A W Smith
Philosopher
Now the earth spin has been changed.
Paul
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Don't laugh!
http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed06.htm#transcript
Imagine that an object is falling towards the earth.
An apple is falling towards the earth from a height, say, of, hmm, I'd say 100 meters.
And let's calculate how long it takes for this apple to hit the earth which should for you be trivial, of course.
So here's the earth...
and the mass of the earth is about 6 times 10 to the 24 kilograms.
And here at a distance, h--
for which we will take 100 meters--
is this apple, m, which, say, has a mass of half a kilogram.
There's a force from the earth onto the apple and this is that force.
And the magnitude of that force is mg and that is 5 newton.
I make g ten and just round it off a little.
Now, how long does it take this object to hit the earth? So, we know that 1/2 gt squared equals h.
It doesn't start with any initial speed, so that is 100.
G is 10, this is 5, so t squared is 20.
So t is about 4½ seconds.
So after 4½ seconds, it hits the earth--
so far, so good.
But now, according to the Third Law the earth must experience exactly the same force as the apple does but in opposite direction.
So therefore the earth will experience this same force, f--
5 newton, in this direction.
What is the earth going to do? Well, the earth is going to fall towards the apple--
f equals ma.
So the force on the earth is the mass of the earth times the acceleration of the earth.
The force, we know, is 5.
We know the mass, 6 times 10 to the 24 so the acceleration will be 5 divided by 6 times 10 to the 24 which is about 8 times 10 to the minus 25 meters per second squared.
How long will the earth fall? Well, the earth will fall roughly 4½ seconds before they collide.
How far does the earth move in the 4½ seconds? Well, it moves one-half a earth t squared.
That's the distance that it moves.
We know a and we know t squared, which is 20.
One-half times 20 is 10 so that means this distance becomes that number times 10.
It's about 8 times 10 to the minus 24 meters.
The earth moves 8 times 10 to the minus 24 meters.
That, of course, is impossible to measure.
But just imagine what a wonderful concept this is! When this ball falls back to me the earth and you and I and MIT are falling towards the ball.
Every time that the ball comes down we're falling towards the ball.
Imagine the power I have over you and over the earth!
But you may want to think about this--
if I throw the ball up, going to be away from the earth I'll bet you anything that the earth will also go away from the ball.
So as I do this, casually playing--
believe me, man, what a glorious feeling it is--
earth is going down, earth is coming towards the ball.
The earth is going down and I'm part of the earth and I'm shaking this earth up and down by simply playing with this ball.
That is the consequence of Newton's Third Law even though the amount by which the earth moves is, of course, too small to be measured.