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The mass of the boat multiplied by the acceleration due to gravity is less than the mass of the water displaced by the boat multiplied by the force of gravity.

Archimedes' principle applies to the weights (not mass) and so it is important that the acceleration due to gravity is included in the answer.

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What paper boat floats the longest?

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Why a wooden boat floats on water?

Well, wood is lighter than water, so it floats, but that has very little to do with why a boat floats. You could make a boat out of just about any material that was rigid enough to hold its shape, and strong enough to not crack under the pressure a boat is subjected to, and, if built to the correct dimensions, it would float. A boat floats because the volume of water it displaces when placed in water has a higher weight than the weight of the boat and everything in it. When you put a boat in the water, it "displaces" (pushes aside) a volume of water equal to the volume of the boat up to the waterline. How much water is displaced depends on how heavy the boat and its contents are. As long as that weight is not greater than the volume of water the boat displaces, the boat will float. But remember, as you place more weight in the boat, it sinks lower in the water, therefore displacing more water, so the weight of water being dispaced is increasing too, though not as fast as the weight of the boat. Eventually, if you keep adding weight to the boat, the boat will weigh more than the water it displaces, and the top of the boat will sink below the water. At that point, water will get inside the boat and quickly add more weight to the boat, causing it to sink rapidly. Another way of looking at it. A boat floats by spreading out the weight of its contents over a larger volume than they would normally occupy, thereby lowering the density of the boat and its contents. This would not work if the boat was a flat piece of wood. The wood itself would float, but you couldn't put much weight on it before it sank. However, if you took that same piece of wood and built a structure (a box with the top side open is the simplest) that had a hollow volume that was prevented from being filled with water, the inclusion of that hollow volume increases volume without increasing weight, which means the density decreases. Ultimately, when you place any object in water, whether it floats or not depends on its density. Adding passengers or other dense objects to the inside of the boat will increase its weight (it will also increase the volume of the boat, if the objects are not fully contained within the volume below the top of the boat, but volume does not increase as much as weight does, so density increases.) At the point where the density of the boat and its contents exceeds the density of the water, the boat will sink. However, some time before that point, the density of the boat will be high enough to push it down in the water enough for water to start spilling over the sides, which will rapidly increase the weight of the boat, with no increase in volume, resulting in a rapid increase in density, causing the boat to sink like a rock. So, if you're looking at in terms of density rather than displacement, you need to assume that objects placed inside the boat, even if they do not fit in the original volume of the boat, do not increase the volume of the boat used in your calculations. In other words, assume that all objects fit neatly inside the original volume of the boat without increasing its volume. So that, when you are computing the density of the boat and its contents, the volume in the denominator remains constant at the original volume of the boat alone.


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