Is it true that with buoyancy, the weight of the displaced water equals the weight of the complete object, even if only a part of the object is submerged? If so, why, since the weight of a larger object would be greater than that of a smaller one?
It is true if the body is floating.
The force upward from the water is equal to the weight of the water displaced.
If the body is floating, that water weight must be equal to the weight of the body and the body rises in the water until that is true. That is how ships float.
If the total body volume is such that it displaces WHILE SUBMERGED a weight of water exactly equal to the weight of water displaced, the body is neutrally buoyant. If you operate a submarine you work very hard with ballast tanks to achieve this exact equilibrium, not sinking and not floating. If you want to float your submarine on the surface, you blow ballast tanks, or in other words throw weight away, until your weight of water displaced is equal to the now reduced ship weight with some of the ship sticking above water.
Sorry for the long explanation. I am a naval architect and this subject is close to me :)
Yes, it is true that with buoyancy, the weight of the displaced water equals the weight of the complete object, even if only a part of the object is submerged. This principle is known as Archimedes' principle.
To understand why this is the case, let's break it down step by step:
1. When an object is submerged in a fluid (such as water), it experiences an upward force known as buoyant force. This force is exerted by the fluid and counteracts the weight of the object.
2. The buoyant force is equal to the weight of the fluid that the object displaces. In other words, it is equal to the weight of the volume of fluid that would occupy the space occupied by the submerged part of the object.
3. According to Archimedes' principle, if the buoyant force is equal to or greater than the weight of the object, the object will float. If the buoyant force is less than the weight of the object, the object will sink.
4. When only a part of the object is submerged, the buoyant force still acts on the entire object. This is because the fluid exerts pressure on the entire surface of the object, not just the submerged part. The pressure exerted by the fluid varies with depth, but it acts on the entire submerged surface of the object.
5. Since the buoyant force acts on the entire object, it can be thought of as a force equal to the weight of the fluid displaced by the entire object, even if only a part of it is submerged.
6. Now, let's address your question about the weight of a larger object being greater than that of a smaller one. While it is true that the weight of a larger object is greater, the buoyant force is not dependent on the weight of the object itself but rather on the weight of the fluid displaced. So, as long as the object displaces a volume of fluid equal to its own weight, it will experience a buoyant force equal to its weight and will float.
In summary, with buoyancy, the weight of the displaced water does equal the weight of the complete object, even if only a part of the object is submerged. This is because the buoyant force acts on the entire object and is equal to the weight of the fluid displaced by the object itself, not the weight of the object itself.