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- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/06%3A_Applications_of_Integration/6.05%3A_Hydrostatic_Force_and_PressureThis section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force...This section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force, and depth, and provides formulas for computing these quantities. The section includes practical examples, such as finding the force on submerged plates or walls, and emphasizes setting up integrals based on geometric and physical principles.
- https://math.libretexts.org/Under_Construction/Purgatory/Book%3A_Active_Calculus_(Boelkins_et_al.)/06%3A_Using_Definite_Integrals/6.04%3A_Physics_Applications_-_Work_Force_and_PressureWhile there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar ...While there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar to several others that we’ve encountered in applications of the definite integral. In particular, the basic idea is to take a difficult problem and somehow slice it into more manageable pieces that we understand, and then use a definite integral to add up these simpler pieces.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/02%3A_Applications_of_Integration/2.06%3A_Hydrostatic_Force_and_PressureThis section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force...This section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force, and depth, and provides formulas for computing these quantities. The section includes practical examples, such as finding the force on submerged plates or walls, and emphasizes setting up integrals based on geometric and physical principles.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/01%3A_Applications_of_Integration/1.07%3A_Hydrostatic_Force_and_PressureThis section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force...This section covers hydrostatic force and pressure, explaining how to calculate the force exerted by a fluid at rest on a surface using integration. It introduces the concepts of fluid pressure, force, and depth, and provides formulas for computing these quantities. The section includes practical examples, such as finding the force on submerged plates or walls, and emphasizes setting up integrals based on geometric and physical principles.
- https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/06%3A_Using_Definite_Integrals/6.04%3A_Physics_Applications_-_Work_Force_and_PressureWhile there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar ...While there are many different formulas that we use in solving problems involving work, force, and pressure, it is important to understand that the fundamental ideas behind these problems are similar to several others that we’ve encountered in applications of the definite integral. In particular, the basic idea is to take a difficult problem and somehow slice it into more manageable pieces that we understand, and then use a definite integral to add up these simpler pieces.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.05%3A_Physical_Applications_of_Integration/2.5E%3A_Exercises_for_Section_2.5This page offers a series of exercises on calculating work done in various scenarios, including lifting objects, applying forces, and determining masses. It covers spring constant calculations and wor...This page offers a series of exercises on calculating work done in various scenarios, including lifting objects, applying forces, and determining masses. It covers spring constant calculations and work related to pumping fluids, featuring problems on constant and variable forces, density functions, and hydrostatic calculations. Answers for these exercises are included, reinforcing fundamental principles of physics and calculus associated with work and mass.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/07%3A_Applications_of_Integration/7.06%3A_Fluid_ForcesIn the unfortunate situation of a car driving into a body of water, the conventional wisdom is that the water pressure on the doors will quickly be so great that they will be effectively unopenable. H...In the unfortunate situation of a car driving into a body of water, the conventional wisdom is that the water pressure on the doors will quickly be so great that they will be effectively unopenable. How can this be true? How much force does it take to open the door of a submerged car? In this section we will find the answer to this question by examining the forces exerted by fluids.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus_Lecture_Notes_(Simpson)/01%3A_Applications_of_Integration/1.06%3A_Hydrostatic_Force_and_PressureIn this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to d...In this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to determine the mass of an object if its density function is known. Work can also be calculated from integrating a force function, or when counteracting the force of gravity, as in a pumping problem. Definite integrals can also be used to calculate the force exerted on an object submerged in a liquid.
