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.
- Created by: Laurenthellama
- Created on: 08-04-17 18:59
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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
- Straight line through the origin
- 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
- F = k e
- 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
- Material temporarily weakens and a very small amount of stress can cause a vast amount of strain
- U = Ultimate tensile stress (UTS)
- Material loses its strength and becomes narrower at its weakest point.
- B = Breaking point
- Where the material breaks
- P = Limit of proportionality
- Curves for glass, copper and steel
- Stress strain graph image for reference
- Young's Modulus
- Tensile stress / tensile strain
- For a graph of stress against strain...
- Gradient is Young's modulus
- For a graph of stress against strain...
- Tensile stress / tensile strain
- 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
- Area under the gradient is work done
- 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
- For a graph of F against e...
- 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
- F/A
- 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
- e/L
- Tensile stress
- 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
- Straight line through the origin
- 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
- Spring
- Deformation that stretches an object is TENSILE
- 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
- Metal wire
- Hooke's law
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