[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 78
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ЗАДАЧА №4:
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На весы поставили 2 одинаковых баллона и соединили их шлангом (см. рисунок).
Баллон N1 - изначально на 40% наполнен сжиженным газом "Пропан-Бутан".
Баллон N2 - изначально наполнен сжиженным газом "Пропан-Бутан" на 60%.
Вентили обоих баллонов открыли.
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Вопрос: Какой из балонов будет весить больше после того, как давление газов в баллонах уравновесится и температуры газов в баллонах станут одинаковыми?
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None. Due to the continuous gas-liquid transition, after some time the volume of liquid phase and pressure (and therefore the amount of gaseous phase) will level out.
It does not matter whether the hose is at the top or at the bottom. It may affect the speed of equilibration, but I am not sure about that.
TASK #5:
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Two exactly the same bulbs (LON, 220 volts) are connected in series to a 220 volt mains (see figure).
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Question: What is the current consumption when one bulb is switched into the mains is 1 amp?
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The answer to the problem will be given tomorrow.
Question: What would the current consumption be if the current when one lamp is plugged in is 1 amp?
The answer is 0.5)
TASK #6:
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Ametal nut weighing 100 grams fell into a 10 litre galvanised steel bucket with clean cold water from a height of 1 metre, floated for 2 minutes and then flew out of the bucket and fell to the floor. The temperature of the nut equals the temperature of the water. The bucket is filled to 2/3 of its height with water.
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Question: Explain how this is possible? How did it fly out?
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The answer to the problem will be given tomorrow.
ЗАДАЧА №5:
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Две абсолютно одинаковые лампочки (ЛОН, 220 вольт) включили последовательно в сеть 220 вольт (см.рисунок).
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Вопрос: Какой будет потребляемый ток при этом, если ток при включении одной лампы в сеть составляет 1 ампер?
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Ответ на задачу будет завтра.
half-opera.
ЗАДАЧА №6:
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В стальное оцинкованное ведро объёмом 10 литров с чистой холодной водой с высоты 1 метр упала металлическая гайка массой 100 грамм, 2 минуты плавала, а потом сама вылетела из ведра и упала на пол. Температура гайки равна температуре воды. Ведро заполнено водой на 2\3 своей высоты.
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Вопрос: Объясните, как такое возможно? Как она вылетела?
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Ответ на задачу будет дан завтра.
It was the nut from the T-1000 and he called it out.
Maybe she was spinning?
TASK #7:
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Two identical steel nails were dropped into a beaker of table salt solution. One nail is dipped into the solution to 70% of its length and the other to 50%.
A voltmeter was connected to the nails.
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Question: What will the voltmeter show? What voltage will it show?
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The answer to the problem will come tomorrow.
Mischek, who did you leave us for?
The Bolsheviks seized power, established a dictatorship of the proletariat, and dispersed the intelligentsia. Instead of decent food the people are being accustomed to fast food at an accelerated pace.
We have to take the power back, we can't go anywhere without you!
P.S. Here's an attempt to get people back to normal food (light):
There are 21 numbers. We know that the sum of any 5 of them is positive. Prove that the sum of all the numbers is positive.
Mischek, ты куда сорвался? Ветка-то только на тебе и держится...
P.S. Свой дурацкий намек, который можно понять как упрек (он им не был), я удалил.
It's all right, Alexei, it's just the squabbling that's wearing you out.
-How many is five? -Five.
-Fool
-You're the fool, there's no question mark.
-I'm from the MAI (traffic police, interior ministry, KGB...)
-We need to vote, who is in favor of the answer 10, Most...
Next question: ........
There are 21 numbers. We know that the sum of any 5 of them is positive. Prove that the sum of all the numbers is positive.
If sum of any 5 numbers from 21 is positive, then all these 21 numbers are positive, hence their sum cannot be negative.