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Chapter 4: Problem 22

Why does the buoyant force always act upward?

Short Answer

Expert verified
Answer: The buoyant force always acts upward on objects submerged in fluids because of the pressure difference at different depths in the fluid. The pressure at the bottom of an object is greater than the pressure at the top due to the difference in depth, which results in a net upward force on the object. This upward force is equal to the weight of the fluid displaced by the object, as described by Archimedes' Principle.

Step by step solution

01

Introduction to Buoyancy

Buoyancy is a force experienced by objects submerged in fluids (like liquids or gases). This force is caused by the pressure difference in the fluid at different depths. When an object is submerged in a fluid, it displaces the fluid, and the fluid pushes back on the object with a force called the buoyant force.
02

Archimedes' Principle

Archimedes' Principle states that the upward buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Mathematically, this can be expressed as: F_{b} = ρ_f V_f g where F_{b} is the buoyant force, ρ_f is the density of the fluid, V_f is the volume of fluid displaced, and g is the acceleration due to gravity.
03

Fluid Pressure and Depth

The pressure in a fluid increases with depth due to the weight of the fluid above a specific point. The pressure at a given depth in a fluid can be calculated using the formula: P = ρ_f g h where P is the pressure, ρ_f is the fluid density, g is the acceleration due to gravity, and h is the depth below the fluid surface.
04

Fluid Pressure Difference and Buoyant Force

The pressure at the bottom of an object immersed in a fluid is higher than the pressure at the top of the object due to the difference in depth. This pressure difference results in a net upward force acting on the object. The greater the depth difference, the larger the pressure difference, and the larger the resultant buoyant force.
05

Conclusion

The buoyant force always acts upward because of the pressure difference in fluids at different depths. The pressure at the bottom of an object submerged in a fluid is greater than the pressure at the top, resulting in an upward force on the object. This upward buoyant force is equal to the weight of the fluid displaced by the object, as described by Archimedes' Principle.

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