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 SphereStokes’ 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 ModulusYM = Stress/StrainYM = (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 Characteristics1. 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