[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 103
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Это я и сам знаю. Построить прямую а затем прилепить к ней две окружности ?
Yeah. Or put a ruler on both at once, aim carefully and draw. ;-)
Ну там же в знаменателе везде степени двойки. Поэтому те числа в пропорции, которые я предложил, всегда будут сокращаться и оба последних числа получатся вида 1/М1, 1/М2
I don't really understand it. But come on - I take your word for it.
That's original, Yuri.
Same proportions here. Let there be a distance d between the centres. First draw line m through centres of circles. The centre of small circle is A, the centre of large one is B. Find the external tangent.
Suppose the construction is done and the point of intersection of line m with the tangent is known, O. We have two rays from O.
OA:(OA+d) = r:R. From here we find OA (geometrically), and then we plot the segment and obtain O.
Naturally, we build correctly, not by applying a ruler to circles. That is, we draw a circle with diameter OB and find the point of intersection with the great circle. And then connect O to this point.
I can't think of a simpler way to do this yet.
TASK #8:
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A conical bucket was filled with 30% pure water. There was a plastic ball at the bottom of the bucket.
Clean water was added to 97% of the bucket's volume. The ball then floated up and began to float on the surface of the
water.
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PS: The water in the bucket was clean, no impurities. Water temperatures - before and after topping up, ball and bucket - are the same.
The plastic ball does not chemically interact with the water or the bucket. The water is not chemically interacting
with the bucket. Magnetically and electrostatically, the ball does not interact with anything.
The density of the ball and its dimensions do not change.
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Question: Why did the ball float? Explain how and why this happened.
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TASK #9:
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There is a centrifugal fan.
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Question: How will the power consumption of the fan change if the outlet of the fan is completely closed?
TASK #10:
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An electric wire, through which a direct current of 10 amperes is flowing, is brought close to a
a compass and found that the wire did not produce a magnetic field. The compass is not faulty.
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Question: Why is the current flowing through the wire, but the compass does not indicate a magnetic field?
ЗАДАЧА №8:
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Коническое ведро было заполнено чистой водой на 30% своего объёма. На дне ведра находился пластиковый шарик.
В ведро добавили чистой воды до объёма 97% от объёма ведра. После этого шарик всплыл и стал плавать на поверхности
воды.
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PS: Вода в ведре чистая, никаких примесей. Температуры воды - до и после долива, шарика и ведра - одинаковые.
Пластиковый шарик никак химически не взаимодействует с водой и ведром. Вода не взаимедействует химически
с ведром. Магнитным и электростатическим образом шарик ни с чем не взаимодействует.
Плотность шарика и его размеры не меняются.
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Вопрос: Почему шарик всплыл? Объясните, как и почему это произошло.
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If you take away little things like atmospheric pressure difference at height H1 (water surface at the beginning) and H2 (surface at the end).
The upper half of the ball is affected by pressure Pv1 (formed by the mass of water above the middle of the ball) + Pa2 (atmospheric pressure above the water surface).
on the lower half Pv2 (Pv1 + pressure formed by water from the middle of the ball to its lower point).
We see that nothing depends here on the atmospheric pressure on the surface, as it seems at the beginning. It depends on V1 (volume of water above the middle of the ball) and V2 (volume of water above the lower point of the ball).
And the difference of these volumes in the first and second experiments is different (pun intended).
ЗАДАЧА №10:
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К электрическому проводу, по которому течёт постоянный ток, сила которого 10 ампер, близко поднесли
компас и обнаружили, что магнитного поля провод не создаёт. Компас исправен.
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Вопрос: Почему ток по проводу течёт, а компас наличие магнитного поля не показывает?
Is the wire in the "right" direction?