[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 21
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P=m*g. Ничто не меняется в этой формуле от того, что мухи решили перекурить сидя на самолете.
Well there is one exception to the moment in time, you probably know about the weight of the hourglass counting down timeНу вот пусть эта и будет общей. Тему уже переименовал.
2 AlexEro: помните тот мерзкий предельчик? Жирную точку ставить рановато, оказывается. Все не так просто, на мехматовском форуме тоже спор разгорелся. Если интересно - загляните сюда.
(slightly puzzled) Whoopsie.
That's right, though: a function can be defined on a very tricky subset of the number scale. And the limit of a function really just requires that ANY sequence of points of the argument x, (it can be a discontinuous, tricky, but PREVIOUS sequence), converging to a given limit point, causes the corresponding values of the function to converge.
It is just that mathematicians are so used to operating on smooth and even segments, where the function is defined, that they sometimes forget that the function can also exist and converge on such a strongly discontinuous set.
OK, another experiment. There's a loaded gun that fires a pellet without gunpowder. It's standing on a scale. It weighs a ton.
Now it's fired. The bolt weighs 100 kilograms. It flew upwards of a kilometre. The scales have calmed down from the shot during this time. How much do they show? Obviously, 900 kilograms.
Now enclose that whole kilo in a sealed vessel. It'll be the same 900 as long as the dummy is in the air. But when the dummy falls, it will be a ton again (when the scales calm down).
Ну есть одно исключение в моменте времени, наверно знаете про вес песочных часов, отсчитывающих времяThis is correct. At a certain point in time there will be a jump in the scales' readings, the moment a ton of flies land on the plane at the same time, the kinetic energy of the flies' movement will change into the static energy of the scales' compressed spring, then, after an oscillating movement of the pad, the arrow will stop at the weight value, as it was when the flies were hovering merrily around the plane.
Взвешивается Замкнутая система со своей внутренней энергией. От перемещения компонентов системы в нутри неё, общая энергия (читаем - масса) не меняется. Тут нет разницы, что на что давит внутри системы.
So any hermetically sealed tin can is an insulated system? All right, then. You've probably seen those big inflatable balloons like this in the commercials:
people climb into them, they're hermetically sealed and they can walk on water, jump and do all sorts of sporty stuff. Let's say a child climbs into such a balloon. He is weighed along with the balloon. And let's say the child jumps up (but in a way that doesn't touch his head). And at the moment of jumping, his whole "closed" system is weighed. Will the weight of this system change?
OK, another experiment. There's a loaded gun firing pellets without gunpowder. It stands on a scale. It weighs a ton.
Now it has fired. The baton weighs 100 kilograms. It has flown upwards of a kilometre. The scales have calmed down from the shot during this time. How much do they show? Apparently 900 kilograms.
Now enclose that entire kilometre in a sealed vessel.
You want to ask how much the vessel weighs?
In fact, wheels don't play the least part in this detective story. And as long as the plane is on the runway, I'm afraid there's no need for wheels. Now, if it were in the air, we'd leave them alone.
Regarding the wheels. For some reason (probably out of habit) it is implicitly assumed that the transporter will move the belt against the movement of the plane. Well how, the plane is forward, the runway is backward, the wheels spin backward, everything is clear ! But that's not the case. As correctly stated, the plane does not give a damn about the runway, it accelerates on its own thrust - from the propeller or jet engines. So it pushes the runway forward, not backwards like a car. So even if there is friction, the transporter will push the lane forward. In other words, by the terms of the problem, the transporter will ensure that the aircraft at take-off is completely frictionless against the runway, i.e. it will accelerate and facilitate its ascent.
Относительно колес. Почему-то (наверное по привычке) неявно предполагается, что транспортер будет двигать ленту против движения самолета. Ну как же, самолет вперед, взетная полоса - назад, колеса крутятся назад, все ясно ! Но это же не так. Как верно было сказано, самолету по барабану полоса, он разгоняется на собственной тяге - от винта или реактивных двигателей. Поэтому он толкает полосу вперед, а не назад, как автомобиль. Так что если даже трение есть, то транспортер будет мотать полосу вперед. Иными словами, по условию задачи транспортер обеспечит самолету при взлете полное отсутствие трения об полосу, т.е. ускорит и облегчит его подъем.
i.e. the plane will take off??????!!!!!!
Richie, OK, let the shell be a ball of rubber weighing another thousand tonnes. That shell weighs a thousand tonnes and it will still weigh a thousand tonnes.