AS physics

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AS physics
2013-11-17 06:49:44
unit two section materials

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  1. what is density
    • density is a measure of the "compactness" of a substance . it relates the mass of a substance to how much space it takes up . the density of a material is its mass per unit volume : 
    • p = m/v 
    • p = density in kg m^-3 
    • m = mass in kg 
    • v = volume in m^3 
    • however if you are given the mass in g and the volume in cm^3 you can work out the density of an object in in kg cm^-3
  2. the density of an object depends on
    what it's made of . Density of a material doesn't vary with shape or size
  3. the average density of an object determines whether
    it sinks or floats
  4. A solid object will float on a fluid if it has
    a lower density than the fluid
  5. 1 g cm^-3 = ...... kg m^-3
  6. why does an empty bottle float on water
    the average density of the bottle and the air inside it combined is lower than the density of the water
  7. you can work out the volume of a sphere using
    V = 4/3 x Pi x r^3
  8. how can you measure the density of regular solids
    • find the mass 
    • find the volume by using length , width and height measurements 
    • use the formula : density = mass /volume
  9. how can you measure the density of irregular solids
    • fill a displacement can and let the water run out of the spout
    • place the object in the can and measure the volume of water displaced 
    • find the mass 
    • use the formula : density = mass/volume
  10. alloys are
    • mixtures of metals 
    • e.g. brass is a mixture of copper and zinc
  11. to calculate the mass of an alloy use the formula
    M = PaVa + PbVb
  12. to calculate the density of an alloy use the formula
    • P = PaVa + PbVb 
    •       ---------------
    •                V
  13. what is Hooke's law
    if a metal wire of original length L is supported at the top and then a weight attached to the bottom , it stretches  . The weight pulls down with force F , producing an equal and opposite force at the support
  14. draw a diagram to show a supported metal wire extending by ΔL when a weight is attached
  15. Robert Hooke discovered in 1676 that the extension of a stretched wire , ΔL , is
    proportional to the load or force , F . This relationship is now called Hooke's law .
  16. Hooke's law can be written as
    • F = KΔL 
    • F = force in newtons 
    • k = the stiffness constant Nm^-1
    • ΔL = extension in m 
    • k is a constant that depends on the object being stretched
  17. an object's stiffness constant is the
    force needed to extend it by 1m . It depends on the material that it's made from , as well as its length and shape .
  18. a metal spring also changes length when you apply a pair of opposite forces . the extension or compression of a spring is proportional to the
    force applied - so Hooke's law applies
  19. draw a diagram to show metal springs with tensile and compressive forces acting on them
  20. if two things are proportional , it means
    that if one increases , the other increases by the same proportion
  21. a tensile force
    stretches something
  22. a compressive force
    squashes it
  23. for springs , K , in the formula F=KΔL is usually called the
    spring stiffness or spring constant
  24. Hooke's law works just as well for compressive forces as tensile forces . For a spring , k , has the same value whether the forces are
    tensile or compressive (though some springs and many other objects can't compress)
  25. don't be put off if you're asked a question that involves 2 or more springs . the formula F=KΔL still applies ...
    for each spring
  26. there's a limit to the force you can apply for Hooke's law to stay true . Draw a diagram to show load against extension for a typical metal wire
  27. explain the graph on the previous slide
    • the first part of the graph shows Hooke's law being obeyed - there's a straight-line relationship between load and extension and it goes straight through the origin . The gradient of the straight line is stiffness constant , k . 
    • when the load becomes great enough , the graph starts to curve . The point marked E on the graph is called the elastic limit . If you increase the load past the elastic limit , the material will be permanently stretched . When all the force is removed , the material will be longer than at the start 
    • metals generally obey Hooke's law up to the limit of proportionality , marked P on the graph , which is very near the elastic limit . The limit of proportionality is the point beyond which the force is no longer proportional to the extension  . The limit of proportionality is also known as the Hooke's law limit 
  28. there are some materials such as rubber that only obey Hooke's law for
    really small extensions
  29. you may be asked to give two features of a graph which show that the material under test obeys Hooke's law . Just remember , the graph of a material which obeys Hooke's law will start with
    straight line through the origin 
  30. the limit of proportionality can be described as
    the point beyond which the load-extension graph is no longer linear
  31. draw a diagram to show the experimental set up you could use in the lab to investigate how the extension of an object varies with the force used to extend it 
    and explain how you would use the equipment
    • the object under test should be supported at the top, e.g. using a clamp and a measurement of its original length taken using a ruler . Weights should then be added one at a time to the other end of the object . 
    • the weights used will depend on the object being tested - you should do a trial investigation if you can to work out the range and size of weights needed . You want to be able to add the same size weight each time and add a large number of weights before the point the object breaks to get a good point of how the extension of the object varies with the force applied to it. 
    • after each weight is added , the extension of the object should be calculated . This can be done by measuring the new length of the object with a ruler and then using : extension = new length - original length
    • finally a graph of load against extension should be plotted to show the results 
  32. if a deformation is elastic , what happens to the material once the forces are removed 
    the material returns to it's original shape so it has no permanent extension 
  33. annotate a graph to show loading and unloading of an elastic material
  34. loading just means
    increasing the force on the material
  35. unloading means
    reducing the force on the material
  36. what happens when an elastic material is put under tension
    the atoms of the materials are pulled apart from one another . Atoms can move small distances relative to their equilibrium positions without actually changing position in the material . Once the load is removed , the atoms return to their equilibrium distance apart .
  37. for a metal , elastic deformation happens as long as
    Hooke's law is obeyed
  38. if a deformation is plastic , what happens to the material once the forces are removed
    the material is permanently stretched . some atoms in the material move position relative to one another . When the load is removed , the atoms don't return to their original positions . A metal stretched past its elastic limit shows plastic deformation 
  39. for springs in series what are the equations
    • extension a = f/ka
    • extension b = f/kb
    • total extension = extension a + extension b
    • total extension = f/ka + f/kb 
    • the effective spring constant :
    • 1/k = 1/ka + 1/kb
  40. the important thing to remember about springs in series
    each spring experiences the same force
  41. remember that weight =
    • mass x gravitational field strength 
    • kg x 9.81 m/s2

