MIT 8.01 Physics I Classical Mechanics, Fall 1999
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Alternative wording: What would happen when a man inside a boat floating on river pees into the river?
no change .
NO CHANGE IN WATER LEVEL . AS WE CAN CONSIDER WATER TO BE INITIALLY FLOATING ON SURFACE!
No change in water level.
The boat level sinks slightly because, the water is taken from an external source and added to the total weight of boat and person.
No prashant, you are wrong. You are missing the point that the man is floating in the water. After he has consumed some water , you can imagine that volume of water "floating" in the water body. This reqiures some volume of the water to be displaced equal to the weight of the water he has drunk by Archimedies principle. The volume of the water to be displaced will be equal to the volume of water he has taken out. This rise in level of water due to displacement of water will exactly cancel out the effect of decrese in level due to taking out some water out of the sea. If however, as in second case , the density of the man's piss(!) is larger than the density of water, water level will decrease because the volume of the water that was initially being displaced was more than the volume of what he pissed(gross!) because the weight of the latter is more than the former because of density difference.
prashanthashri is correct. The boat has more weight and will displace more water therefore it will be lower in the water. The water level will not change, just the relative position of the boat in the water.
Yes, the boat sinks further as the downward force acting on it is increased. But the river level is assumed to be constant, since its size is too large compared to the boat and the change in its water level can safely be neglected. However, if the boat was in a tank of comparable size, then one must consider the level change in the water also.