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Chapter 10: Problem 7

If a submarine is completely submerged, does the buoyant force depend on its depth?

Short Answer

Expert verified
Buoyant force does not depend on depth for a completely submerged submarine.

Step by step solution

01

Understanding Buoyant Force

Buoyant force is the upward force experienced by an object submerged in a fluid. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object.
02

Analyzing the Role of Depth

The buoyant force depends on the volume of fluid displaced, which relates to the object's volume and not its depth. While depth affects fluid pressure, it does not affect the buoyant force on a completely submerged object because pressure differences at different depths cancel out across the object's surface.
03

Conclusion on Buoyant Force and Depth

A completely submerged submarine displaces a constant volume of water, thus the buoyant force remains constant regardless of depth. The only determining factors for the buoyant force are the submarine's volume and the density of the water, neither of which changes with depth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Archimedes' Principle
Archimedes' Principle is a fundamental concept in fluid mechanics, crucial for understanding how objects behave in fluids. This principle states that any object completely or partially submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.

It's important to remember:
  • The buoyant force acts upwards, opposing the weight of the object.
  • This force is independent of the object's position or depth in the fluid.
  • Both the volume of the object and the fluid's density determine the amount of fluid displaced.
This principle explains why certain objects float while others sink, depending on whether the buoyant force is enough to counteract the object's weight. When dealing with large objects like submarines, it helps engineers design these vessels to navigate underwater efficiently by balancing forces.
Fluid Displacement
Fluid displacement is a central idea in understanding buoyancy and is directly linked to Archimedes' Principle. When an object is submerged in a fluid, it pushes the fluid out of the way, which is known as displacing the fluid.

Key aspects to note include:
  • The volume of fluid displaced is the same as the volume of the submerged part of the object.
  • Objects displace more fluid when they are more deeply submerged, but the buoyant force remains consistent for fully submerged objects.
  • The density of the displaced fluid affects the magnitude of the buoyant force.
Since the density and volume of the displaced fluid are critical, engineers leverage this understanding to calculate and predict whether objects will float or sink, and at what level they will stay buoyant within the fluid.
Submarine Physics
Submarine physics involves using principles of buoyancy and fluid mechanics to control a submarine's depth and stability. Submarines, when fully submerged, rely on maintaining a neutral buoyancy to hover at a desired depth.

In submarine operations:
  • The submarine's buoyant force is modulated by altering its volume through ballast tanks.
  • Water is pumped in or out of these tanks to change the submarine's overall density.
  • When the submarine's weight equals the buoyant force, it achieves neutral buoyancy.
This ability to control buoyancy and depth makes submarines highly versatile vehicles, capable of navigating various oceanic conditions without the buoyant force being affected by changes in depth.

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Most popular questions from this chapter

A hydraulic lift has pistons with areas \(0.50 \mathrm{~m}^{2}\) and \(5.60 \mathrm{~m}^{2}\), and they're at the same height. With a \(2.0-\mathrm{kN}\) force on the smaller piston, how much mass can the larger piston support?

Fish control their buoyancy with a gas-filled organ called a swim bladder. The average density of a particular fish's tissues, not including gas in the bladder, is \(1050 \mathrm{~kg} / \mathrm{m}^{3}\). If the fish's mass is \(9.5 \mathrm{~kg}\), what volume of gas in its swim bladder will keep it in neutral buoyancy - neither sinking nor rising - at a depth where the density of the surrounding seawater is \(1028 \mathrm{~kg} / \mathrm{m}^{3}\) ? Neglect the mass of the bladder gas.

To make it flow more easily through a pipeline, crude oil is warmed to \(50^{\circ} \mathrm{C}\), at which its viscosity is only \(0.016 \mathrm{~Pa} \cdot \mathrm{s}\). What pressure difference will drive a \(0.50-\mathrm{m}^{3} / \mathrm{s}\) flow through a \(20-\mathrm{km}\) pipeline with diameter \(0.76 \mathrm{~m} ?\)

Oil flowing through a pipeline passes point \(A\) at \(1.55 \mathrm{~m} / \mathrm{s}\) with gauge pressure \(180 \mathrm{kPa}\). At point \(\mathrm{B},\) the pipe is \(7.50 \mathrm{~m}\) higher in elevation and the flow speed is \(1.75 \mathrm{~m} / \mathrm{s}\). Find the gauge pressure at \(\mathrm{B}\).

Aluminum's density is \(2700 \mathrm{~kg} / \mathrm{m}^{3}\). An aluminum cube \(5.0 \mathrm{~cm}\) on a side is placed on a scale. What does the scale read when the cube is entirely (a) in air, (b) under water?
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