  42. draw a diagram to show springs in series
  43. draw a diagram to show two springs in parallel 
  44. for springs in parallel what are the equations
    • force needed to stretch a -> fa = ka x extension
    • force needed to stretch a when there is weight bar or a weight equally between the two springs is half the force on the weight bar 
    • force needed to stretch b -> fb = kb x extension 
    • force needed to stretch b when there is a weight bar or a weight equally between both springs is half the force on the weight bar 
    • NB the extensions are only the same if there is a weight bar or the weight is placed equally between two springs
    • total force = fa + fb = (ka x extension) + (kb x extension) 
    • the effective spring constant = ka + kb
  45. weight and force are equivalent in this topic
  46. two samples of the same material with different dimensions will stretch different amounts under the same force . Stress and strain are
    measurements that take into account the size of the sample , so the stress strain graph is the same for any sample of a particular material 
  47. a material subjected to a pair of opposite forces may
    deform i.e. change shape . 
  48. if the forces stretch the material , they're 
  49. if the forces squash the material they're 
  50. tensile stress is defined as 
    the force applied , F , divided by the cross-sectional area , A : stress = F/A 
  51. the units of stress are 
    Nm2- or Pascals , Pa 
  52. a stress causes a 
  53. tensile strain is defined as 
    the change in length , i.e. the extension , divided by the original length of the material : strain = extension/L 
  54. what are the units of strain
    strain doesn't have units it's just a number 
  55. NB it doesn't matter whether the forces producing the stress and strain are tensile or compressive - the same equations apply . the only difference is that you tend to think of tensile forces as positive and compressive forces as negative 
  56. as a greater tensile force is applied to a material , the stress on it 
  57. draw a diagram to show a stress-strain graph showing the ultimate tensile strength and breaking stress of a material
  58. the effect of stress is to
    start to pull the atoms apart from one another . Eventually stress becomes so great that atoms separate completely and the material breaks . This is shown by point B on the previous graph . the Stress at which this occurs is called the breaking stress - the stress that's big enough to break the material .
  59. the point marked UTS on the recent graph is called the
    ultimate tensile stress . This is the maximum stress that the material can withstand . Engineers have to consider the UTS and breaking stress of materials when designing a structure
  60. 1MPa is the same as 
    1 x 10Pa 
  61. when a material is stretched , work has to be done to in stretching the material . Before the elastic limit , all the work done in stretching is stored as potential energy in the material . This stored energy is called 
    elastic strain energy 
  62. on a force against extension the , the elastic strain energy is given by the
    area under the graph 
  63. draw a graph with a title "the area under a force extension graph for a stretched material is the elastic strain energy stored by it"
  64. provided a material obeys Hooke's law , the potential energy stored inside it can be calculate quite easily using a formula . This formula can be derived using 
    a force extension graph and work done  
  65. the energy stored by a stretched material is equal to the .... on the material in stretching it . so on a force extension graph , the area underneath the straight line from the origin to the extension represents the ...... or the ...........
    • work done 
    • energy stored or the work done
  66. work done is equal to 
    force x displacement 
  67. on a force displacement graph the force acting on the material is not constant . therefore you need to
    work out the average force acting on the material , from zero to F which is 1/2F . So it's the area underneath the graph : work done = 1/2 F x extension 
  68. and so the elastic energy is 
    E = 1/2 F x extension 
  69. because Hooke's law is being obeyed 
    F = k x extension which means F can be replaced in the equation to give 
    E = 1/2 K x extension x extension 
  70. if the material is stretched beyond the elastic limit , some work is done 
    changing the positions of atoms . This will not be stored as strain energy and so isn't available when the force is released 
  71. to calculate the elastic strain energy the force has to be in ... and the extension has to be in .........
    • newtons 
    • metres 
  72. the young modulus is a measure of 
    how stiff a material is , it is really useful for comparing the stiffness of different materials , for example if you're trying to find out the best material for making a particular product 
  73. when you apply a load to stretch a material , it experiences a 
    tensile stress and a tensile strain 
  74. up to a point called the limit of proportionality the stress and strain are
    proportional to each other .   
  75. below this limit of proportioaniliity , for a particular material , stress divided by strain is a constant . this constant is called
    the young modulus , 
  76. E = 
    E = tensile stress / tensile strain

