The Story of Archimedes' Principle
The Approach to the problem
The moment of Epiphany
He realized that when he got into his bath, the water level rose around him because his body was displacing the water and that this was linked to the feeling of weight loss; that uplifting feeling that everyone experiences in the bath. As the baths were public places, he probably noticed as well that smaller people displaced less water. This was the key to solving this problem. It is to be noted that displaced water has nothing to do with the weight but rather its the volume that is the culprit. When Archimedes placed both crowns in the water he noted both of those crowns had different weights or experienced different loss in weight. Understand this in figure 1.1
Figure 1.1: Crown Displacing volume of waterIn figure 1.1 the crown displaces volume of water in another container by means of an overflow pipe. The interesting part is that the volume of water collected by overflow pipe in the container is exactly equal to the volume of the crown. Moreover, the weight of the displaced volume is equal to the loss in weight of the crown (Due to natural upward push of water) . Which in turn means Archimedes measured the weight of the displaced volume i.e weight of an equal volume of water to that of the crown.
Formal Definitions
Archimedes' principle states that:
An object, fully or partially submerged in a fluid (liquid or gas), experiences an upward buoyant force. This force is equal in magnitude to the weight of the fluid displaced by the object.
where,
- Buoyant force: The upward push exerted by the fluid on the object.
- Displaced fluid: The amount of fluid pushed out of the way by the submerged object.
Examples:
- Ships: Designed to displace a large volume of water, creating a significant buoyant force to stay afloat.
- Submarines: Control their buoyancy by adjusting internal water tanks (ballast) to rise or sink.
- Hot air balloons: Heated air inside the balloon is less dense than surrounding air, creating a large buoyant force for lift.
Conclusion:
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