Hi Al... Just a few comments back...
Ans: Lightning travels faster than sound, so we see the light flash before we hear the thunder clap. The sound wave arrives after the light wave because sound travels slower than light. The distance to the lightning strike can be calculated this way by timing the time between the light flash and sound of the thunder clap.
Well, some of us lucky folks, with really sharp, and in depth perception, can hear the thunder before we see the lightning, so does that change the rules?
Does the timing go...one Mississippi, two Mississippi....three Missip....Whoa!!
Ans: Yes or No, depending on who makes the decision of what stamp to use. If you do the weighing, then yes, if the post office does the weighing, then No. That's because when you do the weighing you do it before the stamp is placed on the envelope, but when they do it they get it after you already placed the stamp on it, so it weighs slightly more. If they are making the decision though then they weight it before placing the stamp, so the weight is lower. I would bet they have a tolerance though so more generally the answer would be No.
A solution would be to put a dry stamp on then weigh it, but then the lick factor comes into play! It's getting too complex, I'll just email it!
Ans: A relatively simple problem involving specific heat capacity.
I guess that's something like my wife's old British cookery book, regarding making custard.
'Test the custard's temperature with your finger. It will be right when you put your finger into the pudding and you can count to 5. Less, it's too hot. More it's too cool'
Ever notice the 'soldering experts' on YouTube, they melt and smear. Probably became certified through a training session at Sam's Drywall Finishing School!
(I really do need a different hobby!)
I am not sure what you are trying to say about the lightening.
Sound travels much more slowly than light, so in the normal case we'll see the light before we hear the sound.
If you dont agree then you'll have to elaborate by setting up a case where your view might be valid. When we talk about logical things like this we often have to spell out the assumptions. My assumptions are only that the normal case is where the flash is maybe one or two miles or more away, and we are not blind.
As to the 'lick' factor, you've now introduced another dimension into the discussion that was not there previously. If i were allowed to do that i could disprove almost anything simply because the other party had no chance to consider that option yet.
But assume we allow this new issue, if you hurry up to the post office then it might still be wet so it might weigh even more. If you let it dry, it may weight the same depending on what you ate or drank that day and maybe the day before. There are also self sticking stamps that i use exclusively so this does not apply to me
The main point was that if you weight the envelope first, then you only know the weight of the envelope, so after you put the stamp on it weights more and could break over the threshold to the next price level. A solution would be to use a numerical approach similar to some electrical problems, which would mean all we have to do is weigh both the envelope and the stamp at the same time, and if it goes over the price break point then add another stamp and that should do it because the next price point will be much higher in weight than a single stamp.
A funny idea would be to tape a nickle on the envelope or maybe two quarters. People used to do this a long time ago in a pinch. That makes it weight more and we might get into a situation where when we add a coin it keeps going to the next level (ha ha) so we end up piling on coin after coin with no end in sight, until we realize that we ran out of money and so we cant send the envelope (he he).
The hot needle in the ocean issue was solved by specific heat capacity. The temperature and mass and material of the needle hold a certain amount of energy when hot and when placed into water of a known temperature will transfer some of the heat to the water. Since it is a static problem we only have to look at final values, and that would come from the point where everything is again in equilibrium. That would mean the water is a little hotter.
Easier to start with a small beaker of water. The temperature may not increase much, but in theory it could be calculated under a reasonable set of assumptions. IF one of those is to allow cooling through surface area, then there is a chance that the whole setup will cool down to the same temperature of the air in a certain amount of time.
Each of these kinds of questions are often meant to draw attention to some fact about accuracy or approach or both. Another example is the rail road track problem, where we have a rail road tract something like two miles long and it is straight and flat. We are told to jack it up with a jack underneath right in the center, so as to lift the very center up by 1 inch. The question is, how much do the ends move in toward the center? It is a very small amount and it may not be possible to calculate it on some hand calculators because of the limited precision, but going to a higher precision will allow it.
There are other issues that come up too, such as should we consider the curvature of the earths surface that een a flat track has a slight curve to begin with. And we have to be able to convert from miles to inches, etc. We always need some geometry of course.
Then there are the finer points, like what is the temperature of the steel rails, that affects their elasticity, so we dont necessarily end up with a straight track on both sides of the jack. We could specify that it is always straight though to make the problem easier.
So you see there are problems with most questions because there is always an underlying philosophy behind them. We always start with a set of assumptions and end with those same assumptions, unless we find that the solution was just too unreasonable to be accurate.