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Materials • • • • Fluids and Fluid Flow 1 Fluids and Fluid Flow 2 Force and Extension Stress, Strain, and the Young Modulus Turbulent + Laminar Flow • Laminar /Streamline Flow– layers do not cross each others paths. Occurs at lower speeds. • Turbulent Flow – layers cross and mix. Occurs at higher speeds. Viscous Drag Force • The force of friction caused by a flowing fluid • Is in the opposite direction to movement Upthrust Force • Upthrust is a force that acts vertically upwards on an object in a fluid • Upthrust = weight of fluid displaced Density • A measure of how close-packed the particles are in a substance. EG: gases are much less dense than solids and liquids because their particles are more widespread. Terminal Velocity • As an object falls it’s speed increases. The drag on it will also increase. Eventually a speed is reached where the drag force = the weight. As there is no net force on the object, the acceleration will be zero. Viscosity • The higher the viscosity of a fluid, the slower it flows. • Viscosities of most fluids decrease as the temperature increases. Fluids generally flow faster if they are hotter. Stokes’ Law • Calculates the drag force on a sphere as it travels through a fluid. • F = viscous drag force acting on the sphere • r = radius of the sphere • n = viscosity of the fluid • v = velocity of sphere ALL Forces on a Falling Sphere Stokes’ Law + Upthrust = Weight Hooke’s Law • The extension of a sample of material is directly proportional to the force applied. • Hooke’s Law does not apply to all materials • k = stiffness = the gradient = F/x Force v Extension/Compression Graphs • Limit of Proportionality – The point beyond which force is no longer directly proportional to extension (line is no longer straight) • Elastic Limit – This is when the force is taken away, the material no longer goes back to its original length • Yield Point – Material shows a greater increase in extension for a given increase in force • Ultimate Tensile Stress – The maximum stress that the material can withstand • Breaking Stress – the point at which the material breaks • Ultimate Tensile Strength: the maximum stress (force) a material can withstand. • Breaking Stress: the stress at which the material breaks. Can be the same as UTS. Stress and Strain •Stress (N/m2) = Force (N) / Area (m2) •Strain (no units) = Extension (m) / Original Length (m) Young Modulus YM = Stress/Strain YM = (F/A)/(E/L) YM = FL/EA • YM = the gradient of a stress/strain graph • The greater the YM (the steeper the gradient) the stiffer the material. Ie: the less it stretches for a given force. Elastic and Plastic Deformation • At point A, Masses (Force) are unloaded from the material. • Plastic deformation has occurred as the material has not gone back to it’s original length. Material Characteristics 1. Brittle: Breaks suddenly without deforming plastically. Follows Hooke’s Law until it snaps. Glass. 2. Ductile: Undergos plastic deformation by being pulled into wire. Retains strength. Copper. 3. Malleable: Undergos plastic deformation by being hammered or rolled into shape. Loses strength. Gold. 4. Hard: Resist plastic deformation by compression or scratching rather than stretching. Diamond. 5. Stiff: Measure of how much a material stretches for a given force. Bamboo. 6. Tough: Measure of the amount of energy a material can absorb before it breaks. Toffee. Elastic Strain Energy • Plastically deformed material: – E = ½ x Force x Extension (Similar to W=Fs) • Elastically deformed material: – E = area under force/extension graph