# Re: A Question of Physics 101

"Roy Smith" <roy@xxxxxxxxx> wrote in message
news:roy-A7F7EC.10510821042007@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
In article <ncpWh.23932\$PL.22433@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Glen <gNOSPAM@xxxxxxxxxxxxxxxxxxxx> wrote:

efgh wrote:
"GROVER" <joseph.golaine@xxxxxxxxx> wrote in message
news:1177091182.736587.218780@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Since I've been enjoying the topics and discussions of this news
group, and I see that there are many posters who are quite bright, I
decided to pose a question concerning the laws of physics to
stimulate the group's curiosity.

The question is: If you hang two plumb bobs, say 50 feet apart are the
strings parallel?

I would say they are as close to parallel as one would care for them to
be.
If you want to get technical, they are not exactly parallel due to the
curvature of the earth. One would assume that the bottom of the plumb
bob
is pointing at the exact centre of the earth due to gravity and since
we're
on a ball, they wouldn't be exactly parallel. At 50 feet apart, the
difference wouldn't be enough to care about.

I was in HS when they built the Verrazano Bridge in NY. I remember one
of my teachers explaining that the uprights had to be 6" out of parallel
due to the curvature of the earth. I don't know if the number is
accurate, but that is what I recall (after forty years or so).

Glen

Let's do some quick math.

The towers are about 700 feet tall, and the Earth's radius is about 4000
miles. 700 feet / 4000 miles is about 1 part in 30,000.

Since arc length is proportional to radius, the tops of the towers are 1
part in 30,000 further apart from each other than their bases. The towers
are about a mile (call it 5000 feet) apart, so the tops are about 5000 /
30,000, or 1/6 of a foot further apart than the tops. Call it two inches.

Now, let's got to the video tape. Wikipedia says:

Due to the height of the towers (690') and their distance apart (4260'),
the
curvature of the earth's surface had to be taken into account when
designing
the bridge -- the towers are 1-5/8 inches farther apart at their tops
than at
their bases.

Not bad for back of the envelope, huh?

You're a star. :)

.

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