Materials - Detailed

• Density is the mass per unit volume of an object
• Objects made from low-density materials typically have a lower mass
• Density = Mass / Volume
• Volume of a sphere: 4/3pi^3
• Volume of a cylinder: pir^2l
• Archimedes' Principle - An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object
• The object sinks until the weight of the fluid displaced is equal to its own weight, therefore the object floats when the magnitude of the upthrust equals the weight of the object
• The magnitude of upthrust can be calculate by:

  1. Find the volume of submerged object, which is also the volume of displaced fluid
  2. Find weight of displaced fluid
  3. Since m = pV, upthrust is equal to F=mg, which is the weight of the fluid displaced by the object
• Viscous drag is defined as the frictional force between an object and a fluid which opposes the motion between the object and the fluid
• Viscous drag is calculated using Stoke's law; Force = 6 x pi x viscosity x radius x terminal velocity
• Fluids with low viscosity are easy to pour, while those with high viscosity are difficult to pour
• The coefficient of viscosity is a property of the fluid (at a given temperature) that indicated how much it will resist flow. Therefore, the rate of flow of a fluid is inversely proportional to the coefficient of viscosity
• At terminal velocity, W = F + U, where W is weight, F is drag and U is upthrust
• Stokes law can only be used when:

  1. Flow is laminar
  2. Object is small and spherical
  3. Motion between the sphere and the fluid is at a slow speed
•  

  Laminar flow:

  1. All layers are moving ni the same direction and do not mix
  2. Tends to happen for slow moving objects, or slow flowing liquids
• Turbulent flow:

  1. Layers move in different directions and the layers do mix
• Liquids are less viscous as temperature increases

  Gases get more viscous as temperature increases
• When a force is added to the bottom of a vertical metal wire of length L, the wire stretches
• A material obeys Hooke's Law if: The extension of the material is directly proportional to the applied force up to the limit of proportionality
• Force = spring constant x extension
• Spring constant is a property of the material being stretched and measures the stiffness of a material, the large the spring constant, the stiffer the material
•  

  Hooke's Law applies to both extensions and compressions:

  • The extension of an object is determined by how much it has increased in length
  • The compression of an object is determined by how much it was decreased in length
• Limit of proportionality: point beyond which Hooke's law is no longer true when stretching a material, and the gradient is no longer straight
• Elastic limit: maximum amount a material can be stretched and still return to its original length. Always after the limit of proportionality
• Stress is the applied force per unit cross sectional area of a material

  Forces can be;

  1. Tensile (pull on an object and extends it)
  2. Compressive (push on an object and compresses it)
• Stress = Force / Area, unit is Pa
•  

  Ultimate tensile stress is the maximum force per original area a wire is able to support before it breaks
• Strain is the extension per unit length

  • It a deformation of a solid due to stress in the form of elongation or contraction
  • Strain is a dimensionless unit because it's the ratio of lengths
• Strain = extension / length
• Young Modulus

  • Is the measure of the ability of a material to withstand changes in length with added load
  • Gives information about the elasticity of a material
  • The ratio of stress and strain
• Young Modulus = Stress / Strain, where the unit is Pa
• Every material has a unique force-extension graph, depending on how brittle or ductile it is
• Limit of Proportionality: the point beyond which Hooke's law is no longer true when stretching or compressing a material
• Elastic Limit: the point before which a material will return to its original shape or length when the deforming force is removed, after the limit of proportionality
• Yield point: where the material continues to stretch even though no extra force is being applied to it
• Elastic deformation: a change of shape where the material will return to its original shape when the load is removed
•  

  Plastic deformation: after the yield point, will not return to its original shape when the load is removed
• Young Modulus is found from the gradient of the straight part of the graph
• Breaking stress is the stress at the point where the material breaks

  • At the yield point, atoms in the material had started to move relative to each other, at the breaking stress they separate completely
  • Breaking stress is not the same as ultimate tensile stress
• Can be found by finding the area under a force-extension graph