simple physic test (Home made)?

Question

A 15 Tonnes boat is about to go through a deep aqueduct which can stand the weight of 20 cube meter of fresh water. The aqueduct is already 74% of its weight capacity with the water it supports..

what happens when the boat stand above the aqueduct ?
A. The aqueduct collapse under the weight
B The aqueduct is OK and the boat goes through
C The boat get stuck

The first one to provide the right answer gets his 4 stars rating but please provide justification for your answer

Answer 1

C The boat gets stuck !!!!

At 74% full there is less than 15 Tonnes of water in the aquaduct. (20t x 74% = 14.8t)
The boat weights 15 tonnes so it is displacing 15 tonnes of seawater in order to float.

There is not enough seawater in the aquaduct (`14.8 tonnes) to support the boat (15 tonnes) so it will ground and get stuck in the Aquaduct.


Edit:
Note a boat enters the aquaduct it displaces a volumne of water equal to the boats weight. An auqaduct allows water to flow freely so as the boat enters the aquaduct an equal volume of water is pushed out (displaced). There is no change in the total weight since water is allowed to flow into and out of the aquaduct freely.
The size of the boats dimensions and shape relative to the dimensions of the aquaduct would come into play if you were comparing a shallow draft vessle like a barge to a sleek hull shaped like a sail boat which would have a deeper draft.

But in this problem there just isn't enough water available in the Aquaduct to support 15T so the shape of the boat is irrelavant. Answer C!

Answer 2

An aqueduct that holds only 20 tonnes of water is either not very deep, wide, or long. Chances are therefore quite good that it will be too narrow or shallow for the boat to pass through. To be able to float, the boat must be able to displace 15 tonnes of water. However, there isn't enough water in the aqueduct to float the boat in its entirety. If the aqueduct is deep enough, as the problem's wording implies, and long to fit the entire draft of the boat, the aqueduct will necessarily be too narrow.

However, assuming that the aqueduct is very short and the cross section of the aqueduct is suitable for the boat to pass without chafing or bottoming, part of the boat's draft will be supported by the water beyond either end of the aqueduct for the entire time part of the boat is in the aqueduct. In that case, the boat could pass through without overloading the aqueduct's supporting structure because the added weight of that part of the boat would be subtracted by the water displaced out of the aqueduct. Aside from some small transients and side loads, the aqueduct's supporting structure would therefore hardly be affected by the passing boat.

Answer 3

The aqua duct can stand the weight of 20 cu meter. Which happens to be 20 ton. At the present time it is loaded to 74% of capacity. So there appears to be 14.8 ton of water in it. That means if a boat that displaces 5.2 ton comes in it will be at 100% capacity of 20 ton. THAT boat won't float but the aquaduct wont collapse under the weight, unless someone puts a straw on it. Anyway, when a much bigger 15 ton boat comes in bad things will happen. You say it is a deep aquaduct. I would imagine the 15 ton boat will displace all of the water and go to the bottom. The water will then have no place to go. Too bad because there is now the weight of the boat (15 ton) plus the weight of the water (14.8 ton) for a total of 29.8 ton. Since the max weight the aquaduct can support is 20 ton the whole thing collapses under the weight.

A

Answer 4

A floating object displaces its own weight of water. So provided the aqueduct is wide enough for the boat not to go aground (and you did say it was deep), there is no change in the load on the aqueduct as the boat crosses. Hence B.

This does assume that the boat moves slowly enough to allow time for the water to be displaced. A 15-tonne speedboat might be a very different matter, but they shouldn't be crossing aqueducts anyway!

Answer 5

I'm tempted to go with C. Assuming the water is free to move, the boat will displace 15 tonnes of water 74% of 20m³ of water is a shade less than 15 tonnes of water. This means the boat will bottom out. However, if the water is not free to move, the aqueduct is under the weight of nearly 30 tonnes of water. Given this is only an additional 50% of the quoted weight capacity, the aqueduct will probably groan a little, and might well collapse, but isn't likely to. Most things like this were engineered to survive these sorts of things. Hang on. A "deep" aqueduct? 20 cubic metres? Assuming it's a metre deep and a metre wide and twenty metres long, this is a tiny aqueduct - certainly not something you could realistically run a 15 tonne boat through, which would have to have a volume of at least 15 cubic metres. I'd therefore be tempted to answer B - the bridge is okay, and the boat goes through fine, on the river which the aqueduct runs over! Hope I'm right, I might be wrong.

Answer 6

20 cubic meters of water a 1 g/cc or 1,000 kg/m^3 would weigh 20,000 kg or 20 tonnes.

If the boat weighs 15 tonnes and the aqueduct is holding .74*20 tons............... 15+14.8= 29.8 tonnes.

A. The aqueduct is falling!!!

Answer 7

The boat will displace a mass of water equal to its own mass
(as boats do) this displaced water will leave the aquaduct fore and aft into the channel leading too and from it.So the answer is B.because aquaducts are usually short relative to the channel which they connect.

Answer 8

Although we don't have enough information, the boat will most probably float fine.

As a basic physics rule,if you place something in the water it will replace with the same volume of water as it's sinking volume.Therefore you need to know the volume of boat's sinking part and also the density.

#Mark C: boat will displace same volume of water not the same weight.

Answer 9

B

The boat displaces 15 tonnes of water

Answer 10

B
cos i said so