will it take off?

[daTeacha]

Tom -- when your single giant sand grain hits the bottom of the hourglass, the kinetic energy of the grain will momentarily register as an increase on any scale you have it on. Try jumping onto your bathroom scale and see it go over your stationary weight for a bit. In a real hourglass the weight lost by the sand losing contact with the upper chamber is compensated for by the increase in apparent weight caused by the force of the impacts with the lower chamber. The work done on the system to invert the hourglass originally will eventually leave the system in the form of an increase in enthalpy, but you won't observe a change in the weight of the hourglass in the real world.

We have wrestlers who are firmly convinced that if they are close to making weight, they can weigh a bit less if they stand on their head for 5 minutes immediately prior to stepping on the scales.

Moss Road -- think of a front wheel drive car with the rear wheels on a dynamometer. The dyno is wirelessly communicating with the car's computer. The front wheels are on the ground in the normal fashion. The dyno is programmed so that any motion of the car will result in an immediate, equal, and opposite motion of the dyno, causing the rear wheels to spin backward. If you put the car in gear, it will go forward, won't it? Of course it will since the retardation force on the rear wheels is negligible compared to forward force from the front ones. The two actions are totally independent. There is a correlation between the two, but the only thing the forces have in common is that they both act on the car. The size of the forces is nowhere near the same. Your line of reasoning would have the car sitting there burning the tread off the front tires while the rears were spinning backward.

The plane works the same way. Any force backwards on the wheels is negligible compared to the force forwards from the engine. The force on the wheels is not caused by the forward motion of the plane, but is an independent (and much smaller) consequence of it.

 

[HTWT]

Originally Posted by HTWT
I want to know how to find the three points of intersection of the 2 equations

1. Y= 2^x
2. Y= X^2

Two solutions are easy by inspection but what about the negative value for X.

Tom
the two solutions in the first quadrant are (2,4) as you stated and (4,16) but there is one other point in the fourth quadrant. The X-axis is the asympotate for the exponential equation but the parabols is symetrical with respect to the Y-axis. There is one more point of intersection very close to the origin.

 

[patrick_g]

dateacha, Depends on which set of assumptions you use. If you assume the MCB equals (in the opposite directioin) the speed of the plane, the plane experiences a littel more drag from wheel frictioin and inertia and takes off pretty mormally.

If you assume the more fun version (NO-FLY) of the MCB then it accelerates at a rate required such that the inertia of the wheels and friction of the bearings is sufficient to generate a force equal to the thrust of the planes propulsion and the plane remains totally stationery with respect to the world although its wheels are accelerating with no upper bound to ever higher speeds.

I didn't really follw the applicability of the dyno thing but since the above two cases cover the two possibilities if the dyno thing disagrees with both of the abhove it is flawed.

Pat

 

[daTeacha]

The dyno thing is like the rubber band thing I posted several pages back -- In the real world, the forward acting force from the engine is independent of the spinning of the wheels, therefore the plane will fly.

The more fun argument regarding the conveyor belt spinning fast enough to counteract any motion of the plane presumes (I think) motion is sensed through wheel rotation, not motion of the plane as a whole, and is therefore a moot argument. Besides, counteracting motion is not the same as moving at the same speed in the opposite direction. The problem stated motion of the plane, not its individual parts. If you want to start counting parts and not the whole plane, the conveyor should start running backwards (or sideways! or up and down!) as soon as the engine started turning over.

Point of information -- atomic sizes are generally in the range of 2 to 3 nanometers (10^-9 meters), which is billionths of a meter. This is for neutral atoms, not ions or molecules.

 

[patrick_g]

The dyno thing is like the rubber band thing I posted several pages back --

It certainly was the same for me, I didn't get that one either.

In the real world, the forward acting force from the engine is independent of the spinning of the wheels, therefore the plane will fly.[/QUOTE[

Actually the two forces (This makes the "WILL FLY" assumption): 1. thrust, and 2. counteracting force generated through inertia of the wheels as they are accelerated and aided by friction, both 1 and 2 above act directly on the plane and as they are equal in magnitude but opposite in direction they cancel and the plane does not move.

The more fun argument regarding the conveyor belt spinning fast enough to counteract any motion of the plane presumes (I think) motion is sensed through wheel rotation, not motion of the plane as a whole, and is therefore a moot argument.

I guess you don't get that part. There is no requirement whatsoever to sense the wheels rotation. Consider a simple summing amp with a "-" and a "+" input with an input resistor and a feedback resistor connecting the output to the "-" input. The output tracks the input +/- any zero shift and inversion but the output is amplified by the ratio of the two resistors. there is not a significant phase shift or time lag between input and output fluctuations.

