Weight under water

[John Vigor]

Gee, I dont know . . . every time I ask a simple question about a spinning propeller or a dimpled hull, I get swamped with complicated answers. Why do things always lurch out of control?

I have always had a hard time understanding Archimedes. I could never see why a king's crown made of gold would displace more water than the very same-sized crown made of iron. If both their volumes are the same, then the same amount of water should be displaced, surely? But no, apparently not.

And although I might have snoozed through physics classes, I do understand the difference between mass and weight. They are not the same. Mass is volume times density. It's burned into my brain.

I lived in South Africa when the government peremptorily announced the country was going metric. This aroused a lot of resentment, and I felt it my duty as a daily newspaper columnist to launch a resistance movement. After all, why should we now have to buy butter by its mass instead of its weight, as the government insisted?

I had so much ammunition, and so many troops on my side, that the Metrication Board got worried and flew its chairman down to take me to lunch and soft-soap me. He appealed to my patriotism and my duty to the country and various other things. He tried to point of the benefits of the metric system and made excuses for the fact that the French mismeasured the meter in the first place. Whereas before we could measure things in practical terms, like the length of a human foot or the width of a thumb (an inch), now suddenly the meter could only be defined as 1,650,763.72 wavelengths of the orange-red radiation of an isotope of krypton.
Very handy when you wanted to check how fast your kids were growing.

My resistance movement got nowhere, of course. The country went metric anyway, and I had to be satisfied with sniping from behind the lines. But at least I learned what the word mass really meant. It means you get the same amount of butter at sea level and at 10,000 feet, no matter what the scales say.

I thank Greg for figuring that I could once haul more than 100 pounds up and over my anchor roller without mechanical aid. No wonder it felt like hard work. But, of course, you must remember that with each foot of chain hauled in, the load gets lighter, so it isn't 100 pounds all the way up.

Many thanks to all of you who tried to enlighten me. It's a hopeless task, I fear.

Cheers,

John Vigor

[Carl Thunberg]

John,

Just listen to Greg. He answered your question directly and simply. Sorry if I made things unnecessarily complex, but this particular topic is how I feed my family so it's near and dear to my heart. Bridges fall down and tanks pop out of the ground if I get this wrong, but it's of little consequence to lifting an anchor.

[Bill Goldsmith]

Shortly thereafter the goldsmith was put to death....

Oh my! . . . . .

[marilou]

The board weighs 90 lbs. out of the water, and there is 4' of it in the water when fully lowered (and 18" still out of the water), how much does it weigh when fully lowered?

[Neil Gordon]

>> . . . every time I ask a simple question about a spinning propeller or a dimpled hull, I get swamped with complicated answers.<<

Don't forget the block and tackle with the weights.

>>I have always had a hard time understanding Archimedes. I could never see why a king's crown made of gold would displace more water than the very same-sized crown made of iron. If both their volumes are the same, then the same amount of water should be displaced, surely? But no, apparently not.<<

You didn't read this thread? You hold the crown in your lap in a canoe in a pool. Measure the height of the water, then toss the crown from the canoe (without falling overboard, of course) and measure again.

>>Mass is volume times density. It's burned into my brain.<<

Don't forget the part where the faster it goes, the more the mass increases. That's why you never rush hauling in the anchor.

>>... now suddenly the meter could only be defined as 1,650,763.72 wavelengths of the orange-red radiation of an isotope of krypton.<<

That's because they weren't drunken fraternity kids. The Mass Ave Bridge (no pun intended) from Cambridge to Boston was easily measured, and still marked, in "Smoots."

>>But, of course, you must remember that with each foot of chain hauled in, the load gets lighter, so it isn't 100 pounds all the way up.<<

I'm picturing the illustration we've all seen. The anchor is on the bottom, then there's most of the chain, stretched out and also on the bottom, then it rises slowly to the boat. How the load gets lighter with each foot of chain hauled in? Anyway, the part where the anchor has to go from the water to the boat is always the heaviest part. Ask anyone here.

As an aside, would anyone here actually let the neighbors see them sitting in a canoe with a cannonball in a swimming pool?

[river-rat]

Too many words. Not enough numbers.

If you know the densities of the metal and the liquid , the weight is easy. The density can be variable depending on many factors but for a rough estimate I used the following all in pounds per cubic inch:
Water=0.037
Iron=0.283
Aluminum=0.094
Take the above water weight and multiply by the following factors to get the under water weight.
Iron 0.87
Aluminum 0.62

The calculation for iron (.283-.037)/.283=0.87

Now, John, you need to run naked through the streets hollering "Eureka! I have found it."

