The Dropping Experiment of Newton and Hooke.

[peteshimmon]

This has been a bit of a puzzle to me over the
years. Long ago I read a short biography of
Newton by Knight that described how Newton
wrote to Hooke proposing an experiment dropping
a stone from a height that would show the
tangential velocity of the stone caused by the
rotation of the Earth. Hooke wrote back that the
stone would fall to the south east rather than
due east because London was not on the equator.
Because I had read unkind referances to Hooke I
thought you fraud, you have done the experiment
and found this out! Years later I obtained
Never at Reft by Westfall, a much detailed
biog of Newton. He spends several pages
describing this episode and finishes by
stating that Hooke did the experiment and
described his positive results to the Royal
Society. But Westfall than says that Hooke must
have been mistaken and does not explain! Why?
I think now that if a plumb line is used to
find the point directly under the dropping
point (or a point displaced a small distance)
then there will be an error as these lines only
point to the centre of the Earth at three
places, the poles and the equator. Well the
equator is a line but you know what I mean. Is
this the answer? The maximum error would be at
plus and minus 30 degrees latitude I think. It
is a possible experiment for schools anyway and
I wonder if any educators around here have come
across it. Like dropping marbles from a height
into trays of modeling clay. Plenty of details
to get right but it must be possible to show the
effect!

[grant hutchison]

I think Newton and Hooke were discussing what's now called Coriolis effect: the deflective pseudoforce experienced by an object moving in a rotating reference frame (such as the Earth). As the falling object moves closer to the centre of the rotating Earth, it is deflected in the direction of Earth's rotation: from west to east.

Grant Hutchison

[hhEb09'1]

I think Newton and Hooke were discussing what's now called Coriolis effect: the deflective pseudoforce experienced by an object moving in a rotating reference frame (such as the Earth). As the falling object moves closer to the centre of the rotating Earth, it is deflected in the direction of Earth's rotation: from west to east.

Possibly Hooke's reference to the east and south deflection was that the object would have an easterly velocity at ground level, and would be deflected to the right (south). Or, I guess equivalently, when it's dropped, it's in orbit about the earth, so its path is a great circle, which would be deflected away from the west-east line.

[Disinfo Agent]

Because I had read unkind referances to Hooke I

From whom, if I may ask?

[peteshimmon]

Cannot remember specifically, just general
reading at the time indicating Hooke was
argumentative, sneaky, an all round bad egg1
Some 300 years of bad press I suppose. This
was counterbalanced somewhat by a generally
excellent one hour television documentary a
few years ago. I say generally, the sound
editor needs shaking warmly by the throat and
informed that folk weilding drumsticks was not
really the background sounds of the time buts
thats another problem. I have seen a pendulum
kept running by a pocket watch movement at the
London science museum and this experiment comes
down from Hooke as I remember. He was
considered an excellent experimenter which
makes this subject a puzzle. Just what did he
show. Anyway I can think of a few things to
make a successful experiment here like
releasing marbles from a clothes peg operated
by a string with a length of elastic to
prevent jerks giving the marble a slight
sideways velocity masking the effect we would
be trying to find. And other tricks no doubt.
I think it is a good physics project!

[Disinfo Agent]

I asked this because it seems that Newton himself could be a rather unsavory character, and he had an ugly dispute with Hooke, so what you heard may have come from Newton or his supporters, and, in short, be biased. See here.

[peteshimmon]

Well Newton came up with the goods, a scientific
tract proving much mechanics mathematically
down to the last detail. This masks a deal of
faults. Hooke did much good work but in
general, the bad that men do lives after them,
the good is oft interred with their bones.

[Fazor]

I think Newton and Hooke were discussing what's now called Coriolis effect: the deflective pseudoforce experienced by an object moving in a rotating reference frame (such as the Earth). As the falling object moves closer to the centre of the rotating Earth, it is deflected in the direction of Earth's rotation: from west to east.
Grant Hutchison

Coriolis Effect
I too think this is the effect he's describing. I suggest checking that out if you haven't already Pete.

Not too long ago I was watching something on the science channel explaining the implications of this. Was kinda neat when it talked about ship-launched missles during WWII, and how in campaigns in the southern hemisphere there were cases where they corrected the wrong way and horribly missed all thier targets until they realised they had to reverse correction in the south.

[peteshimmon]

The development of mechanical fire control
computers was an ongoing thing for the first
50 years last century. The massive naval guns
would lob shells that were in the air for up to
several minutes. I think the scientists
employed would have thought of the difference
between north and south hemispheres, maybe it
was simplified equipment for ships expecting to
stay in the north. Anyway although this subject
is intimately connected with the coriolis effect
I think this simple experiment shows a simple
thing. Just do it on the Equator

[peteshimmon]

I can let my mind wander and dream up an
automated version of this experiment for
Science museums around the World. Especially
those who have scrapped or moved their
Foucault Pendulums. A high foot square tower
with perspex sides where water drops fall
alongside a plumb line. The starting and
finishing positions of the drops with respect
to the line are monitored with optical
assemblies and the data displayed on
monitors as well as on a website. Might
be worthwhile.

