(4.2) Materials

• What is the definition of density?

  Mass per unit volume
• What does Hooke's law state about extension?

  Extension is directly proportional to applied force
• What does a straight line graph through the origin indicate?

  Force and extension are directly proportional
• What is the limit of proportionality?

  Point after which Hooke's law fails
• What happens if the force applied exceeds the elastic limit?

  The material deforms plastically
• What is the equation for Hooke's law?

  F = kΔL
• What does the spring constant (k) measure?

  Stiffness of the spring
• What is tensile stress defined as?

  Force applied per unit cross-sectional area
• What is tensile strain defined as?

  Extension over the original length
• How is elastic strain energy calculated?

  Area under a force-extension graph

  
• What is the formula for elastic strain energy?

  Elastic strain energy = $\frac{1}{2}FΔL$
• What is breaking stress?

  Stress value at which material breaks
• What are the two main behaviors of materials on a force-extension graph?

  • Plastic: Large extension beyond elastic limit
  • Brittle: Little extension, likely to fracture

  
• What happens to a force-extension graph after a material is stretched beyond its elastic limit?

  Graph does not return to origin

  
• What does the area between loading and unloading lines represent?

  Work done to permanently deform material

  
• What happens to energy during elastic stretching?

  All work is stored as elastic strain energy
• How do crumple zones in cars utilize plastic deformation?

  To decrease kinetic energy during a crash
• What happens to kinetic energy when a spring is stretched and then released?

  Converted back to kinetic energy
• What do stress-strain graphs show about materials?

  • Ultimate tensile stress (UTS)
  • Material behavior: ductile, brittle, or plastic

  
• What is the Young modulus a measure of?

  Stiffness of a material
• How is the Young modulus defined mathematically?

  Stress over strain is constant

  
• What is the formula for Young modulus?

  Y = $\frac{Tensile \ Stress}{Tensile \ Strain}$

  
• How can Young modulus be calculated from a stress-strain graph?

  By finding the gradient of the straight part

  
• What is the rewritten formula for Young modulus using force and area?

  E = $\frac{FL}{ΔLA}$