Burl Romick

[Neil Gordon]

Water=0.037
Iron=0.283
Aluminum=0.094

You toss crowns made from gold, iron and aluminum overboard. They all sink. Not only don't you know which ones were the fakes, you now need to hire a diver to get the gold back.

[darmoose]

[quote="John Vigor"]Gee, I dont know . . . every time I ask a simple question about a spinning propeller or a dimpled hull, I get swamped with complicated answers. Why do things always lurch out of control?

I have always had a hard time understanding Archimedes. I could never see why a king's crown made of gold would displace more water than the very same-sized crown made of iron. If both their volumes are the same, then the same amount of water should be displaced, surely? But no, apparently not.



John,

dont feel bad. i seem rarely to get it right anymore. be it freewheeling propellers or sinking anchors, oh well

but with reference to your paragraph immediately above, surely this is not correct....you seem to have reversed the conclusion of this thread, wouldn't you say?

i only mention it, not because its of any importance, but because if left unnoted it further complicates and confuses some of us (me), which you do do ever so nimbly.

darrell

[Ed Haley]

I have always had a hard time understanding Archimedes. I could never see why a king's crown made of gold would displace more water than the very same-sized crown made of iron. If both their volumes are the same, then the same amount of water should be displaced, surely? But no, apparently not.

Darmoose:
Of course they do. Why do you abandon truth? Stand up and be counted among the righteous!

But, there are two ways to look at it and thus the discrepancy. Underwater, the two equal volumes displace the same volume of water (since they themselves have the same volume).

However, when sitting in a canoe, the two crowns each displace their own weight on the water.

If you hang each crown on a string under water they would both lose the same weight if suspended by a scale. However, the gold would weigh more since it is denser. It had more weight (for the same volume as iron) to begin with. Scales measure weight.

[S/V Necessity]

"I have always had a hard time understanding Archimedes. I could never see why a king's crown made of gold would displace more water than the very same-sized crown made of iron. If both their volumes are the same, then the same amount of water should be displaced, surely? But no, apparently not."

No you are correct, both crown should displace the same amount of water. The catch is that they *CAN NOT* weigh the same amount... If both crowns weigh the same and displace the same amount, then they posess the same density. The iron crown will weigh less (if it displaces the same amount of water).

[Neil Gordon]

The iron crown will weigh less (if it displaces the same amount of water).

If you have an iron crown and a gold one, to compare, you don't need Archimedes. You simply hang each one on a balance and see which weighs more. To see if it's gold when there's only one, you weigh the crown, weigh the water it displaces, divide one into the other and see if the ratio is for gold or for iron. Then you deal with the goldsmith accordingly.

[M. R. Bober]

...
I lived in South Africa when the government peremptorily announced the country was going metric. ...

Odd, I would have thought that they would have done it "Pretorialy."

Mitchell Bober
Sunny Lancaster (From where it's a long march to Peoria), VA

[John Vigor]

The board weighs 90 lbs. out of the water, and there is 4' of it in the water when fully lowered (and 18" still out of the water), how much does it weigh when fully lowered?

Ahem . . . well, Marilou, since none of the experts answered, let me take a stab at this with my new-found knowledge.

Let's divide the board into the piece out of the water (18 inches) and the bit in the water (48 inches.)

Now already we come to the hard part. In fact, we can't go any farther because we don't know what the board is made of. But we shall not let that hinder us. Let's pretend it's steel.

Thanks to Greg and our other resident experts, we know that steel has a density of about 500 pounds per cubic foot, whereas seawater runs at 64 pounds a cubic foot.

Now the bit of steel out of the water will weigh 18/48 of 90 pounds, or 33.75 pounds. The bit in the seawater will weigh 30/48 of 90 pounds, or 56.25 pounds, less the weight of the seawater it displaces. Now 56.25 pounds represents about 11.25 percent of 500 pounds, and 11.25 percent of 56.25 pounds is about 6 pounds.

So, subtracting 6 pounds from 56.25 pounds, we get 50.25 pounds for the underwater weight of a steel centerboard, plus 33.75 pounds for the weight above the water, or a total of 84 pounds--or half a medium-sized crewmember.

Europa!

John Vigor