Buoyancy
- In physics, buoyancy is an upward acting force exerted by a fluid that opposes an object's weight.
- In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid.
- Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the column than at the top.
- This difference in pressure results in a net force that tends to accelerate an object upwards.
- An object whose density is greater than that of the fluid in which it is submerged tends to sink.
- If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat.
Archimedes’ Principle
- “Any floating object displaces its own weight of fluid.”
- “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”
- In other words: Buoyancy = weight of displaced fluid
- The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). In simple terms, the principle states that the buoyancy force on an object is going to be equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational constant, g.
- Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.
Example Problem
· Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water
Equations
· Assuming Archimedes' principle to be reformulated as follows,
· then inserted into the quotient of weights, which has been expanded by the mutual volume
· yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes:
Density
· If the weight of an object is less than the weight of the displaced fluid when fully submerged, then the object has an average density that is less than the fluid and when fully submerged will experience a buoyancy force greater than its own weight.
· If the fluid has a surface, such as water in a lake or the sea, the object will float and settle at a level where it displaces the same weight of fluid as the weight of the object.
· A ship will float even though it may be made of steel (which is much denser than water), because it encloses a volume of air (which is much less dense than water), and the resulting shape has an average density less than that of the water.
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