Originally posted by wolfgang59
mmmmmmm yes using that method a rough calculation gives me 1cm!
The ball at the top of the 50m tower travels further than the base of the tower by 100 * pi = approx 300m
300m in 24 hours = 300/(24 * 60 * 60) = 1/288 =approx 1/300
A 50m fall is approx 3 secs
3/300 = 1/100 metres = 1 cm
I forgot the ball would still have a velocity 2 meters up. So I get 2*PI*1000 meters=
6,283,185.307 mm circumference at the inner surface of the outer rim and 2 meters from that floor, it would travel 12,566.37 mm less. So divide that by 63 seconds (one revolution) and you get 199.46 mm/second difference and it takes 0.63 seconds to fall 2 meters at one G which puts the ball traveling 125 mm from the dropping point. A bit different than my original 70 meters for sure. The principle is still the same.
Anyone else get those #'s, 125 mm? About 5 inches. Ah, I see Wolfy did it to a couple of decimal places.
The guitar string was not a red herring, it can also be used to measure the circumference because you can slide the string under the 2 meter ruler if the 'floor' is sufficiently smooth, and you can make a decent measurement of the chord and figure the circumference that way and work out the radius. You can't just use the ruler by itself because you don't know the distance from the center of the line to the top of the curve. The guitar string gives you two pieces of information:
If the circumference is circular, the distance from where the string intersects the curve to the ends will be symmetrical, the same distance to the end of the ruler from both sides but if it is an ellipse, that distance will be non-symmetrical, say a 10 percent difference between the readings at one end V the other, to pick a # out of a hat.
All in all instructive at least to me! Good Catch!
It is clear there would be a coriolis effect almost all the way to the north and south poles, I wonder what the graph of the coriolis effect would look like plotted from pole to pole? It is not as obvious as it looks because the distance around the earth changes at each latitude so the velocity changes too.
Can anyone figure the distance a ball would move dropped from that same 50 meter high tower at a latitude of 45 degrees? If you got sticky enough, the top of the tower would not be at the same latitude, but slightly less, it sounds like a great problem for someone to solve!
Another angle: At what latitude would the ball drop 1 mm from the tower?