Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

MLD

"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

MLD

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.

--
Jim Rusling
Partially Retired
Mustang, OK
http://www.rusling.org

Jim Rusling wrote:
"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.

Are insulating aerated blocks ever called cinder blocks?
Might any have a density under 1?

"MLD" wrote in message
...
Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

It has been a while since high school, but c=pi*d, so if c increases by 6, d
increases by 2.

2. Small boat in a pond. In the boat is a boy and a large cinder block.
The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown
overboard?
Obviously, assuming that the change in water level could be measured or
observed.

It goes down until the cinder block hits, then it goes back up, since the
displacement goes back to where it was.

I don't think you will get many variations on these.

"Jim Rusling" wrote in message
news:3s07c.9923$0h.1750@okepread04...
"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block.
The
boy throws the cinder block overboard and it promptly sinks to the
bottom.
Does the level of the pond rise or fall after the block is thrown
overboard?
Obviously, assuming that the change in water level could be measured or
observed.

MLD

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.


Argh, you are right! Dumb, dumb, dumb.

Ian Stirling wrote:

Jim Rusling wrote:
"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.

Are insulating aerated blocks ever called cinder blocks?
Might any have a density under 1?

Then it would not sink to the bottom.

--
Jim Rusling
Partially Retired
Mustang, OK
http://www.rusling.org

MLD wrote:
Recognizing that this is a Home Repair forum one must admit that
posting some interesting problems did invoke many comments and
variations of the solutions. Having said this I thought that a
couple more might not be objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and
pull it snug. Now cut it and then add another piece of rope 6
ft.long (rope is now 25,000 miles + 6 ft.). Fix it up so that the
rope stands off the ground evenly all around the earth. How far off
the ground is the rope?

About 1 foot.

Remember, 1 second ~= picocentury.

Jim Rusling wrote:
Ian Stirling wrote:

Jim Rusling wrote:
"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.

Are insulating aerated blocks ever called cinder blocks?
Might any have a density under 1?

Then it would not sink to the bottom.

And the level of the lake would remain unchanged.

Ian Stirling wrote:

Jim Rusling wrote:
Ian Stirling wrote:

Jim Rusling wrote:
"MLD" wrote:

snip
2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

The pond level will actually fall a little. While the block is in the
boat it is displacing its weight in water. Once it is in the water it
is displacing its volume of water.

Are insulating aerated blocks ever called cinder blocks?
Might any have a density under 1?

Then it would not sink to the bottom.

And the level of the lake would remain unchanged.

If the block floated, then you are right the lake level would be
unchanged. The question stated that the block sank to the bottom of
the lake.

--
Jim Rusling
Partially Retired
Mustang, OK
http://www.rusling.org

"Toller" wrote in message
...

"MLD" wrote in message
...
Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and
pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope
is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

It has been a while since high school, but c=pi*d, so if c increases by 6,
d
increases by 2.

I am as rusty as anyone. I think 2 is not quite right because (1) it ignores
pi and (2) you have found (almost) the increase in diameter, but you really
need the increase in radius which is half the diameter.
after some furious hen scratching I came up with 0.955 ft.

Educated arguments and rantings are welcome

Charlie

1. C = pi D

25000 = pi D1 = D1 = 25000 / pi
25000 + 6/5280 = pi D2 = D2 = (25000 + 6/5280) / pi

D2 - D1 = 6/5280 pi = 3.6171E-4 miles = 1.91 feet

Assuming the circumference of the Earth were 25000 miles, and
perfectly spherical, and the rope were equally distant from the Earth
at all points, the rope will be 1/2 (1.91 feet), or .955 feet above
the surface.

