Materials

• Hooke’s Law

  • weights attached to a spring. The more weights = the bigger the extension
  • when plotted, we can see a line going through origin and directly proportional of f and x
  • Hooke’s Law = the extension is proportional to the force applied, providing the limit of proportionally has not been breached
  • F = kx
• Springs in parallel and series (not in spec but comes up in exams):

  When in parallel:

  • 1/2 extension for the same force so higher spring constant
  • spring constant = k1 + k2

  When in series:

  • both springs extend and experience same force so extension = 2x
  • spring constant (lower) = 1/kt = 1/k1 + 1/k2

  Basically just the opposite of resistors

  
• Elastic potential energy in springs:

  • area under f x graph = elastic potential energy stored
  • area = 1/2 fx
  • area = 1/2(kx)x
• Stress, strain and young’s modulus:

  • Stress = force / area (nm^-2)
  • Strain = extension / original length (no units)
  • stress / strain = young‘s modulus
• Stress-strain graph:

  • Limit of proportionality = any further young’s modulus won’t be true
  • elastic limit = if load is retracted, the material will still return to its original form
  • yield point = so much stress causes lots of strain. (like blue tack when you hardly pull it yet it extends a lot)
  • ultimate tensile strength - failure occurs here

  
• Ductile and brittle materials:

  • Brittle materials tolerate a lot of stress and don’t have much strain. Have a higher gradient. Have a higher UTS (ultimate tensile strength) (crunchie)
  • Ductile materials are most metals - has a lower yield point and a long period of increased strain. (Mars)
  • Polymers have a much lower elastic limit and yield point - massive amount of strain accepted. (Lowest gradient)
• Behaviour of rubber:

  • a plotted stress strain graph of rubber creates a hysteresis loop
  • the area inside the loop is the energy transferred per unit volume
  • it doesn’t obey hooke’s law so stress is not directly proportional to strain
  • With cars, they undergo a lot of compression and extension whilst driving. This causes the tyres to heat up