Solids & Fluids cheat sheet
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The document provides an overview of key concepts and formulas relating to mechanics of solids and fluids in physics. It defines important terms like the different states of matter, density, pressure, stress and strain. It also outlines fundamental principles including Pascal's principle describing pressure variations in fluids, Archimedes' principle of buoyancy, and Bernoulli's equation relating pressure, velocity and height along a streamline. The document concludes by listing common variables and units used and some example formulas for topics like thermal expansion, stress, and fluid flow properties.
Solids & Fluids cheat sheet
- 1. RapidLearningCenter.com © Rapid Learning Inc. All Rights Reserved AP Physics - Core Concept Cheat Sheet 11: Mechanics of Solids and Fluids Key Terms • Matter: Anything that has mass and takes up space. • States of Matter: The different forms that matter can take, and whose properties differ due to differences in the motions and forces of the molecules that form the matter. • Solid: Matter with definite shape and volume, which resists changes to these physical properties. • Fluid: Matter with indefinite shape and definite volume Liquids and gases are both fluids. • Crystalline Solid: Solid with ordered molecular-structure and fixed melting point. • Amorphous Solids: Solid with unordered molecular- structure and without melting point. • Density: Mass per unit volume. • Pressure: Force per unit area. • Thermal expansion: An increase in length or volume of matter due to a temperature change. • Stress: The force per unit area that causes deformation. • Strain: The amount by which matter is deformed. • Stress-Strain Curve: A graphical representation of relationship between stress and strain for a solid, usually showing distinct regions of response. • Elastic Region: Material returns to original length when force is removed. • Elastic limit: The maximum stress after which the solid will enter plastic deformation region. • Plastic Region: Material remains permanently deformed even when force is removed. • Breaking Point: Stress at which a material fractures or buckles. • Young’s modulus: Ratio of stress to strain when solids is under tension. • Shear modulus: Ratio of stress to strain when solids is under shear. • Bulk modulus: Ratio of stress to strain when solids is under hydraulic pressure. • Buoyancy: The upward force that keeps afloat objects immersed in a fluid, it results from an increase in pressure at greater depth in the fluid. • Atmospheric Pressure (atm): The pressure due to earth’s atmosphere, usually taken as that at sea level since it changes with height. 1 atm = 1.013 x 105 N/m2 • Hydraulic amplification: To get a high force on a large piston at one end of a fluid tank by applying small force on a small position at the other end of the fluid tank. • Surface tension: The force to attract surfaced molecular to make the surface area of fluid as small as possible. • Capillary action: The phenomena of fluids automatically rising in open-ended tubes. • Contact angle: The angle from the boundary surface to the tangent line of the fluid drop. • Unwettable action: Fluid-boundary action when the contact angle is large. • Wettable action: Fluid-boundary action when the contact angle is small • Continuity: The net rate of flow of mass inward across any closed surface is equal to the rate of increase of the mass within the surface. • Viscosity: The inter-friction mechanism in fluid to dissipate energy. • Laminar flow: Every particle passing a particular point moves exactly along the smooth path followed by particles passing that point early. Velocity is low. • Turbulent flow: The irregular flow when the velocity of the flow is high. • Ideal flow: Non-viscous & non-compressible laminar flow. Variables Used and Their Metric Units • L = Length, m • P = Pressure, Pa • h = Depth below surface, m • A = Area, m2 • V = Volume, m3 • T = Temperature, °C or K • v = Velocity, m/s2 • ρ = Density, kg/m3 • g = Acceleration due to gravity = 9.8 m/s2 • α = Linear expansion coefficient, °C-1 • β = Volume expansion coefficient, °C-1 • γ = Surface tension, N/m • ϕ = Contact angle,° • r = radius, m Key Formulas • Linear thermal expansion: ( ) ( )0 0L - L = α T - T • Linear thermal expansion: ( ) ( )0 0V - V = β T - T • Stress Applied force Loaded area = , N/m2 • Modulus Stress Strain = , N/m2 • Fluids: • Pressure variation with depth: P = ρgh , N/m2 • Buoyancy (Archimedes’ principle): imB = ρgV ,N • Continuity law: 1 1 1 2 2 2ρ A v = ρ A v • Bernoulli’s equation (along any streamline): • 21 P + ρv + ρgy = const 2 Solids and Fluids Fundamental Principles • Law of thermal expansion: The change in dimension of a solid is a linear function with respect to the change in its temperature. • Pascal’s principle: The pressure at a depth of h below the surface of a fluid open to the atmosphere is greater than atmospheric pressure by the amount ρgh. • Archimedes’ principle: Any body completely or partially submerged in a fluid is buoyed up by a force whose magnitude is equal to the weight of the fluid displaced by the body. • Bernoulli’s equation: For an ideal flow, the sum of the pressure (P), the kinetic energy per unit volume (1/2ρv2 ), and the potential energy per unit volume (ρgy) has the same value at all points along a stream line. How to Use This Cheat Sheet: These are the keys related this topic. Try to read through it carefully twice then recite it out on a blank sheet of paper. Review it again before the exams. A1A2 A2 ρ2 v2 ρ1