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Old 12-01-2012, 12:31   #46
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Re: Anchor Riddle

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Originally Posted by bstreep View Post
OK, here's the experiment. Tank is pint beer glass. Boat is the plastic shot glass. Anchor is the 2 ball bearings:

...

Answer: Water level in tank goes down. Just like I said EIGHT MINUTES AFTER THE PROBLEM WAS POSTED.
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Old 12-01-2012, 14:09   #47
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Re: Anchor Riddle

BStreep Rules!
So we can solve the rising water level in the oceans, by dropping anchors of our boats...
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Old 12-01-2012, 20:27   #48
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Quote:
Originally Posted by bstreep

Dan, whether or not the anchor is in the boat or hanging from the boat, doesn't matter. It still adds dramatically to the displacement. However, when the anchor is resting on the bottom, it now only displaces 1 cubic foot.

To settle this, I have a 29 gallon fish tank sitting in my home office. It needs to be cleaned up anyway - it's half full of SALT water - just make this right. I have a RC sailboat in the garage. It's just barely big enough to get into the tank, I think. It has a lead keel. I have some steel somewhere that would be equivalent to an anchor. I think I'll do this experiment this weekend, since we aren't going to the boat!
Everything I wrote mathematically concurs with everything you state and validate with experiment. Whether the anchor is in the boat or hanging the boat weighs 4450. The volume of the boat increases by 1 cu ft with a suspended anchor.

When the anchor hits the bottom the boat unloads to 4000 pounds and the anchor is no longer part of the boat volume.

I think there is no disagreement.
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Old 12-01-2012, 20:30   #49
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Re: Anchor Riddle

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Originally Posted by Ex-Calif View Post
Everything I wrote mathematically concurs with everything you state and validate with experiment. Whether the anchor is in the boat or hanging the boat weighs 4450. The volume of the boat increases by 1 cu ft with a suspended anchor.

When the anchor hits the bottom the boat unloads to 4000 pounds and the anchor is no longer part of the boat volume.

I think there is no disagreement.
Agreed.
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Old 12-01-2012, 21:00   #50
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Re: Anchor Riddle

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Originally Posted by Ex-Calif View Post
Everything I wrote mathematically concurs with everything you state and validate with experiment. Whether the anchor is in the boat or hanging the boat weighs 4450. The volume of the boat increases by 1 cu ft with a suspended anchor.

When the anchor hits the bottom the boat unloads to 4000 pounds and the anchor is no longer part of the boat volume.

I think there is no disagreement.
I hate to rain on your parade, but when the anchor is hanging in the water the boat will boat will weigh 4450 - 62 = 4388 lbs. However, the water level will not change until anchor hits the bottom.
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Old 12-01-2012, 23:20   #51
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Re: Anchor Riddle

BIll,

Nice job not wasting beer! Water worked just fine.

Regards,
Brad
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Old 13-01-2012, 00:29   #52
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Re: Anchor Riddle

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Originally Posted by Ex-Calif View Post
Whether the anchor is in the boat or hanging the boat weighs 4450. The volume of the boat increases by 1 cu ft with a suspended anchor.
Disagree. The boat/anchor combination weigh less when the anchor is suspended in the water. The anchor weighs less in the water. But the displacement is the same.

Think of an anchor made from wood. On the boat it weighs , say, a tonne. but in the water it weighs nothing though displaces a tonne, the overall displacement is the same.
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Old 13-01-2012, 02:09   #53
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Re: Anchor Riddle

+1

Perfect analysis!

Quote:
Originally Posted by Ex-Calif View Post
Let's try to add a little math to the problem... (i did this over my first cup of coffee. Corrections welcome)

I have a square hulled boat of 30ft X 8ft X 6ft. This is a volume of 1440 cu ft. It weighs 4,000 pounds. Its density is 2.7 lbs per cubic foot. Water has a density of 62 lbs/cu ft. So my boat floats as it has less density.

I add a square anchor of 450 lbs. Steel weighs about 450 per cubic foot. I add this anchor to the boat.

The boat now weighs 4450 and the volume is the same. The density of the boat is now 3.09 lb/cu ft. The change is only 0.39 and the boat still floats.

In the test tank, the boat sinks a bit and displaces water. Water rises.

We take the anchor out of the boat and put it on the dock. The boat rises the water level goes down.

