Brain Teasers ? or 50 Years On........... ?

It certainly looks like it. Both Willy and myself have to labour through the classical route of resolving forces and calculus to find an answer. I seem to recall a few of my fellow class mates who could "see" how to solve complex problems at a glance. They went on to do maths and physics at university. I was stuck with engineering

Nothing wrong with Engineering!

Regards,

Willy BSc PhD CEng MIMechE

Think my daughter did more. She just finished her last exam of final year of Biochemistry today. Signed up for a Doctorate next. My son was a reluctant A level student but is now doing a BTec in Computing (and coming top of his class no less) and starting an apprenticeship next month. Both enjoying what they're doing, which is after all the important bit. Ok the second most important bit after becoming financially self sufficient so I have more money left for toys.

Regards,

Willy.

I have a pair of scales with identical jars each containing equal quantities of water. Read Graham Clarke’s thread on Naim Pricing for my inspiration here ! (I don't really have a pair of scales etc its all theoretical)

In the left hand jar I have placed a very light "ping-pong" ball attached to the base of the jar by a thin, light wire. I had thought of using the empty shell of a Statement but……..

In the right hand jar is an identical empty shell of a Statement…."ping-pong" ball, completely filled with lead and attached by a thin light wire to an external structure such that it is entirely immersed in the water, without touching the sides or base of the jar.

Do the scales stay level, or do they go down on the left or do they go down on the right ?

My ability to "see" answers is surely not universal. It worked on the second teaser, but not on the first one. While I spent some time thinking about that one as well, I was not even close to figuring it out. It has been like that as long as I can remember. It used to drive some of my teachers nuts, when one of the "normal" children bettered the acknolewged geniuses .

Lets see how I get along with this one...

Both jars hold the same amount of water and have the same weight. The Ball floating in the left one is attatched to the jar. This should add its (very small) mass to the total. The Ball in the right jar is heavier then its counterpart, but not attatched to the jar. Its mass should therefore not be added to that of the jar. The left side of the scale should go down a little.

You can't do much better in life than a happy family and a well-paid job that you really enjoy.

Let's see what others have to say...........

There seems to be a consensus of two (politicians might claim this to be unanimous since all who voted are in agreement).

+1

Both of my children are quite young (son 3 yrs, daughter 1), lively and healthy. They bring a lot of joy into our lives. While my wife stays at home for the moment, both of us like ours jobs, as well.

In that case, I feel compelled to upset the balance by guessing that the scales will stay level! 

New recruit to the LibDems ????

The right hand scale goes down.

The load at the right hand is equal to the water in the jar, plus the weight of water displaced by the ball. I think.

Quite a bit of "thinking" going on here.

Obviously at least one person has the right answer. Note, two people obviously also qualify as "at least one person".

Nope! The only thing this thread is going to do is push me towards the MRL party......

Nope. The scales will go down on the right. The water in the right jar is pushing up on (trying to float) the immersed ball, making the tension in the wire a bit less than would otherwise be due to the weight of the ball. The upwards force on the ball is matched by a downwards force on the base of the jar, and scale.

Yep. What I said, but more succinct.

Both balls have the same volume, irrespecive of their very different mass, and are fully submerged.Because of that, they should displace the same amount of water.

Hi Don, I've missed your brainteasers!

To extend the fencing question, could you utilise the fencing in any other shape (ie other than the rectangle) which would create an even larger area (albeit perhaps not so efficient for lorry parking!)?

Steve D

True that. But there is no change in the net force on the left tank. In contrast, When the suspended ball on the right is immersed, it exerts a downwards force equal to the weight of water it displaces. Interestingly, it's weight is irrelevant once it is heavy enough to not float.

This sounds plausible. I just can't get over the fact, that both jars have the same amount of water displaced.

It is true that they have the same amount of water displaced. But the jar on the left has no net  external force to do so. The ball is pulled under by the wire attached to the bottom which "lifts" the jar by an equal amount. Then think of the jar on the right as having the ball pushed down into the water by gravity. The force to balance this comes through the scales.

Pan on the right will go down. The mass of the lead, or at least part of it, is being supported by the water.

I know because I carried out a simple experiment at home.