College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
Pascals are the units used to measure pressure, specifically the force exerted per unit area. They are named after the French mathematician and physicist Blaise Pascal, who made significant contributions to the understanding of fluid mechanics and hydrostatics.
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One pascal is defined as one newton per square meter (1 Pa = 1 N/m²), which is a very small unit of pressure.
Pascals are commonly used to measure the pressure of liquids and gases, such as the pressure in a tire or the pressure in a hydraulic system.
Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object, which can be expressed in pascals.
The pressure exerted by a fluid, such as water, increases with depth, and this increase in pressure is measured in pascals.
Atmospheric pressure, which is the pressure exerted by the weight of the Earth's atmosphere, is typically measured in pascals or millibars (1 millibar = 100 pascals).
Review Questions
Explain how pascals are used to measure the pressure in a hydraulic system.
In a hydraulic system, such as a car's braking system or a hydraulic lift, the pressure is measured in pascals. The pressure in the fluid, which is typically a liquid like hydraulic fluid, is directly proportional to the force applied and inversely proportional to the area over which the force is applied. This relationship is described by the formula $P = F/A$, where $P$ is the pressure in pascals, $F$ is the force in newtons, and $A$ is the area in square meters. By measuring the pressure in pascals, engineers can design and optimize the components of the hydraulic system to ensure the desired force and motion are achieved.
Describe how the concept of pascals is related to Archimedes' Principle and buoyancy.
Archimedes' Principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. This buoyant force can be expressed in terms of pascals, the unit of pressure. Specifically, the buoyant force is equal to the product of the fluid's density, the volume of the object, and the acceleration due to gravity. This can be written as $F_b = \rho V g$, where $F_b$ is the buoyant force, $\rho$ is the fluid density, $V$ is the volume of the object, and $g$ is the acceleration due to gravity. By understanding the relationship between buoyant force and pressure in pascals, we can predict the behavior of objects submerged in fluids and explain phenomena like objects floating or sinking.
Analyze how changes in depth affect the pressure in a fluid, as measured in pascals.
The pressure in a fluid, such as water or air, increases with depth. This is known as hydrostatic pressure, and it can be expressed using the formula $P = \rho g h$, where $P$ is the pressure in pascals, $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $h$ is the depth of the fluid. As the depth increases, the weight of the fluid above the point of interest increases, resulting in a higher pressure measured in pascals. This relationship between depth and pressure is crucial for understanding the behavior of objects submerged in fluids, as well as the design of structures and systems that operate under different fluid pressures, such as submarines, hydraulic systems, and atmospheric pressure changes.