonko had two or three other posts, that have since been deleted, in which he increased his trash talk and claimed to be a physics professor and came down very strongly against the stated answer to this teaser. Those posts are what cause me and others to defend the validity of the stated answer. This teaser did cause quite a stir though.
Kollonel_Rabbit
Jan 16, 2005

so just so i understand how it works. the angular momentum of the parts of the broom has to be equal in magnitude but their direction is opposite right??
drussel3*us*
Jun 10, 2005

One incorrect statement that was made in the question, the center of gravity was probably in the rod of the broom, thus the brrom resting on his finger was not at the center of gravity. Just a technicality.
(user deleted)
Dec 05, 2005

excellent teaser!
(user deleted)
Dec 05, 2005

excellent teaser!
(user deleted)
Dec 05, 2005

excellent teaser!
(user deleted)
Dec 05, 2005

excellent teaser!
(user deleted)
Dec 05, 2005

excellent teaser!
azbee123*us*
Dec 05, 2005

well curtiss sure is modest... good teaser!
bluehawk*us*
Dec 05, 2005

Logically the shorter end would weigh more as thats where the bristles (the sweeping end)are. , whats all the ado???Good job. I liked it.
tbech7430
Dec 05, 2005

I think most people thought to hard on this one it was an easy one.
speediebean**
Dec 05, 2005

I got the answer right, and for the right reasons, because I discussed it with my son, who, here in the US, takes physics, and just so happens to have teachers who know a bit of something about it.
So, technically, my son got the answer right! Thank God he finds the subject breath-takingly fascinating!!
speediebean**
Dec 05, 2005

Pardon me, but a little addendum;
I am a Mom whose temprament is such that I would not have hit him with either of the pieces, I would have hit him with his wallet instead... is suddenly considerably LIGHTER wallet, after he bought me a new broom!
geniesue**
Dec 05, 2005

I'm no physics genius, but this isn't that difficult to understand. The see saw is a perfect example. Great teaser!
mischievousmiss
Dec 05, 2005

that was the most retarded one i have seen yet
orthogap
Dec 05, 2005

Actually, you have all failed. Read the original teaser. It instructs you to cut the broom IN HALF. By definition, two halves must be equal. Regardless of where you mark the center of gravity, If you cut the broom in half, you have two equal lengths, so there is no short piece to weigh! Perhaps physics students should be required to take a few more English courses. (Granted, you could also cut the broom in half by weight, in which case the shorter end would weigh exactly the same as the long end. If you cut the broom in half based on torgue applied at a single fulcrum, then you have the brain teaser!) Cut the broom "in TWO", not in half.
christine77**
Dec 05, 2005

wow, an easy teaser to start the day, I hope that coincides with the rest of the day, we all love easy days right?? easy Mondays?? hmmmmm....wishful thinking!!
shawneeo*us*
Dec 05, 2005

Uh-huh... Yes, I get it, although, before I looked at the hint and thought about it, I was all ready to write a comment saying, NO! WRONG! I'm glad I didn't! LOL! I'm learning. BUT, ortho and the other DO have a point, and that is that, although it does say you have a shorter and longer piece, it would be better to say "cut the broom IN TWO." instead of "...in half" because being a teaser, one might think the "in half" is a tricky clue. Otherwise, this very simple question, one we deal with in real life all the time, has apparently got some people really WORKED UP!
kimberlykayAus*
Dec 05, 2005

It has been awhile since I was a schoolgirl, but obviously paying attention in class served me well. I actually remembered an experiment of this sort and got the answer quickly.
I just wish we could see some more recent teasers. Seems that, as of late, all the teasers are being retrieved from the archives. This was a fun one though!
amyu05
Dec 05, 2005

ahhhhh ummmm well this was interesting. So I really want to know what the true answer is so I am going to conduct this perplexing experiment and figure it out for myself. Also just an "FYI" we don't use brooms anymore I SWIFFER SWEEP my floors! Thats the only cool way!!!
mogur*
Dec 05, 2005

Perfect, ElectronJohn, you got me. Duh, in my over-confident rush to judgement, I quickly assumed both pieces must have equal weight as in the simple balance scale (I'm a Libra). Forgot for a 'moment' that rotational inertia equals mass times the square of the radial distance.