Similarly a well designed (Hey if we can have a MCB why not a well designed controller with feedback) to cotrol the acceleration of the MCB? The controller for the MCB detects a displacement (arbitrarily small) in the planes position with respect to its initial position and accelerates the MCB as required to null that displacement.

Given a decent design of the controller the plane would never get more than a very small distance ahead or behind of its initial position. The plane was not a VTO or helo or jump jet and requires a fair take off run and speed along that run to take off. A good controller would hold the plane within a very small fraction of in inch of its original positioin. There is no accumulation of errors so the plane does not "creep" down the runway or slowly back up. It may microscopically oscillate around the initial position but those oscillaltioins can be made arbitrarily small such as to approach zero at any instant in time and to average out to be way close to zero over time.

Point of information -- atomic sizes are generally in the range of 2 to 3 nanometers (10^-9 meters), which is billionths of a meter. This is for neutral atoms, not ions or molecules.

Yes quite true. Also note that light at the wavelength of 340 nanometers is in the near UV spectrum and that if you slice an avacado in halves end to end and give each half a contrarotating twist it will come apart in two nice nearly equal pieces with the seed remaining in one piece (the larger piece if the two "halves" aren't so equal. How to get the seed out of the other half without smashing the fruit??? Hold the seeded half in the palm of your hand with fingers not curled around the fruit and smack the seed with a knife, embedding the blade in the seed. Give the knife a twist and the seed comes out leaving the fruit intact. Thumb pushing on the seed from behind (same hand as holds the knife) dislogdges the seed which should be held above a trash can.

Again, I can argue or discuss from either the FLY or NO FLY position and have no grudge or axe to grind with anyone in either camp as regards the physics. This is especially true if we can avoid religioius fanaticism and getting into ad hominem comments. This can and has been a very fun exercise (for most participants) especilly those with an open mind and sense of humor. The rest I fear may be arming themselves in preparation for purging the wrong believers off the face of the earth while chanting, "If you don't believe what we believe the way we believe it we will kill you!"

Pat

 

[Tom_Veatch]

Tom
the two solutions in the first quadrant are (2,4) as you stated and (4,16) but there is one other point in the fourth quadrant. The X-axis is the asympotate for the exponential equation but the parabols is symetrical with respect to the Y-axis. There is one more point of intersection very close to the origin.

You are absolutely right. I quickly, and not too accurately, sketched the functions and totally missed the fact that the exponential cuts a shallow chord across the parabola between the (2,4) and (4,16) intersections.

The other point of intersection in the 4th quadrant is very near (-0.76666469596, 0.58777475603). This value doesn't change after about the 5th iteration of a Newtonian iteration process - if round-off error in my calculator didn't have too great an influence.

To show you how long it's been since I fooled with any of this stuff, I had to go back to the textbooks to get the derivative of 2^X.

 

[patrick_g]

Tom, What did the math exercise relate to??? It was interesting and I like what you did with it but...

Oh, and you are a better man than I Gunga Din... I could see the other point (better sketch) but not give it values.

Somehow I am reminded of the friend who called me up and left a phone message for me to write down the following number.. 619-345-9876 and I dutifully did. He then informed me that if I ever need a wrong number to dial it as it was in fact a wrong number.

Pat

 

[Tom_Veatch]

Tom -- when your single giant sand grain hits the bottom of the hourglass, the kinetic energy of the grain will momentarily register as an increase on any scale you have it on.
...

Mea culpa, I totally ignored start/stop transients. My excuse is that my time quanta are too large and all transients decayed between two ticks of the cosmic clock.

 

[patrick_g]

Mea culpa, I totally ignored start/stop transients. My excuse is that my time quanta are too large and all transients decayed between two ticks of the cosmic clock.

Either that or your inertial frame of reference is highly accelerated and your time is different.

As an undergrad physics student taking tests where you were required to show the units I found the answers to some problems to be in radians after taking a square root and wondered where the square radians were supposed to come from. Then I realized that when I squared radians in other problems the results did not contain units of square radians. I suppose there is some sort of conservation of square radians and they aren't really being created or destroyed!

Pat

 

[Tom_Veatch]

Tom, What did the math exercise relate to??? It was interesting and I like what you did with it but...

I really don't know what it relates to. It just kinda rolled in on the MCB and got tangled up in the plane's landing gear about post #551 of this thread.

I'm intrigued by the idea of coupling the conveyor and the airplane via the rotational inertia of the wheels. I'm getting really curious what kind of acceleration would be needed to balance the thrust. It'd be interesting to run some numbers but I'm still resisting the temptation.