The limitations of common sense

I would like to propose a topic here that would investigate the notion of common sense and how much of what we normally take for granted is not so necessarily common sense.The means by which I would like to proceed are by the fleshing out of understanding of the world around us by examining the "common sense" idea that the earth rotates about its axis. {no flat earthers please as there is a 300 post limit}
In doing so I would like to challenge people to try and resolve the questions that naturally arise which tend to be overlooked by people who merely absorb "facts" and not delve into implications of those "facts".
I would also enjoy input from our resident cosmologists and other scientists with the caveat that you stick with statements and questions on the basics of science to allow us an insight into how you think about these questions. As we progress {into different side topics as well as continuation of this one} I would like to see a learning process take place wherein gaps in knowledge and understanding on both sides are realized {or not as the case may be} It would be great if you could present questions to allow us to excercise our brains with actual thinking.First off, we will start with the "fact" taught to us that the earth rotates on its axis in a spin that is completed once every 24 hours.{23 hours 56 minutes 4.09053 seconds for those who care}Depending on where you are located on earth the rotaional velocity is from a little more 1000 miles per hour at the equator {25000 miles divided by 24 hours} to the pole where the velocity diminishes to near zero.
Now we ask the question how do we explain an example of motion meant to test this "fact"?
If we are located at the equator and take take a cannon ,point it straight up and fire a round, does the fact that the earth is rotating at 1000 miles per hour{roughly 1500 feet per second} mean that the round will be many miles away from us when it lands? Why or why not?This would probably be best located in Is it science. moved by the QueenThis message has been edited by sidelined, Sun, 2006-04-09 11:14 AM

I dunno. I suppose that if I were at the Equator and I jumped four feet straight up that I would land in roughly the same spot, no?

PhatCertainly that is the result of experiment. How do we justify the position that the earth rotates around at that speed though if experiment denies what common sense would tell us should happen in that event?

Common sense tells me that the firing of the projectile is like throwing a ball in a car.The projectile starts out with the initial velocity of the earth as well as the velocity imparted by firing it so it'll land in roughly the same spot as where it is fired from if fired directly up.Now on the other hand if you fired the projectile directly up (from the equator) and managed to stop the earth down to zero at the second it was fired you'd see that projectile fly very far away from where you were initially started. (on top of that you'd probably destroy earth to but who really wants to get into the physics of stopping the earth.)

Oh yeah how do justifiy aproximatly 1000 mph on the equator anyways? (for completeness so people don't think you pulled it out of thin air).

One of my favorite examples of something that doesn't add up according to common sense comes from the field of statistics.Say you're taking a survey that consists of a single question, the answer to which can only be yes or no. Assuming you're able to select people randomly, how many people would you have to survey to have an assurance of 95% that your result is correct within 5% for all the people in:

1. The state of Wyoming (population 453,588)
2. The state of South Carolina (population 4,012,012)
3. The state of California (population 33,871,648)
4. The United States (population 281,421,906)

The answer? Actually, I've forgotten the exactly correct answer, but it's a little more than 1700 people, and it's the same no matter what the population (as long as the population is significantly larger than 1700). Imagine that! It makes no difference whether you're surveying a population of 10 million or 10 billion, you only need to survey a little more than 1700 people!If anyone has a common sense explanation for why that should be the case, I'm listening!--Percy

I will believe whatever idea has the highest quantity and quality evidence. The collection of these beliefs is what drives my common sense.

quote:

---

I dunno. I suppose that if I were at the Equator and I jumped four feet straight up that I would land in roughly the same spot, no?

---

Yeah, I agree that you would. But a cannon ball rises miles into the air. In order for you to feel any possible effects to the same scale, you would have to jump as high as a cannonball flies.

quote:

---

Common sense tells me that the firing of the projectile is like throwing a ball in a car.

---

I was thinking that too, until it came to me that a car travels linearly, while anything on the equator would be on a path rotating around the center of the earth. My common sense tells me that it should land away from the cannon opposite the motion of the earth. Does anyone know if that's right?I personally come to common-sense conclusions simply by playing out ideas or situations such as this one in my head. (So I concede that I may be wrong from time to time!)

