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# science question

## goofy grandpa

#### dibbern2

10:29 pm on May 27, 2009 (gmt 0)

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My grandson has posed this question to me and I'm too science-dumb to give him an answer. But I did say "I know just where to ask!" So here goes:

Pretend there is a train that has very tall cars, say, 30-40 feet. Also pretend (assume) the train can go very fast. 500 MPH sounds good.

You are in one of the cars. You paint a bulls-eye on the floor of the car. You set-up a ladder that allows you to climb to the top of the car. From there, you position yourself to drop a golf ball exactly over the bulls-eye on the floor below.

Will the ball land exactly below where you drop it, or will it land a little behind the bulls eye, loosing delta while it falls and car is rushing forward at 500 mph?

I think I know that the ball will hit the bulls-eye with no effect from the car moving forward, but common sense tells me it will land behind.

Of course, if it did land behind the mark, then things dropped from any great height would always land a little west of straight down as the earth turned during the fall, wouldn't they?

#### Leosghost

11:56 pm on May 29, 2009 (gmt 0)

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a difference is a difference .like Albert said some people think they get it ..some say they do ..very few really do ...
all of those posters who do get it ..even only because it feels right .Albert would be proud .( no surprises in there, reading your posts on other totally unrelated subjects still lets one understand imagination and or lack of ) ..willybefriendly ..you put it so nicely ..saved a diagram or 3 ..merci

shaddows ..:) "or not" ..ah one who has really seen the light ..relatively speaking ..

#### Leosghost

12:02 am on May 30, 2009 (gmt 0)

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to dibbern2 ..just show your grandson this thread ..if he can ask those kind of questions ( then the kid has a working brain ..encourage that ) ..he can handle this thread ..tell him we are all his grandpas friends and colleagues ..and here is what we think ..he can join in ( if he's under 13 he can have you type it ..if lawman Mike says it's OK ?..so as to accord with TOS ? )..foo is friendly ..:)

[edited by: Leosghost at 12:04 am (utc) on May 30, 2009]

#### dibbern2

12:15 am on May 30, 2009 (gmt 0)

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Much thanks, Leosghost. And everyone else, too.

#### kaled

12:28 pm on May 30, 2009 (gmt 0)

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it's just one of those things that I either intuitively know or willingly accept

You cannot "know" something that is untrue, you can only "believe" that which is untrue.

s = ut + 1/2 at2 where...
s = displacement (distance)
u = initial velocity (speed)
t = time (seconds)
a = acceleration (9.8 m/s2 but we'll call it 10 m/s2)

The initial vertical velocity is 0 m/s therefore
t2 = 2s/a
t = sqrt(2s/a)

So, if an object is dropped from a height of 5 m, it will take about one second to fall.

Let's assume the train is travelling at 100 m/s (~225 mph) i.e. the train will travel 100 metres while the object falls.
The Earth has a radius of about 6400 km, so this represents an arc of about one thousandth of one degree which yields a potential "deflection" of roughly 0.08 mm.

No information is available as to position or direction of the train on the Earth, however, since the maximum speed of rotation of the Earth is about 1000 mph, we can assume that the maximum potential "deflection" would be about 0.4 mm but this might be forwards, backwards or sideways. Ignoring the rotation of the earth, the "deflection" would be forwards.

Kaled.

#### Leosghost

12:33 pm on May 30, 2009 (gmt 0)

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let us point out that the OP dibbern2 never mentioned what if any planet the train was on :)..so all those carefull calculations and inferences are only relative to your personal assumption as to all the parameters which apply ..

whereas all other answers work anywhere ..including here .

#### Leosghost

12:44 pm on May 30, 2009 (gmt 0)

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BTW ..if you'd ever done free fall skydiving ( I have done many jumps ..beats all other "extreme sports" ..and all other "rushes" ) you'd know that in order to land on target ..you have to jump when you are past the target ..or move your arms , hands , legs head , body or combinations of all of these parts ( or skyboard or whatever) to track towards "target" before you pull the ring and deploy your chute ..

otherwise in a straight down ( put your head down feet up ) fall you'll land behind the target ..corse if you dont pull the ring you wont care much about the difference between splat and fell short ..;)

#### swa66

1:12 pm on May 30, 2009 (gmt 0)

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At 40ft height and 500mph it's trivial: bulls-eye as there the Coriolis forces and the relativistic effects can easily be ignored.
Air currents, spin on the ball, inaccurate release, etc would have far greater impact.

