Seneca » October 10th, 2016, 2:23 pm wrote: In order words: Miles Mathis predicts an apparent speed-up of 21% precisely at the end of the curve and the beginning of the straight part. And this is what we are trying to prove or disprove here. He would call it "apparent" because the speed-up is only observed if you measure the distance using the "wrong pi" (3.14..) as we are doing in this experiment. It would not be observed from the viewpoint of the ball. I hope you can follow me. If we see that there is a speed-up, there is no way this can be caused by friction so it would prove M.M. is right. If we see no speed-up that would prove M.M. is wrong. I don't see how you could argue that there is a speed-up but you can't see it because of friction. Daddie_o, what do you think?
I think the set-up is sound. Ultimately whether it's viable depends on how much loss of speed there is due solely to friction over, say 25-50cm. If there was a massive (gradual) slowdown due to friction, then the speed at the end might be lower than in the curve. But from Steve's video, it appears there is very little loss due to friction. So in that case, it should work: it should take the ball more time to go from the mid-point of the bend to the end, covering 25cm of 'length', than it would take for it to go down the straight end that was also measured at 25cm long. It probably won't be 21% longer due to friction, but even 10% or 15% would be astonishing (though I predict it will be very close to the expected value).
You pointed out that there is a tradeoff with how long the segments are that you're measuring, and I agree. Last night I started imagining what it would take to do the experiment. I was thinking that you could actually mark off segments of the tube every, say, 5cm. So then you could compare speeds at various segment lengths with the same experiment, going all the way up to the entire length of the curve, which in my example was 50cm.
Just to be clear, though: there is no speed-up or speed-down. I guess you could say 'apparent' speed-up/down, but technically his argument is that the speed is constant but the distance traveled is longer in the curved tube (and it is made longer precisely by curving it). So if I'm driving my car at 100km/hr, you might measure my average speed by seeing how long it takes me to drive a certain distance, say San Francisco to Los Angeles. But if I drive at the same speed and you time how long it takes me to drive from San Francisco to San Diego, which is further away, you wouldn't conclude that I'm driving slower just because it takes more time. You would have to take into account that I've driven a longer distance. That's all we're doing here. I'm not sure anyone would describe the shorter amount of time it takes to drive to LA as 'speed up.' It's just a shorter drive.
I don't want to be a tight-ass, and I do get your drift. I think it's just important to be precise since there has been such confusion on this issue. I was also a bit confused and uncertain about this, too, but it has since become crystal clear to me as I've tried to explain it. I did get an answer from Miles about Simon's question, but I am now certain that the answer is B (and am also certain that is what Miles would answer).