2. Floating objects displace their WEIGHT in water, not their volume.
Concrete weighs 150 pcf, water weighs 62.4 pcf.

Assume that the cinder block (concrete masonry) is 1 cubic foot in
volume and SOLID. It will weigh 150 lbs and displace 150 lb / 62.4
lb/ft^3 of water, or 2.4 cubic feet of water displaced. When it is
submerged, the block displaces its volume in water, or 1 cubic foot of
water displaced. Therefore, there is less water displaced when the
block is thrown in, so the level of the pond will actually be lower
with the block fully IN the water than when it is supported ON the
water.

Just for hoots, assume that the pond surface before throwing the
block in was 30 feet in diameter, and the surface of the bottom of the
pond were a perfect cone sloping down at 15 degrees toward the center.
How far does the pond surface go down when the 1 cu. ft. block is
thrown in?

Thanks for the fun,
Giz


"MLD" wrote in message news:BQZ6c.832

...
Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

MLD

using the formuls would only work if the earth had no mountians or canyons and
were perfectly round assumeing that without math my guess would be that 6'
added to 25000 miles would only raise it a few .001 of an inch if that.
2, The water level would fall because the block sinks it's density is more than
water. so on the surface the boat would displace it's weight once thrown in it
would displace it's volume that is less than the volume that it displaced from
the boat being pressed into the water by the blocks weight.
Regards
Gary
WWW.LIsheds.com
Storage Sheds for the NY tri state area

In article , (Gary) wrote:
using the formuls would only work if the earth had no mountians or canyons and
were perfectly round assumeing that without math my guess would be that 6'
added to 25000 miles would only raise it a few .001 of an inch if that.

Try again.

Even *with* mountains, canyons, etc the earth is actually very close to a
uniform oblate spheroid. (Not a sphe due to centifugal force, the
equatorial circumference is some 1000 miles greater than the polar
circumference.) The difference between the highest and lowest points on the
Earth's surface is some 30,000 feet; when compared to a radius of some 21
*million* feet, this is insignificant. Any random latitudinal cross-section of
the earth deviates from a circle by no more than about one-tenth of one
percent.

Increasing the circumference of a circle by six feet increases its radius by
6 / 2pi feet, or about 11.5 inches.

At times like this I miss Martin Gardner.

RB

MLD wrote:
Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

MLD

MLD wrote:
Recognizing that this is a Home Repair forum one must admit that posting
some interesting problems did invoke many comments and variations of the
solutions. Having said this I thought that a couple more might not be
objectionable to the HR group.
The first one is more enlightening than difficult--
1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

About one foot. The original rope is Pi * D long. you add 6 feet to
that, the new D also went up by 6/pi or 1.91 feet, which is split on both
sides: .955 feet.

2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.

While in the boat, the cinder block displaced water equal to it's weight.
When in the water it dispalces water equal to it's volume. Since it
sinks, we know that it's volume of water weighs less than it does, so
while it was in the boat it was displacing more water than it does on the
bottom, thus the level of the watergoes down.



John
--
Remove the dead poet to e-mail, tho CC'd posts are unwelcome.
Ask me about joining the NRA.

1. Place a rope (about 25,000 miles long) around the entire earth and pull
it snug. Now cut it and then add another piece of rope 6 ft.long (rope is
now 25,000 miles + 6 ft.). Fix it up so that the rope stands off the
ground evenly all around the earth. How far off the ground is the rope?

Forget the long math. We know that pi is the ratio between
circumference and diameter. C=Pi*D

If circumference grows by 6, then diameter grows by 6/pi = 1.909.
Divide diameter in half = 0.9549 it is this many feet above the surface
= 11.45 inches.




2. Small boat in a pond. In the boat is a boy and a large cinder block. The
boy throws the cinder block overboard and it promptly sinks to the bottom.
Does the level of the pond rise or fall after the block is thrown overboard?
Obviously, assuming that the change in water level could be measured or
observed.


It sank promptly, therefore it is much more dense than water. It took a
lot of water to equal its weight in displacement. What is now displaced
is its volume which we know must be less than the volume of that weight
of water because it sank promptly. The water level in the pond went
down.