There is presently an internet article circulating about a channel bridge over the River Elbe. The bridge has been constructed to let barges and other water craft pass over the river.
As an aside to the article, a question is directed at armchair engineers. The question is, " Did the engineers designing the channel bridge have to allow for the additional weight of the boats?". The given answer is that no matter how heavily the boats are loaded, Archimedes principle states that the weight will be countered by an upward force and so the engineers didn’t have to account for the weight of the craft on the channel.
I disagree. I even constructed an experiment to prove I am right. I placed a beaker filled with water on a scale. After noting the weight, I added a floating cork to the beaker. The measured weight increased.
If I’m wrong or if my experiment didn’t define the system correctly, please let me know. I’m really going to feel stupid, but it has happened before.
Unless the bridge has locks at either end, it’s not a closed system. So when a boat enters the bridge, the level of water does not rise.
To replicate this effect in your experiment, fill the beaker to the absolute brink. Drop in your cork. Carefully dry all the water that has been displaced and reweigh.
Archimedes’ law states that a floating boat will displace water equal in weight to the boat. In general, in a canal, that water is going to flow somewhere else; that is, off the bridge. In your experiment, you left nowhere for the displaced water to flow to, so the weight of your experiment was increased.
If, when the boat came along, the water level in the canal increased, then the weight on the bridge would increase, but I don’t think that is going to happen.
You are not using displacement. That’s what Arhicmedes discovered. He was tasked with finding a way to weigh something. The catch? He couldn’t weigh it direcftly or estimate based on size and material. According to legend, he got into the bathtub, noticed that the water moved outward, well, shouted “Eureka!”
In short, if other masses, floating in the water, displace some of it, it will get spread out over a larger area. That will probably seem to be a very small increase, but water weighs a heckuva lot, and a small increase over a very large area can amount to a huge mass being spread out.
In short, as long as the water can go somewhere, and the vessel is bouyant, it won’t increase the total pressure on the riverbed.
I’ll note that the load on the bridge has to do with the height of the surface of the water it carries. Since this is maintained as a navigable waterway, it’s almost certainly a semi-closed system delimited by downstream locks. It’s thus fully plausible that the precise water level is affected by the barges and boats afloat on it - albeit not much if the surface area is large.
It’s certainly true that the engineers would have had to design it for the maximum possible water level. They need not have worried about exactly what craft were directly over the bridge at any particular moment.
No, weighing something directly is easy; that wasn’t the problem. The trick was in finding the object’s volume, which is tricky to do directly for something of a complicated shape (like, say, a gold-alloy crown).
No, the legend says that he was tasked with determining if the amount of the gold given to the creator of the crown was in the finished product. By first weighing it and then determining the volume, he determined the density. Then, by determining the density of gold and the density of the alloying materials used, he could determine how much gold was actually in the finished product.
No it doesn’t. Chronos is right. Displacement won’t tell you anything about weight; it gives you volume. Separately, Archimedes then weighed the crown and then used this to determine the density. (At least, in the canonical legend. The given link notes that what actually happened was probably a little different, since measuring the displacement to sufficient accuracy was probably too difficult.)
Uh, no. The trick is to determine the object’s volume. Supposedly the crown had been made of a quantity of gold and there was a question of whether or not the goldsmith had replaced some of the gold with lead. By determining the volume of the crown (say, 20 cubic inches) and comparing its weight to 20 cubic inches of pure gold, Archimedes could tell if something fishy had happened. If the crown weighed less, it had been adulterated, since lead weighs less than gold.
Archimedes wasn’t working on some homework problem or fun little exercise, with arbitrary restrictions; he was looking to get a practical result. The only thing he wasn’t allowed to do was to destroy the crown-- Any goldsmith could have determined if it was pure by melting it down, but then the King would have been screwed out of a fine piece of workmanship if it turned out to be pure.