You should have challenged Jonko to split a broom made of solid gold at its center of gravity. And take the shorter half.
Aarghonautsus*
Dec 05, 2005

My, my, my! Tempers will flair over these braingles! Guess it's good, though, to keep the mind racing and the blood boiling Thanks for a great teaser which, by the by, I got wrong!
mogur*
Dec 05, 2005

What makes this teaser counter-intuitive is that in most situations, mass and gravity are strictly porportional. That is, the force that an unencumbered object exerts in a gravitational field (its weight) is always directly proportional to its mass. But in a rotational system (such as a see-saw), mass and gravitational force no longer bear such a lock-step relationship. If you had suggested dividing the broom vertically through its center of mass, then the resulting pieces would have both the same mass, and equal weight. However, the center of gravity is not the same as the center of mass in a non-symetrical rotational system. What makes this teaser so counter-intuitive is that both shift in the same direction (toward the largest mass), but not at the same rate. It is intuitive for us to assume the equivalence of weight and mass and therefore jump to the wrong conclusion.
srichardson1066**
Dec 05, 2005

I liked it, especially the clever part about one's mother. By the way, I was unaware you knew Mom!
trueJesusfreak**
Dec 05, 2005

FUN! the thing about the mom was funny. Totally correct! Very easy!
redraptor50*us*
Dec 05, 2005

Loved this one, and got it right away, can just see my Mom now!!!
facr_1Amx*
Dec 05, 2005

Very easy! EXTREMELY easy. I don't understand why there's so many comments.
leroy_h*
Dec 05, 2005

i got it right. even the part about the center of gravity.
shopaholic918*
Dec 05, 2005

I think that one was kind of dumb. i mean come on who cares about how much it wighs? i don't!
shopaholic918*
Dec 05, 2005

i think that this one was kind of dumb. i mean come on... who cares about a broomstick? i dont! and that if you cut it in half it will weight the same.
whatever
POPSca*
Dec 05, 2005

Good one and the answer is correct.And I got it right away
lorelle_b*us*
Dec 05, 2005

Wow...a lot of people know how to leave a negative comment...ANYWAYS congratz and good job
southerngirl13*
Dec 05, 2005

you know it's just a freakin riddle. you don't have to go and do the experiment!!! that gets on my freakin nerves.
qtpie9148**
Dec 05, 2005

OMG i actually got that onje right away and i didnt even the hint to help me good teaser but yeah how can you balance a broom on your finger????
hockeygirl*mx*
Dec 05, 2005

that was a great teaser espacally cause i got it right!!!
hockeygirl*mx*
Dec 05, 2005

ps this was easy u all need to think less !! well most of u no offense
Cute-1*
Dec 05, 2005

Love it
Pascal
Dec 05, 2005

This is NOT torque! It is MOMENT. In this puzzle, we are analyzing a "free body diagram". We are making equal the "moment" on each side of the broom. We call this "summing the moments" about a certain point (that point being where your finger is). The moment is the force (weight) times the distance from your finger. When the moments are equal, it is balanced. TORQUE is when you have a cylinder and you attempt to "spin" the cylinder at one end and hold the other end fixed.
kandd*us*
Dec 05, 2005

Whoa! Everyone is taking this teaser a little too seriously.
Lighten up, it's Monday. For those who didn't get the right answer ... shame on you, it was easy.
kman613**
Dec 05, 2005

as i science freak, i loved it -good one, &although it was easy for some of us and harder and more difficult to understand for others - thats the whole point... you can't make every teaser the same amount of fun and challenge. we all come from different backgrounds, etc.
FulanitoGM*sv*
Dec 05, 2005

And here I thought all the comments would be about Mom smacking you upside the head with two pieces of a perfectly good broom that you just ruined just to prove some silly Braingle Teaser...

By the way, I got it right by just thinking about it and imagining the two pieces of broom. The theories and laws of physics that everyone mentions proves it scientifically, but I think you can get it right by virtue of common sense.

