S5 - Materials

• What is density?

  A physical quantity/ measure of how tightly packed the atoms of an object are
• What is the equation for density?

  Density (ρ) = mass (m) / volume (V)

  
  

  Measured in kgm^-3 or gcm^-3
• How do you convert between m^3 and cm^3?

  cm^3 x 100^3 = m^3
• What does the average density affect?

  Whether the object sinks or floats in a liquid
• How do you find the mass of an object?

  Use a top-pan balance
• How do you find the area of an irregular object?

  Use Archimedes' principle
• What is Archimedes' principle?

  The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces
• What is Hooke's law?

  When a spring stretches, the extension of the spring is directly proportional to the force stretching it, provided that the limit of proportionality of the spring is not exceeded.

  
  

  F ∝ Δl
• What is displacement in a spring? (extension)

  The difference between its original length and its stretched length (Δl or x)

  
  

  Δl = l_final - l_initial

  
  

  -F = -Δl (compression)
• What is the spring constant?

  A physical quantity of a spring/ object that determines how much force is required to change the extension (Δl) by a set amount
• What is Hooke's law equation?

  F = kΔl = kx
• What are the types of forces found in a spring that is displaced (+ / -)?

  Tensile force - A force that stretches a spring/ object

  (usually a positive force and negative tension)

  
  

  Compressive force - A force that compresses a spring/ object

  (usually a negative force and positive tension)

  
  

  (positive \/- negative /\)
• What is a force-extension graph?

  A plot showing how an object extends as the force applied increases. For an elastic object, the gradient will be linear up to the limit of proportionality. The gradient gives the spring constant (abnormally, F (independent) on y axis and Δl so that grad = k)

  
• What is the limit of proportionality?

  The point at which extension is no longer directly proportional to force (Hooke's law is no longer obeyed but it will return to its original shape)

  
• What is the elastic limit?

  The maximum amount a material can be stretched by a force without permanently deforming (and still return to its original length when the load is removed) (will be just after the limit of proportionality)

  
• How do you find the spring constant? (GCSE practical)

  Use a retort stand to hang a spring with the end of the spring lined up with the zero mark on the ruler (using another clamp to suspend it). Add a mass to the end of
• How do you derive spring constant is series?

  F0 = F1 = F2

  x0 = x1 + x2

  F=kx -> x=F/k

  
  

  F0/k0 = F1/k1 + F2/k2

  
  

  Using F0 = F1 + F2

  F/k0 = F/k1 + F/k2 -> 1/k0 = 1/k1 + 1/k2
• How do you derive spring constant is parallel?

  x0 = x1 = x2

  F0 = F1 + F2

  F=kx

  
  

  k0x0 = k1x1 + k2x2

  
  

  Using x0 = x1 + x2

  k0x = k1x + k2x -> k0 = k1 + k2
• What is energy?

  The integral of a force

  
  

  So we can derive Hooke's law with integrals.

  
  

  E = ∫ F dx

  
  

  E = ∫ kx dx

  
  

  E = (kx)/2
• What is the yield point?

  When elastic deformation ends and plastic deformation begins

  
  

  This is where a small amount of force is required for a large extension

  
  

  It is hard to see on a force-extension graph (easy on a stress-strain graph)
• What is a Hookean object?

  Materials that can be described by Hooke's Law, which states that the strain within an elastic material is directly proportional to the applied stress
• What is elastic deformation?

  The concept that an elastic material will return to its original shape when the load forces is removed.
• What is plastic deformation?

  The concept that an elastic material will not return to its original shape when the load forces is removed. This is because the material is permanently deformed
• When loading and unloading an elastic band (low limit of proportionality, high elastic limit), why are the curves different?

  There is energy lost (internal energy caused by friction between the molecules, sound, etc). This is found by the area between the curves

  
• What is the force-extension graph for plastic deformation?

  A straight parallel line to the x-axis where the line does not go through the origin

  
• What is the force extension graph for a plastic material?

  
• If an object has not been stretched past its limit of proportionality, how could you calculate the work done?


  W = 1/2 T Δl
• What is tensile stress?

  The force applied per unit cross sectional area. (Nm^-2 or Pa)

  
  

  σ = F/A
• What is tensile strain?

  The fractional change in length of an object (No units)

  
  

  ε = Δl/l
• What is young's Modulus?

  A measure of stiffness/ how difficult it is to change the shape of a material

  
  

  Unlike spring constant, its a constant for the material rather than the object

  
  

  E = σ/ε = Fl/A(Δl)
• What is ultimate tensile stress?

  the maximum force per original cross-sectional area a wire can support until it breaks

  
• What is the gradient of a stress-strain graph?

  The Young's modulus of the material
• What is the area underneath a stress-strain curve?

  The energy stored per unit volume

  
  

  E = 1/2 σε
• What is a brittle material?

  A material that doesn't undergo plastic deformation and instead fractures at its elastic limit
• For a brittle material, the force-extension and stress-strain curves are _______

  similar
• What structure does a brittle material usually have?

  crystalline or polycrystalline

  
  

  This is because the material's molecules have strong intermolecular forces which makes it stiff. When enough tension/ force is applied, small fractures start forming until one is big enough to snap or shatter the material. This is called brittle fracture

  
• What is the stress-strain graph of a brittle and ductile material?