#### Leosghost

1:28 pm on May 30, 2009 (gmt 0)

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bulls-eye as there the Coriolis forces and the relativistic effects can easily be ignored.

depends on the size of the bullseye :) a bulls-eye of one micron ? ..as it was not specified ..

in Alberts original example of an elevator car and a beam of light ..one could have ( he could have ) argued that an elevator car width was too small to be important ..and we would not have the theory of relativity if he had thought that the distance was "trivial" ..

all things are related and have effect upon one another ..even the act of observation of the event ..and the position of the observer in relation to it ..etg inside or outside of the train ..at the front of the carriage or at the rear ..etc etc

hence my ref to Heisenburg ..which shaddows got..others may have?

edited for speeling

[edited by: Leosghost at 1:31 pm (utc) on May 30, 2009]

#### willybfriendly

4:01 pm on May 30, 2009 (gmt 0)

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Ignoring the rotation of the earth, the "deflection" would be forwards.

This fails to take into acount the changing gravitational vector. The ball is not falling towards the floor of the train car - it is falling towards the center of the earth's mass, which effectively remains behind the ball due to the fact it (the ball) is traveling on a tangent.

let us point out that the OP dibbern2 never mentioned what if any planet the train was on...

True, but if the ball is to "fall" then we must assume a source of gravitational attraction, which should be treated as a point at the center of mass. Even if we were to assume the train were passing by such a mass on a straight (tengential) line (which implies acceleration), the ball would still miss the target due to the changing gravitational vector, and in this case tidal effects (and yes, I know those would be negligble for something the size of the earth's mass, but certainly not if we are talking something like a neutron star).

The bottom line is - the ball will miss the target regardless of whatever assumptions we add to the original problem.

11:30 pm on May 30, 2009 (gmt 0)

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it is falling towards the center of the earth's mass, which effectively remains behind the ball

No it doesn't, at least on a (perfectly) curved Earth. On a flat earth, sure (as there is only one point where gravity acts straight down).

On a curved earth, gravity acts straight down at any point. As the ball does not lose forwards velocity, the line of force is always through the target. If the gravitational centre were to fall behind the ball, at what rate would you suggest this were to happen? How long until the gravity were at 45 degrees to the cabin?

Othewise, I maintain my poition that relativity, Coriolis effect, quantum uncertainty and uncollapsed waveforms are irrelevant due to the scale of this expreriment. As swa66 says, experimental errors and turbulance will make more difference.

#### kaled

11:36 pm on May 30, 2009 (gmt 0)

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I said
Ignoring the rotation of the earth, the "deflection" would be forwards.

willybfriendly said

This fails to take into acount the changing gravitational vector. The ball is not falling towards the floor of the train car - it is falling towards the center of the earth's mass, which effectively remains behind the ball due to the fact it (the ball) is traveling on a tangent.

Let me put it this way...

Before release, the object that is about to be dropped is travelling faster than the floor of the train (due to the curvature of the Earth) therefore it will travel forwards relative to the floor of the train.

Instead of talking about about changing gravitational vectors, do some maths...

If the floor of the train is travelling at 100 m/s, an object 5 m above it would be travelling at 100 (1 + 5/r) m/s where r is the radius of the earth.

So, relative to the floor of the train, the object will travel forwards by 500/6,400,000 m (since it will fall for one second). This equates to 0.08 mm - it's funny how two different mathematical approaches can yield the same answer!

So, to recap, unless the the train is travelling faster than the rotation of the earth, the direction of deflection will be determined by the direction and position of the train. However, if the train is travelling fast enough the deflection is guaranteed to be forwards, not backwards.

Kaled.

#### willybfriendly

5:00 am on May 31, 2009 (gmt 0)

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On a curved earth, gravity acts straight down at any point. As the ball does not lose forwards velocity, the line of force is always through the target. If the gravitational centre were to fall behind the ball, at what rate would you suggest this were to happen? How long until the gravity were at 45 degrees to the cabin?

And I was accused of being pedantic? Gravity is in fact an attraction through the center of mass of the two objects in question. The momentum of the ball is moving it tangentially away from the earth's center of mass (putting the earth's center "behind" it as observed from the side - as in a diagramatic view). This has the effect of decreasing the "forward" momentum of the ball while causing a "downward" acceleration, resulting in what was previously accurately identified as a suborbital trajectory.

Before release, the object that is about to be dropped is travelling faster than the floor of the train (due to the curvature of the Earth) therefore it will travel forwards relative to the floor of the train.

This is the essence of the tidal effect I referred to earlier, and while true is more than negated by the effect of gravity.

It looks like we all agree that the ball misses the target. The trick of the thought experiment is treating the "forward" trajectory of the train and the ball as parallel lines, when in fact they are not.