Man, I would have loved to have seen Jonko's comments... I could have used a good laugh!
hidentreasure**
Dec 05, 2005

Good teaser I got it.
thimblenogginus*
Dec 05, 2005

Well, duh! It's not rocket surgery.
mrticklesAus*
Dec 05, 2005

Good teaser electrojohn; perfectly correct as written. As previously stated, intuition is not always correct.
poopstain
Dec 06, 2005

honestly though...who cares? just use your broken broom for firewood
luvya92**
Dec 06, 2005

Whoa... thats alot of research you had to do, great Teaser... made me think ALOT!!
speediebean**
Dec 07, 2005

Thimblenoggin, 'rocket surgery'!?
hahahahahahaaa Good one!!!
Amalius*
Dec 07, 2005

very kool but i got right just guessed
PatH*
Dec 14, 2005

Pascal, I suggest you review your lessons on Torque. Torque is "the measure of a force's tendency to produce rotation about an axis..."

Torque and Moment can be used interchangeably in this case. Do your research before you lambaste someone.
__NK__Fire
Dec 15, 2005

I only said D so um ok.....
Warrior_Poet
Jan 19, 2006

If you cut the broom "IN HALF" as you said, there would be no long end or short end. Each end would be the same length, by definition of half.
ElectronJohn*us*
Jan 20, 2006

Many of you have commented that cutting something "in half" means cutting it "in two equal halves" even though in my teaser I clearly, in English, state that the result will give you two parts of different lengths. I feel it is a waste of my time to explain any further to those of you that do not understand this point but I will do so anyway in the faintest hope that I may enlighten some of you.

"In half" does not always mean "in two equal halves" and that for that matter even if it did I would still have to ask you equal in what way (value, weight, length, surface area, number of atoms, volume, moisture content, etc.)?

When someone says that they tore a piece of paper in half do you really think they mean that both resulting pieces are equal in size or some other property? Or do you have the basic intelligence to understand that all they are saying is they tore the piece of paper into two pieces?

In closing, there is a reason we have the terms "in half" and "in two equal halves" and that reason is because they mean two different things!
teen_wizAca*
Feb 04, 2006

Oh my goodness, don't think so hard! I do have to go with electronjohn, though....I've done experiments with this before. Good job!
puttumupus*
Dec 05, 2006

cmon now that was way to easy...of cource answer three would have been corrsckt also..
lmurray*cn*
Dec 05, 2006

THIS WAS A BASIC GENERAL SCIENCE, PHYSICS QUESTION.

WHY ALL THE FUSS. I HAVEN'T SEEN THE WORD TANGENT USED, BUT THERE SEEMS TO BE A LOT OF PEOPLE ON ONE.
cuteandditzyAus*
Dec 05, 2006

I think I learned this in the 8th grade. I don't understand why some people make it so difficult. I guess I've been called a hardhead more than once. Great teaser!
coachpisco*
Dec 05, 2006

Why do I find myself agreeing with Imurray more and more each day. Am I becoming my Imurray? Gosh, I hope not. But there seems to be a lot of friction concerning something that should be just plain fun.
bradon182001*us*
Dec 05, 2006

I'm not getting involved in this one. It's been too many years since I've been in school, so I'll leave this one up to you youngsters to hash out.
OldChinaHand**
Dec 05, 2006

One suggestion, take the short end of the broom and sweep this teaser, and is just a teaser, clean of these entire nay Sayers. We'll not go into the usage of the long end of the broom handle. This is well done teaser much more worthy and creditable than many of the comments. It was fun and educational as well. Thanks.
tpkarth*
Dec 05, 2006

That was some simple science I still remember from school...the see-saw hint makes it very cool
kman613**
Dec 05, 2006

Easy, and good one (I'm a science geek, what can I say). The answere given is correct and accurate. Mass does not equal weight (which I think confused some). Thanks for the good teaser - and thanks for everyone else for all amusing discussions.
auntiesisAus*
Dec 05, 2006

I really loved this teaser.....not for the teaser itself, but for all the dialogue it generated. Great to see people still get excited over things like this. Easy to prove, if your Mom isn't home, but still creating much ado.
undertherift
Dec 05, 2006

Sorry, electronjohn, cut in half means exactly that. You split it equally.