[Fazor]

I can let my mind wander and dream up an
automated version of this experiment for
Science museums around the World. Especially
those who have scrapped or moved their
Foucault Pendulums. A high foot square tower
with perspex sides where water drops fall
alongside a plumb line. The starting and
finishing positions of the drops with respect
to the line are monitored with optical
assemblies and the data displayed on
monitors as well as on a website. Might
be worthwhile.

Might be difficult to get accurate results as you'll have to deal with friction, surface quality, erosion (even at microscopic level), and the fact that the water drop will follow the path of least resistance. Just watch percipitation on a window or windshield of a car (parked of course, else you add wind resistance and all sorts of other factors). How often does the drop fall toward the ground in a straight line?

[peteshimmon]

He He. I was not thinking of the water dribbling
down the perspex sides but falling down the
middle of the tower! Is it always this difficult
to get a simple idea across? Anyway this
experiment would be a modern instrumented form
of a historic experiment and might have some
value illustrating old and new. It could also
have temperature and pressure readings feeding
into a program generating graphs. The idea is
of a continuing 24 hour process allowing the
statistics to build up. It might become a cult
website!

[Fazor]

He He. I was not thinking of the water dribbling
down the perspex sides but falling down the
middle of the tower! Is it always this difficult
to get a simple idea across? Anyway this
experiment would be a modern instrumented form
of a historic experiment and might have some
value illustrating old and new. It could also
have temperature and pressure readings feeding
into a program generating graphs. The idea is
of a continuing 24 hour process allowing the
statistics to build up. It might become a cult
website!

Ah, you Britts are ever soo clever I wonder what the height would have to be to get a measurable deviance.

[peteshimmon]

Clever? Moi? ...More a persistant plodder I
think! I am guessing 25 feet will do.

[hhEb09'1]

think! I am guessing 25 feet will do.

Where's my envelope?

Let's see, it takes about 5/4 sec to drop 25 feet (25 = ¹/₂ g t²), and the top is going 25'/(4000 miles) faster than the ground, which is going about 1000mph/sqrt(2) (at latitude 45), so we have about 4.4fph. Times 5/4 sec, that's 0.0015 feet, or 0.018 inch. A fiftieth of an inch.

You're gonna need a bigger boat.

[Kelfazin]

Hm..what if you fill the tower with a clear liquid that has a lower specific gravity then water, and then drip colored water into the tank. It would sink to the bottom more slowly then freefall. But would the coriolis effect still be noticeable?

[Gsquare]

Not too long ago I was watching something on the science channel explaining the implications of this. Was kinda neat when it talked about ship-launched missles during WWII, and how in campaigns in the southern hemisphere there were cases where they corrected the wrong way and horribly missed all thier targets until they realised they had to reverse correction in the south.

So that's why Saddam's Scud missiles kept missing thier target in the 1st Iraq war. he, he....(the best way to survive was to make sure you WERE the target).

BTW, apparently the Germans were way ahead of the Brits ...they did it successfully in WWI using the 'Paris' cannon from 75 miles out:

From... http://en.wikipedia.org/wiki/Paris_Gun

"The Paris gun was used to shell Paris at a range of 75 miles (120 km). The distance was so far that the Coriolis effect — the rotation of the earth — was substantial enough to affect trajectory calculations. The gun was fired at an azimuth of 232 degrees (west-southwest) from Crépy-en Laon, which was at a latitude of 49.5 degrees North. The gunners had to account for the fact that the projectiles landed 393 metres (1,290 ft) short and 1,343 metres (4,406 ft) to the right of where it would have hit if there were no Coriolis effect."

The projectile had a max. speed of almost Mach 5 ; actually 5200 ft/sec.

That gives an idea of the typical amount of Coriolis deflection possible in warfare.
Personally I think they should have avoided the problem by using GPS guidance.....

G^2

[peteshimmon]

Thanks! Let us say a hundred foot tower then. I
think you are coming to the reason Westfall
noted Hooke as being mistaken. I envisage water
drops falling through two grids about 3 inches
square that has LEDs and photodiodes measuring
the position at the beginning and end of
such a drop. I think eddies of moving air in the
tower might affect the drop so that many
measurements are required. It may still be
possible to use marbles and trays of clay in a
more temporary set up thouugh these days
hard hats may be needed. Yes those shells would
fall short firing from west to east. Hooke made
the point to Newton that the trajectory of a
falling body is a fraction of a very elongated
ellipse, ie if the Earth is reduced to a small
point after dropping, the body would fall and
swing round coming back to the point it was
dropped from.

[peteshimmon]

Doh! East to west!

[peteshimmon]

All this talk about firing shells has made me
dream up another possible experiment. A small
catapult lobs a marble about 5 feet in a
westerly direction onto a blue carbon on top
of a sheet of paper. About 20 lobs are made
with the paper being moved up a fraction each
time. Then the apparatus is rotated to lob in
an easterly direction, the blue carbon
replaced with red and the paper moved down
each time. Hopefully the line of blue dots is
displaced from the red. If we try we can make
physics fun for youngsters!