Larry Niven hit on this in one of the Ringworld books (I don't remember which) when Louis Wu soves the mystery of why people are being killed in a Puppeteer ship orbiting a nuetron star while in stasis. (Forgive me if my memory doesn't capture all the details here.) While statis is "supposed" to provide complete protection to the passengers, Wu realized (almost too late) that extreme tidal forces are at play, and the the only "safe" place in the ship is its center of mass. Anywhere else and the unfortunate result is being splattered, or mashed over the inner walls of the spaceship.

#### lawman

7:52 am on May 31, 2009 (gmt 0)

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Amazing that you all you smart people disagree with each other. If only I were smart enough to disagree with someone.

#### swa66

8:43 am on May 31, 2009 (gmt 0)

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The quantum mechanist will probably says that a you can't know how fast your ball goes if you know where it is (or the reverse: you can't know where your ball is if you know how fast it is.) [Heisenberg, _very_ simplified]

Similarly he'll also point out there's a chance the ball might pass through the floor of the cabin without any damage to either of them [Tunneling, also very simplified]

Even in Newtonian mechanics:
There is another variable all seem to assume: level rails. What about the train heading up a hill or down a hill ;)

Or what if the train were mounted on top of a very long spacecraft with a heavy mass and having a linear trajectory ?

But in practice any of the effects at the described speeds and distances are fully outweighed by the lack of accuracy in releasing the ball. Try releasing a golf ball from 40 feet up and see if you can hit the exact same spot twice in a row ...

#### tangor

9:04 am on May 31, 2009 (gmt 0)

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Ask Nick if the ball falls. In the scheme of things there's a good chance it won't. There ain't no black and white in this scenario, Einsteins involved or not. Think Jimmy the Greek and bet the long shot. And educate the little one at the same time. Even Carl Sagen would say the same billions and billions of times.

#### kaled

9:17 am on May 31, 2009 (gmt 0)

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Amazing that you all you smart people disagree with each other
The smart people agree - it's the not-so-smart people that disagree.

This is the essence of the tidal effect I referred to earlier, and while true is more than negated by the effect of gravity
In ballistics, there is no such thing as a "tidal effect". Tides are caused by the gravitational attraction of the moon (and sun). Since the train is travelling horizontally and since "horizontal" is defined as "perpendicular to local gravity" the only effects at play that could be described as "tidal" are eliminated.

Incidentally, "tidal effects" could not have killed anyone on the Puppeteer ship. If its orbit brought it very close to the neutron star, then gravitational gradients might have done so but would also have ripped the ship apart.

The trick of the thought experiment is treating the "forward" trajectory of the train and the ball as parallel lines, when in fact they are not
If this is a "thought experiment", then the trick is to analyse the problem rather than make silly guesses based on idiotic sci-fi stories. Face it, if this were an exam question, you would have got it WRONG.

The momentum of the ball is moving it tangentially away from the earth's center of mass (putting the earth's center "behind" it as observed from the side - as in a diagramatic view). This has the effect of decreasing the "forward" momentum of the ball while causing a "downward" acceleration, resulting in what was previously accurately identified as a suborbital trajectory.
This is drivel - if it were true, satellites would decelerate and fall out of the sky.

Kaled.

#### incrediBILL

10:05 am on May 31, 2009 (gmt 0)

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Think about this for just a sec, when you're flying in an airplane at 600 mph and drop something it falls straight down because the object is also moving as fast as everything else in the airplane.

Basically, if two objects (train and ball) move uniformly relative to each other the laws of mechanics are the same which is the classical relativity principle.

#### incrediBILL

10:12 am on May 31, 2009 (gmt 0)

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Don't take my word for it, read the 2nd paragraph in The great physicists from Galileo to Einstein
By George Gamow
[books.google.com], very easy to understand language on the subject.

#### dibbern2

10:21 pm on May 31, 2009 (gmt 0)

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Maybe I should just take the kid to a Cubs game, get his mind off this science stuff.

Hold it, baseball is full of physics. I'll probably just get asked to explain how a slider or a curve ball is thrown.

Fishing. Thats the answer.

#### swa66

10:43 pm on May 31, 2009 (gmt 0)

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fishing:
- launch a little weight with a line dragging behind it and unrolling from a spool: now that's an interesting trajectory to calculate :)
- how much air does a given fish need in its swim bladder to function properly ?
- how far can you see into clear water and when do you get only reflection ?
- how many fish can you catch before your boat sinks
- ...
Lots of physics questions possible there too, guess you'll need to find something else ...

#### Leosghost

12:29 am on June 1, 2009 (gmt 0)

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If only I were smart enough to disagree with someone.