If you merely change the words "cut in half" you could avoid much of the confusion.

That being said, the teaser was a good one and your answer is correct.
scallioAus*
Dec 05, 2006

Loved this teaser!

Way cool and can't wait to perform the experiment with my kids.
if_i_may94*au
Dec 05, 2006

that was really weird? and the anser was wrong!
anodyne*us
Dec 05, 2006

I feel both parts would be equal. Even with the explanations, I still dont understand.
HScott13Aen*
Dec 05, 2006

Great teaser. Basic physics, but not the answer that might spring to mind (I got it wrong) and a sense of humour and didn't it get people talking!
I_Write_Books*
Dec 05, 2006

Not bad...although I'm not a big fan of the science teasers!
senther7Aus*
Dec 05, 2006

No sence watso ever.

If u cut it at the center of gravity, both peices would wegih the same. if u cut it in half, THEN they would be diffrent. so if everyhting the same, it would be (c)(mabye d)

o yea, teh joke was funny, so nice one, but mkae sure it mkaes sence next time u make another one plz?

ps: forgive me on my spelling
pi2b10us
Dec 05, 2006

i liked the part about your mom hitting you with both pieces, i don't know about my mom, her temperment would be right, but she does like science...
senther7Aus*
Dec 05, 2006

actually, i really dont get it, please excuse me for my comment. =(
nerys**
Dec 05, 2006

This was an awesome teaser! However, to all of those who seem to think that you have to be some kind of physics professor to understand it, I just want to let you know that my 7 year old, 2nd grade daughter knew the answer. I know she's smart and stuff, but she's certainly no physics genius!
bbbz*
Dec 05, 2006

many teasers are constructed with the idea of interpreting carefully chosen words literally. with that in mind you can not use the words "cut in half" and not mean "cut in two equal parts". if the cut is made at the mark then teaser is valid. if by "cut in half" you mean cut at the center between the end the handle and the bristles, then the end with the bristles still weighs more obviously. if by "cut in half" you mean rip down the center lenthwise then both halves weigh the same. anyway, a very poor choice of words in this teaser.
(user deleted)
Dec 05, 2006

yes i agree with bbbz. see according to m-w.com:

Main Entry: 1half
Pronunciation: 'haf, 'häf
Function: noun
Inflected Form(s): plural halves /'havz, 'hävz/
Etymology: Middle English, from Old English healf; akin to Old High German halb half
1 a : either of two equal parts that compose something; also : a part approximately equal to one of these b : half an hour -- used in designation of time

if i said "half an hour", you wouldn't think forty five minutes, would you? so if you say "half the broom" or "cut the broom in half", i would assume the broom was cut exactly in half, regardless of the mark. therefore the end with the bristles would weigh more, unless there was some kind of weight on the opposite end, in which case it is impossible to know the correct answer if the broom was cut directly in half. I believe it could have been word more accurately, but interesting concept nonetheless. made me think. it would have been great if it was in the trick section.
(user deleted)
Dec 05, 2006

Electronjohn said "When someone says that they tore a piece of paper in half do you really think they mean that both resulting pieces are equal in size or some other property? Or do you have the basic intelligence to understand that all they are saying is they tore the piece of paper into two pieces?"

If someone said they tore a piece of paper in half, technically i would assume the two pieces are of the same size. however, in speaking, the word half is more loosely used to define two pieces. as a slang, if you will. if someone wanted to be more accurate in saying they tore a piece of paper, they would say, "i tore a piece of paper into two pieces". now i would assume they are not of equal size. When deciphering a brain teaser, i look at each word and decide what it means, in the technical sense, before coming to a conclusion.
krystalklearsky*
Dec 05, 2006

it was a lot of fun, i got it right away
ElectronJohn*us*
Dec 06, 2006


OK, one more time.

Many of you have commented that cutting something "in half" means cutting it "in two equal halves" even though in my teaser I clearly, in English, state that the result will give you two parts of different lengths.

"In half" does not always mean "in two equal halves" and that for that matter even if it did I would still have to ask you equal in what way (value, weight, length, surface area, number of atoms, volume, moisture content, etc.)?

