The king ordered Archimedes to measure as much gold as an elephant weighs. Such large scales were nowhere to be found. Archimedes had a raft at his disposal. How did Archimedes solve the problem?
Decision:
A body submerged in water is subjected to an expulsive force directly proportional to the volume of the submerged part of the body. A body floats (is in equilibrium) when the weight of the body is equal to the expulsive force. Therefore, a raft loaded with different loads of the same weight will sink to the same depth. Consequently, to solve the problem, one must get the elephant onto the raft, mark the level of the raft's immersion, then remove the elephant and load the raft with gold until it sinks to the same level.
It should be noted that this method is not very accurate. A slight misalignment of the raft can lead to a large error. There is a more accurate method. You need to place the raft in a small pool filled to the brim with water. Under the weight of the elephant, the raft will sink and some of the water will pour out of the pool. After removing the elephant, you should load the raft with gold until the water rises to the edge of the pool. With this method of measurement, possible distortions of the raft do not affect the accuracy of weighing.
Decision:
A body submerged in water is subjected to an expulsive force directly proportional to the volume of the submerged part of the body. A body floats (is in equilibrium) when the weight of the body is equal to the expulsive force. Therefore, a raft loaded with different loads of the same weight will sink to the same depth. Consequently, to solve the problem, one must get the elephant onto the raft, mark the level of the raft's immersion, then remove the elephant and load the raft with gold until it sinks to the same level.
It should be noted that this method is not very accurate. A slight misalignment of the raft can lead to a large error. There is a more accurate method. You need to place the raft in a small pool filled to the brim with water. Under the weight of the elephant, the raft will sink and some of the water will pour out of the pool. After removing the elephant, you should load the raft with gold until the water rises to the edge of the pool. With this method of measurement, possible distortions of the raft do not affect the accuracy of weighing.