Materials

Mindmap including information about: springs in parallel and series; Hooke's Law; Young's modulus; stress-strain graphs; energy stored in a stretched spring and the deformation of materials.

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  • Materials
    • Hooke's law
      • F = k e
        • The greater the value of k, the stiffer the spring
        • k = spring constant Nm-1
        • e = extension (also delta L) m
        • F = force N
        • For a graph of force against extension...
          • Straight line through the origin
            • As it is proportional
          • Gradient is the spring constant k
      • The force needed to stretch a spring is directly proportional to the extension from its natural length
        • The tension in the spring is equal and opposite to the force needed to stretch the spring
    • Springs in series
      • Extension is double
      • Total e = e1 + e2
        • Total e = W/k1 + W/k2
      • Extension needed to stretch springs...
        • e1 = W / k1 (same for spring 2 replacing '1' with '2'
      • Total e = W/k1 + W/k2
      • k = 1/k1 + 1/k2
    • Springs in parallel
      • Extension is half
      • W = F1 + F2
        • W = k1xe + k2xe
      • Force needed to stretch springs...
        • F1=k1xe (same for spring 2 replacing '1' with '2'
      • k = k1 + k2
      • W = k1xe + k2xe
    • Points on a stress-strain graph
      • Stress strain graph image for reference
        • P = Limit of proportionality
          • The final point where Hooke's law is obeyed. However, past this point, the material will still return to its original length when force is removed
        • E = Elastic limit
          • After this point, the material is permanently stretched and behaves plasticalls
        • Y = Yield point
          • Material temporarily weakens and a very small amount of stress can cause a vast amount of strain
            • e.g. stretching with little force
        • U = Ultimate tensile stress (UTS)
          • Material loses its strength and becomes narrower at its weakest point.
        • B = Breaking point
          • Where the material breaks
      • Curves for glass, copper and steel
    • Young's Modulus
      • Tensile stress / tensile strain
        • For a graph of stress against strain...
          • Gradient is Young's modulus
    • Energy stored in a stretched spring
      • For a graph of F against e...
        • Area under the gradient is work done
          • Work done to stretch a spring by extension = 1/2Fe
      • Elastic potential energy stored
        • If the spring is released, the EP energy is transferred into KE
        • EP stored in a stretched spring = 1/2Fe = 1/2ke^2
    • Tensile stress and strain
      • Tensile stress
        • F/A
          • Pascals (Pa) Nm-2
          • F = force (tension) N
          • A = cross sectional area m^2
        • The tension per unit cross-sectional area
      • Tensile strain
        • e/L
          • No units as it is a ratio
          • e = extension (also delta L) m
          • L = length m
        • The extension per unit length
    • Deformation of solids
      • Deformation that stretches an object is TENSILE
        • Plastic deformation- When a material is stretched beyond it elastic limit and behaves plastically, never returning to its original length
      • Deformation that compresses an object is COMPRESSIVE
      • Elasticity = the ability to regain shape after deformation when the force is released
      • For a graph of F against e...
        • Spring
          • Straight line through the origin
            • Obeys Hooke's law
            • Picture of graph
        • Polyethene *****
          • 'Gives' after initial stiffness is overcome but after that, it extends little and becomes difficult to stretch further
        • Rubber band
          • Initially extends easily when stretched, then becomes very difficult to stretch further
    • Properties of materials
      • Tough- Requires a lot of energy to break
      • Ductile- Can be stretched into a more desirable shape e.g. copper into wires
      • Hard- Not easy to scratch or indent
      • Malleable- Easily moulded into a more useful shape
      • Brittle- Material breaks cleanly without any yield
      • Tensile strength- The largest amount of stress a material can withstand
    • Loading and unloading
      • Metal wire
        • Graph
        • Loading and unloading curves are the same, provided the elastic limit is not exceeded. Beyond that, the unloading line is parallel and has a permanent extension
      • Polyethene *****
        • Graph
        • Example of a polymer
          • Molecules are long chains of atoms. Before stretching, these atoms are tangled together and weak bonds (cross-links) form between molecules
          • When put under tension, the cross-links break and in the stretched state, more bonds form so when tension is removed, it remains stretched
        • Extension during unloading is greater than loading but ***** does not return to its original length
        • Low limit of proportionality and suffers plastic deformation
      • Rubber
        • Graph
        • Change in length during unloading is greater. Has a low limit of proportionality
        • Another polymer but molecules are curled and tangled together in an unstretched state.
          • When placed under tension, molecules straighten out but curl back again when force is removed

Comments

Fakharl

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excellent resource

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