How many people do you need at a party before the probability of there being a shared birthday reaches 50%?Common sense answers only

The cannon has a ground speed based on the rotational velocity of the earth at the point where it is located, this vector is constantly changing direction as the earth rotates due to it's being held down by gravity.When the cannonball departs the cannon it has the muzzle velocity straight up plus the instantaneous horizontal velocity imparted by the cannon's forced rotational velocity, and this does not change direction once it leaves the mouth of the cannon.Strictly speaking, for it to "keep up" with the cannon it would have to speed up in the direction the cannon is rotating and speed up more the further from the surface it gets (to maintain it's angular position).Technically it should land behind the cannon (in direction of rotation), but the problem is that most cannons are incapable of reaching a significant enough height for this to be measurable (ie - within errors induced by wind sheer and true vertical alignment and cannon bore and cannonball spin and .... ).{abe}That's my 'common sense' answer, now for some examples{/abe}Assume it was up for 2.0 minutes, so it reaches it's peak at ~1.0 minutes (ignoring air friction, etc.). That's ~360{^o/day}*(1.0 min/(24{hr/day}*60{min/hr}) = 0.25^o that the cannon has turned ... and the cannonball is somewhere between that and zero behind it.If gravity was constant during the course of the flight of the cannonball and it was over a level non-rotating field, the height reached would be:ha = (1/2)gt²
ha = (1/2)*32.2 {ft/sec/sec} * (1.0 {min} * 60 {sec/min})²/5280 {ft/mile}
ha = 11.0 miles
This is a pretty powerful cannon, as the limits of space are considered to begin at 50 miles up and Mt Everest is ~5.5 mi high, so we should see some effect eh?With the radius of the earth at the equator being 3963 miles this is 0.28% of the earths radius. This could be enough that the gravity function should be switched to F = GmM/d² ... but we'll use F ~ gm for simplicity sake.The instantaneous ground horizontal vector at the muzzle is ~2(pi)(r)²/24 hours
s_ho ~ 2*pi*3963 = 1037.5 mph (check)The instantaneous horizontal vector 11.0 miles up is
~2(pi)(r+11.0)²/24 hours
s_ha ~ 2*pi*3974 = = 1040.4 mph (or 2.9 mph faster)Thus the cannonball is losing 253 ft/min to the rotation of the earth at apogee, which translates to a peak groundspeed of 253*3974/3963 = 252 ft/min, with the distribution being parabolic in time.Groundspeed loss at time t=0.0 = 0.0
Groundspeed loss at time t=1.0 min = 252 ft/min
Groundspeed loss at time t=2.0 min = ~0.0
(neglecting wind, friction etc etc etc)And the area under the curve is the total distance lost to the rotation of the earth under the cannonball.My penscratching makes this formula to be:
Vh_loss = 504*t-252*t²Integrating from 0 to 2 minutes gives me a total ground distance lost of:
Dh_loss = [(1/2)*504*t²-(1/3)*252*t³]_{(t=0 to t=5)}Dh_loss = [252*2²-84*2³] = 336 ft ... a football field ... measurable ... at this "scale" of cannon. (AND neglecting so many things that can cause errors of this magnitude - this is only 0.3% of the travelled distance)A closer approximation of real world cannons would be more like a 10 second flight time, and running the same calculations for that condition gives me a peak height of 402.5 feet and a ground distance of 0.2 ft ... getting harder to measure (while still neglecting so many things that can cause errors of this magnitude - this is only 0.02% of the travelled distance).If my math is right.Enjoy.This message has been edited by RAZD, 04*09*2006 08:07 PM

---

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

---

we are limited in our ability to understand
by our ability to understand

​

RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

5, or some such low number.

Something closer to 20-30, I think--if you pull five date tickets out of a bag, putting each one back after pulling it, the chances of pulling the same one twice seem low.My intuitive draw poker sense tells me that at around 20-30 pulls, the odds of pulling a duplicate are mounting...so I'll guess 25.

The cannonball doesn't lose its rotational velocity just because it's fired upward from a cannon.On a still day, my model rockets always fell close at hand, so I'd think whatever direction the wind is blowing would be more of a determinant of where the cannonball landed.

For those who do NOT want the calculation results DON'T highlight the following. Enjoy.This message has been edited by Admin, 04-09-2006 09:28 PMThis message has been edited by Admin, 04-09-2006 09:28 PM

---

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

---

we are limited in our ability to understand
by our ability to understand

​

RebelAAmerican.Zen[Deist
... to learn ... to think ... to live ... to laugh ...
to share.

DiscreetLabel

i.e. your taking the circumfrence of the earth and dividing by the time span it takes to go through one complete rotation to arrive at the aproximate linear velocity. (just for clarification sakes and for being specific)