When someone says that they tore a piece of paper in half do you really think they mean that both resulting pieces are equal in size or some other property? Or do you have the basic intelligence to understand that all they are saying is they tore the piece of paper into two pieces?

Also remember that this is a science teaser and not a trick teaser. That should have been another clue.

In closing, there is a reason we have the terms "in half" and "in two equal halves" and that reason is because they mean two different things!
anodyne*us
Dec 06, 2006

I understand fully that you meant cut into two rather than two equal lengths. I am saying, if you have a long handled end and a short end with the bristles.. that balanced equally on one finger.. and you cut the broom at that point.. then if they are equal in weight on your finger, then they should equal the same weight when OFF of your finger. THAT is what I'm not getting. I already understand that you dont mean equal lengths of broom.
QrystalAca**
Dec 12, 2006

I used the definition of center of gravity to figure this out -- I can't help it, I'm a physics teaching assistant.

First, while the broom is in balance, it's like there are two pieces in balance: piece A, which is the long part of the handle, and piece B, which is shorter and has the bristles (B is for Bristles!).

We can pretend that all of the mass of each of the two pieces is located at their respective centers. That is, m(A) is at position x(A) and m(B) is at position x(B).

The center of mass equation is:

CoM = [ m(A) * x(A) + m(B) * x(B) ] / [m(A) + m(B)]

If we call the center of mass zero, then

0 = m(A) * x(A) + m(B) * x(B)

Since x(A) and x(B) are on different sides of zero, one is positive and one is negative. With |x(i)| as the absolute value of x(i):

m(A) * |x(A)| = m(B) * |x(B)|

Since the positions of the centers of masses are different, then the masses must be different.

And: since A was the longer piece, then |x(A)| > |x(B)| , and so m(A) < m(B) in order to balance.

And that, my friends, is exactly what went through my head as I was reading this teaser.
ElectronJohn*us*
Dec 13, 2006

Excellent analysis Qrstal! Hope you enjoyed the problem.

Anodyne, the point is that the two balancing parts do NOT weigh the same. Since the center of mass for the two parts are different distances away from the balancing point (one is closer to the finger and one is farther away) their masses can be different as well. If they were the same distance away from the balancing point then they would have the same mass, assuming they balanced. Try it out on a smaller scale and you will get it. Put a small piece of clay or something on the end of a straw and balance that. Cut it at the balance point into two pieces of different lengths and weigh each one.
vlermaAus*
Dec 15, 2006


this was a tough one, but the idea of the see-saw made it very sensible. More please.
teasermaster**
Dec 19, 2006

Sorry didn't get this one. Not a big fan of science teasers.
ElectronJohn*us*
Dec 20, 2006

"Sorry didn't get this one. Not a big fan of science teasers."

Then you are not a "TeaserMaster" are you.
luckypuppy*us*
May 15, 2008

This was an educational experience... especially with all the comments
doeheadAus*
Dec 05, 2009

Common sense prevails, Very easy.
craniacAus*
Dec 05, 2009

I think what confuses some people is that the balanced broom measures equal torque, not equal weight. The two aren't the same.
UptheHillA*
Dec 05, 2009

Nice one, but so wrong, your mother should beat that brat!!!
braniannd*jm*
Dec 05, 2009

hahaha mom is gonna hit us
talanpoeAus*
Dec 08, 2009

Great teaser! I got it wrong (much to my embarassment) because I confused "center of gravity" with "center of mass"; I failed to note that the object wasn't uniform.
EpikHigh
Dec 14, 2009

This was tricky but easy one
royale-ninja
Jul 24, 2012

i got the option D
Babe*
Dec 05, 2012

cutebugAus*
Dec 05, 2012

Alot of fuss over a very easy teaser.
CaramellAen*
Dec 05, 2012

I guessed the short piece would weigh more then I found out I was right. I just took a huge guess.
quads84*
Dec 06, 2012

Kinda easy. Most broom heads I've encountered weigh more than the handle they're screwed to. Therefore, it was a no brainer that the short piece would HAVE to weigh more.



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