Now we put the anchor in the tank. It is 1 cubic foot, at 450 lb/cu ft it is much denser than water at 62 lb/cu ft so it sinks. It also displaces 1 cu foot of water. Anything with a density higher than water (62 cu ft) will displace its volume so over that point the weight doesnt matter. (aluminum ball vs. steel ball question)

When then anchor is suspended and not touching the bottom the anchor as part of the boat "system" increases the boat volume by 1 cu ft. It is like I added any appendage outside the hull that takes up further volume. Another example would be a keel.

So I now have a 4450 lb boat with a volume of 1441 cu ft. This is 3.08 lbs/ cu ft. The boat rises, the water level drops but I doubt you could measure either change.
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Old 13-01-2012, 02:11   #54
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Re: Anchor Riddle

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Disagree. The boat/anchor combination weigh less when the anchor is suspended in the water. The anchor weighs less in the water. But the displacement is the same.

Think of an anchor made from wood. On the boat it weighs , say, a tonne. but in the water it weighs nothing though displaces a tonne, the overall displacement is the same.
True, but the wooden anchor is floating. In the problem, the anchor is resting on the bottom. That makes all the difference.
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Old 13-01-2012, 02:51   #55
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Re: Anchor Riddle

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True, but the wooden anchor is floating. In the problem, the anchor is resting on the bottom. That makes all the difference.
We branched off into 2 different scenarios. One is the anchor in the water hanging off the boat but not touching the bottom.

Quote:
When then anchor is suspended and not touching the bottom the anchor as part of the boat "system" increases the boat volume by 1 cu ft. It is like I added any appendage outside the hull that takes up further volume. Another example would be a keel.

So I now have a 4450 lb boat with a volume of 1441 cu ft. This is 3.08 lbs/ cu ft. The boat rises, the water level drops but I doubt you could measure either change.

This bit I disagree with, when the anchor goes into the water the wieght of the boat/anchor combination gets less. Though the displacement is the same until something else exerts a force on the anchor, like the sea floor.

And you can add as many appendages as you like, the only thing which will alter the displcement is the force exerted on the boat by gravity, i.e. the weight of the boat.

I think.
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Old 13-01-2012, 03:27   #56
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Re: Anchor Riddle

Answered long ago but confused recently!!!!
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Old 13-01-2012, 05:03   #57
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Water weighs 62 lbs cu ft and the anchor weighs 450 lbs cu ft. They both have density.

62/450=.13

This is why the anchor has a negative buoyancy of 86-87%

With the anchor in the boat the boat weighs 4450 and has a volume of 1440 cu ft. Or 3.09 lbs cu ft.

62/3.09=20.06

With the anchor suspended the boat has a volume of 1441 cu ft and a weight of 4391 or a density of 3.04

The boat rise and the water falls but again I dont think anyone can measure this in a lake or ocean.

Maybe Bstreep will suspend his test anchor and show us his results.
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Old 13-01-2012, 05:26   #58
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Re: Anchor Riddle

Quote:
Originally Posted by Ex-Calif View Post
Water weighs 62 lbs cu ft and the anchor weighs 450 lbs cu ft. They both have density.

62/450=.13

This is why the anchor has a negative buoyancy of 86-87%

With the anchor in the boat the boat weighs 4450 and has a volume of 1440 cu ft. Or 3.09 lbs cu ft.

62/3.09=20.06

With the anchor suspended the boat has a volume of 1441 cu ft and a weight of 4391 or a density of 3.04

The boat rise and the water falls but again I dont think anyone can measure this in a lake or ocean.

Maybe Bstreep will suspend his test anchor and show us his results.
Nope, sorry still don't buy it

SO.... when the anchor goes in the water the overall weight goes down, the density of the boat goes down and the boat rises. But when you add on the volume of the anchor now suspended in the water the overall displacement remains the same as before.

maybe...
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Old 13-01-2012, 11:13   #59
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Re: Anchor Riddle

Bstreep,
We need help!
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Old 13-01-2012, 12:23   #60
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Re: Anchor Riddle

Folks, the weight of the anchor does not change when it goes in the water. It still weighs the same, it just now also has an additional buoyancy force on it. It's the same with the boat. The boat doesn't weigh nothing just because the buoyancy and weight forces cancel eachother out.

The boat and anchor as a system have a weight which is counteracted exactly by the bouyancy force, whether the anchor is in the water or not. Only once the anchor touches the ground that a third force (normal force from the ground up on the anchor) is added and the bouyancy force is decreased, decreasing the amount of water displaced by the boat.
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