IQ or logic related question to ask!

[Yewheng]

  On 4/21/2015 at 8:09 AM, Angcheek said:

 

 

There is 1 thing wrong in your post ......... ITS TOO EARLY in the morning to think about this ....

 

 

My best thought is always early in the morning. Haha

[Porker]

  On 4/21/2015 at 1:14 AM, Turboflat4 said:

 

I knew how the balloon was going to go before I watched it, but this is a nice illustration of how something can be counter-intuitive until you think about it a little.

 

"Common experience" dictates that "solid" objects tend to slip back when you accelerate and slip forward when you decelerate. Here the frame of reference is the car, and it should be noted that it is a non-inertial frame (as acceleration is involved). When you write down the equations in a non-inertial reference frame you get "inertial" or "fictitious" non-Newtonian forces entering the picture, but I digress. The simple interpretation is that from the POV of someone accelerating with the car, a heavy object that isn't anchored down by a restraint or friction seems to accelerate in the opposite direction to any acceleration of the car. However, when you consider the perspective of a true inertial observer (the stationary pedestrian on the roadside), you will see that it is the car that accelerates and the object simply continues to move at its previous velocity (which was the velocity of the car before it started accelerating). Frames of reference matter a great deal.

 

In any case, it's "common sense" that solid objects move backward when you give the car sudden throttle. So why is this not behaving the same way? The simple answer is buoyancy. When the car accelerates, from the POV of the car's (non-inertial) reference frame, the air inside is accelerated backward and this causes a pressure gradient with higher pressure in the rear, and lower in the front. The He filled balloon, of lower density than air, experiences a buoyant force in the air causing it to "float" forward toward lower pressure. Easy peasy.

 

A more sophisticated way of looking at it is to consider any acceleration as a proxy for gravity. This is also surprisingly intuitive when you think about the "common experience" of a Helium balloon released from the ground: gravity acts downward, but the balloon floats away upward (neglecting crosswinds). So it seems that a He balloon flies opposite the direction of gravity. Now translate that intuitive understanding to the car, and think of the car's sudden acceleration forward as giving a gravity that is directed to the rear of the car (causing solid objects, including your head, to be thrown backward). The balloon, true to its "principles", flies away from this "artificial gravity" and moves toward the front of the car.

 

In actual fact, these two explanations are basically the same since a pressure gradient cannot exist without a force of some kind. Atmospheric pressure exists because of gravity, and the pressure gradient in an accelerating car exists because of fictitious forces in the car frame.

 

BTW, this is the same reason that when you move a spirit level forward, the bubble inside moves forward also, and vice versa. Again, counter-intuitive unless you think about it, but basically the same explanation - the air bubble is embedded in a higher density fluid (whatever they use in a spirit level) so it behaves the same way as a He balloon in air. And spirit levels are easily accessible, so everyone can immediately try this at home if they're not convinced.

Physics question deh:

 

You're a massive solid object. Will you recoil when I accelerate behind you? 😂😂😂

[1fast1]

  On 4/21/2015 at 3:49 PM, Porker said:

Physics question deh:

 

You're a massive solid object. Will you recoil when I accelerate behind you? 😂😂😂

 

I always recoil when you're anywhere around me.

 

And shudder in disgust.

[Ender]

Try Zeno's Paradoxes. I thing some mathmeticians had disprove the paradoxes..

http://en.wikipedia.org/wiki/Zeno's_paradoxes

 

  Quote

Achilles and the tortoise[edit]

Distance vs. time, assuming the tortoise to run at Achilles' half speed

"Achilles and the Tortoise" redirects here. For the 2008 Japanese film, see Achilles and the Tortoise (film).

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle, PhysicsVI:9, 239b15

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.^[9][10]

 

 

  Quote

Dichotomy paradox[edit]

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.– as recounted by Aristotle, Physics VI:9, 239b10

Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence can be represented as:

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion. An alternative conclusion, proposed by Henri Bergson, is that motion (time and distance) is not actually divisible.

This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. It contains some of the same elements as the Achilles and the Tortoise paradox, but with a more apparent conclusion of motionlessness. It is also known as theRace Course paradox. Some, like Aristotle, regard the Dichotomy as really just another version of Achilles and the Tortoise.^[11]

There are two versions of the dichotomy paradox. In the other version, before Homer could reach the stationary bus, he must reach half of the distance to it. Before reaching the last half, he must complete the next quarter of the distance. Reaching the next quarter, he must then cover the next eighth of the distance, then the next sixteenth, and so on. There are thus an infinite number of steps that must first be accomplished before he could reach the bus. Expressed this way, the dichotomy paradox is very much analogous to that of Achilles and the tortoise.

 

  Quote

Arrow paradox[edit]

If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.^[12]

– as recounted by Aristotle, Physics VI:9, 239b5

In the arrow paradox (also known as the fletcher's paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not.^[13] It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.^[14]

 

[1fast1]

  On 4/22/2015 at 1:05 AM, Ender said:

Try Zeno's Paradoxes. I thing some mathmeticians had disprove the paradoxes..

http://en.wikipedia.org/wiki/Zeno's_paradoxes

 

 

Zeno's paradoxes may never be fully "resolved" to the satisfaction of all. If you ask most mathematicians, they'll tell you it's as obvious as an infinite convergent series giving a finite sum. If you ask many philosophers, they will argue that proves nothing. The bottom line is that philosophers love to argue, otherwise they'd be out of a job. They also eschew real rigour, though they like to dress it up in fancy pseudo-rigorous speak, so they'll never really be able to give a definitive solution to anything.

 

Mathematics and the physical sciences. Empiricism backed with a rigorous logico-axiomatic framework. That's where it's at. That's all we need. Not philosophical mumbo jumbo.

 

Anyway, rather than ZP, I thought the infamous "airplane on a conveyor belt" problem is more apropos of this thread. Care to post it?

[Ender]

  On 4/22/2015 at 2:00 AM, Turboflat4 said:

 

 

 

Anyway, rather than ZP, I thought the infamous "airplane on a conveyor belt" problem is more apropos of this thread. Care to post it?

I google it and got a hit on Mythbuster on youtube. They busted it. But I think they are doing it wrong.

[Porker]

  On 4/22/2015 at 2:00 AM, Turboflat4 said:

 

Mathematics and the physical sciences. Empiricism backed with a rigorous logico-axiomatic framework. That's where it's at. That's all we need. Not philosophical mumbo jumbo.

That's why I love you deep deep 😂

[1fast1]

  On 4/22/2015 at 2:06 AM, Ender said:

I google it and got a hit on Mythbuster on youtube. They busted it. But I think they are doing it wrong.

 

I figured it out right before anyone needed to bust it. The plane moves and takes off. Jet turbines push air backward, and by conservation of linear momentum, there has to be a net momentum gain of the plane relative to the stationary ground frame. All the conveyor does is cause the wheels to rotate even more furiously, but unlike the situation in a car or other road-going vehicle, the plane's wheels do not provide propulsive force.

Edited April 22, 2015 by Turboflat4