Did you change your day job and finally become professional strat stroker while we weren't paying attention ? ..or make judge :) ?

#### BillyS

12:48 am on June 1, 2009 (gmt 0)

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Before release, the object that is about to be dropped is travelling faster than the floor of the train (due to the curvature of the Earth) therefore it will travel forwards relative to the floor of the train.

The ball is traveling faster than the floor of the train, but the floor of the train has to travel a shorter distance to circle the earth. The ball will hit dead center.

You guys are making this overly complex.

#### willybfriendly

5:27 am on June 1, 2009 (gmt 0)

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This is drivel - if it were true, satellites would decelerate and fall out of the sky.

Per Newton, they are. it is because their "falling" and their "fleeing" match that they stay up there.

An empiricist would acknowledge that the ball misses the target. A pragmatist would argue that close is good enough to count as a hit. A rationalist would wonder how we can know, as in really know, such a thing. An existentiallist would ask the meaning of conducting such an experiment in the first place.

But in the end, our intuition should be trusted in as much as the opposite of gravity is...

Comedy:)

#### kaled

6:56 am on June 1, 2009 (gmt 0)

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The ball is traveling faster than the floor of the train, but the floor of the train has to travel a shorter distance to circle the earth. The ball will hit dead center.
You are 75% correct - I knew there was something I was failing to take into account! However, as the object falls, the horizontal distance that needs to be covered will diminish.

Per Newton, they are
NO, THEY ARE NOT. Satellites in a circular orbit do not decelerate as a result of gravity acting tangentially.
Satellites in an elliptic orbit maintain a constant energy but velocity rises and falls.

Kaled.

9:12 am on June 1, 2009 (gmt 0)

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In support of kaled:
Think of a ice scater in a spin. As arms are pulled in, angular velocity increases. For every unit time, MORE orbit is covered as the radius decreases. This is due to conservation of angular momentum.

There will be two componants of angular momentum- one from the velocity of the train, and one from the spin of the Earth.

As the object falls, it will 'speed up' relative to the cabin floor, in both the eastward and train-bound direction.

Per Newton, they are. it is because their "falling" and their "fleeing" match that they stay up there.

Er, yes. So because acceleration is downwards ONLY, and not decelerative relative to the orbital path, orbit can be acheived. Otherwise, their 'fleeing' velocity would decrease with time, and orbit would decay.

#### LifeinAsia

3:40 pm on June 1, 2009 (gmt 0)

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BTW ..if you'd ever done free fall skydiving

That's because you weren't free falling in a vacuum. :)

#### Leosghost

6:03 pm on June 1, 2009 (gmt 0)

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But the train carriage wasn't specified as being a vacuum ..not that it would make any difference ..

#### LifeinAsia

6:19 pm on June 1, 2009 (gmt 0)

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Actually, it makes a huge difference.

If you are sky diving in a non-vacuum, you are subjected to horizontal and vertical deceleration (from air resistance) from the second you leave the airplane. More so once you open the chute.

In a vacuum, there would be no such deceleration, so you would go splat no matter when you pulled the cord to open your chute. Of course, you wouldn't be jumping from a normal plane either, since that couldn't fly in a vacuum.

[edited by: LifeinAsia at 6:23 pm (utc) on June 1, 2009]

#### esllou

6:51 pm on June 1, 2009 (gmt 0)

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BTW, just for the sake of symmetry, I went to AstroPhysicists.com and asked them about creating a 3-col layout using CSS only. Things have gotten a bit nasty over there and three members have been banned.

sorry.

#### Leosghost

7:12 pm on June 1, 2009 (gmt 0)

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I wasnt thinking of skydiving when I said
not that it would make any difference
but the dropping of things in carriages in theoretical trains ..
Neveretheless the imagery in your reply ..as did the reply itself and that of esllou ( <OT .btw I searched for "41 shades of blue" and can find nothing/OT> ?) ..made me smile ..( aint foo grand :)) ..

"splat" ..the technical term in the UK is a "candle or a "roman candle" ..we even have a parachutists song about it ( sung to the tune of "john Brown's body"..includes "they scraped 'im of the runway like a lump of strawberry jam..and 'ee aint gonna jump no more ..one of the few lines clean enough that I could quote here and stay within TOS ) ..

you want to really feel alive ..jump from a flying plane ..you want to stay alive ..take a "chute" with you ..;)

DaveAtIFG ( who is greatly missed ) said to me "you have to be crazy to jump out of a perfectly good working plane" ..he said it with a big smile ..funny how some threads take you back all of a sudden ..a very nice guy Dave :)

[edited by: Leosghost at 7:15 pm (utc) on June 1, 2009]

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