Materials

• Hooke's law states that the extension of an object is directly proportional to the force applied, provided the force does not exceed the elastic limit


  F = K x
• To investigate Hooke's Law

  1. A spring is attached at one end to a clamp, boss and clamp stand.
  2. Measure the initial length is measured
  3. Mass is added and the new length is measured
  4. Extension is calculated by subtracting the initial length from this length
  5. This is then repeated with increasing mass
  6. Finally, a force extension graph is plotted
• For a force extension graph, Hooke's law applies in the linear region
• Elastic deformation is when the material returns to its original shape after the force is removed.
• Plastic deformation is when the material remains partially deformed after the force is removed.
• Force extension graph:

  A) Loading

  B) Elastic Deformation

  C) Plastic deformation

  D) Work done

  E) Unloading

  
• For springs in series, the equivalent spring constant is equal to ...

  
• For springs in parallel, the equivalent spring constant ,

  
• Extensive forces are known as tensile forces
• Compressive forces are known as compressive forces
• Stress is defined the force per unit area applied to the material measured in Newtons (N).


  $\sigma =$$\frac{F}{A}$
• Strain is defined as the ration of a materials deformation to its original length and has no units


  $\epsilon =$$\frac{x}{l}$
• Ultimate tensile strength is the maximum stress a material can withstand before it breaks.
• Breaking stress is the level at which a material fractures
• Elastic potential energy is the energy stored when a material is elastically deformed measured in joules (J)


  E = $\frac{1}{2} F x$ and E = $\frac{1}{2} k x^2$
• Young's modulus is the ratio of stress to strain in a material and indicates how stiff a material is. It is measured in Pascals.


  E = $\frac{\sigma}{\epsilon} =$$\frac{Fl}{Ax}$
• To investigate Young's modulus:

  1. A micrometre is used to measure the diameter of a wire
  2. The wire is fixed at one end and ran over a pulley along a ruler
  3. A marker is added to show the initial position
  4. Mass is added to the wire and the extension of the wire is measured
  5. The stress and strain are calculated and a graph is plotted
  6. The gradient of the line is Young's modulus
• A ductile material is capable of being drawn into a wire or rod without breaking.

  • Initially the material obeys Hooke's Law
  • After this, the material experiences a large strain for a small amount of stress
  • Beyond the yield point, the material is deformed

  
• Strength is indicated by the stress level a material breaks at.


  Material A has a higher breaking stress and therefore is stronger

  
• Stiffness related to how much strain a material experiences under a given stress. A stiffer material will show less strain


  Material A undergoes a lower strain for the same stress and is therefore stiffer

  
• Brittle materials break without significant plastic deformation.

  • Initially the material obeys Hooke's law
  • Then it abruptly ends at the breaking stress

  
• Polymetric materials stress strain graph

  .

  A) Loading

  B) Energy lost as heat

  C) Unloading

  
• Rubber displays elastic behaviour
• Polyethene experiences plastic deformation