$F_b$ is the buoyant force, or the upward force exerted by a fluid on an object immersed in it. This force is a result of the pressure differences acting on the object, as described by Archimedes' Principle.
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The buoyant force $F_b$ is directed upward, opposing the weight of the object.
The magnitude of $F_b$ is equal to the weight of the fluid displaced by the object.
The buoyant force $F_b$ is independent of the material the object is made of, but depends on the volume of the object and the density of the fluid.
When the weight of the object is less than the buoyant force, the object will float. When the weight of the object is greater than the buoyant force, the object will sink.
The buoyant force $F_b$ is an important factor in the design of ships, submarines, and other floating or submerged objects.
Review Questions
Explain how the buoyant force $F_b$ is related to Archimedes' Principle.
According to Archimedes' Principle, the buoyant force $F_b$ acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. This means that the buoyant force is directly proportional to the volume of the object and the density of the fluid. The buoyant force acts in the upward direction, opposing the weight of the object, and is a crucial factor in determining whether an object will float or sink.
Describe how the density of the fluid and the volume of the object affect the magnitude of the buoyant force $F_b$.
The magnitude of the buoyant force $F_b$ is directly proportional to the density of the fluid and the volume of the object. If the density of the fluid increases, the buoyant force will also increase, as the weight of the displaced fluid becomes greater. Similarly, if the volume of the object increases, the buoyant force will increase, as more fluid is displaced. This relationship is the foundation of Archimedes' Principle and is essential for understanding the behavior of objects immersed in fluids.
Analyze the conditions under which an object will float or sink based on the relationship between the object's weight and the buoyant force $F_b$.
The relationship between the weight of an object and the buoyant force $F_b$ acting on it determines whether the object will float or sink. If the weight of the object is less than the buoyant force, the object will float, as the upward buoyant force exceeds the downward force of the object's weight. Conversely, if the weight of the object is greater than the buoyant force, the object will sink, as the downward force of the object's weight overcomes the upward buoyant force. This balance between the object's weight and the buoyant force is a crucial factor in the design and operation of various floating and submerged structures, such as ships, submarines, and hot air balloons.
Fluid pressure is the force per unit area exerted by a fluid on a surface, and it varies with depth according to the density of the fluid and the acceleration due to gravity.