    • E =          F/A
    •        ----------------
    •        EXTENSION/L

    • E =         FL
    •       ---------------
    •       A X Extension 

    • where
    • F = force in newtons 
    • A = cross sectional area in m2  
    • L = initial length in m 
    • and extension is also in m 

    • the units of young modulus are the same as stress (Nm-2 or pascals) , since strain has no units 
  77. draw and label suitable apparatus required for measuring the Young Modulus of a material in the form of a long wire 
  78. list the measurements you would make using the apparatus on the previous slide
    • length of the wire between clamp and mark
    • diameter of wire 
    • extension of wire for known weight 
  79. describe how the measurements on the previous slide would be carried out
    • length measured by metre ruler 
    • diameter using a micrometer at several positions and mean taken
    • known weight added and extension measured by noting the difference between the marker reading and unstretched length
    • repeat readings for increasing loads
  80. explain how you would calculate the young modulus from your measurements
    • graph of force against extension
    • gradient gives F/extension
    • so gradient x unstretch length /cross sectional area of wire  = young modulus

    cross sectional area can be worked out using A = pi(diameter/2)2
  81. the gradient of a stress strain graph gives the 
    young modulus , E 
  82. the area under a stress strain graph gives the
    strain energy (or energy stored) per unit volume 
  83. the stress strain graph for a material is a 
    • straight line provided that Hooke's law is obeyed , so you can calculate the energy per unit volume as 
    • energy per unit volume = 0.5 x stress x strain 
  84. steel has a high young modulus , which means 
    under huge stress there's only a small strain . This makes it an ideal building material for things like bridges 
  85. remember when using the gradient to work out the young modulus 
    you can only use it up to the limit of proportionality , after then the stress and strain are no longer proportional  
  86. don't forget to convert any lengths to ... and areas to ... when working out the young modulus 
    • m2
  87. draw a typical stress strain graph 
  88. explain the graph on the previous slide
    • Before point P , the graph is a straight line through the origin . this shows the material is obeying Hooke's law . The gradient of the line is constant and represents the Young modulus 
    • Point P is the limit of proportionality - after this , the graph is no longer a straight line , but starts to bend . At this point , the material stops obeying Hooke's law but would still return to its original shape if the stress was removed 
    • Point E is the elastic limit p- at this point the material starts to behave plastically . From point E onwards , the material would no longer return to its original shape once the stress was removed 
    • Point Y is the yield point - here the material suddenly starts to stretch without any extra load . The yield point or yield stress is the stress at which a large amount of plastic deformation takes place with a constant or reduced load 
    • the area under the first part of the graph gives the energy stored in the material per unit volume 
  89. plastic deformation is useful if 
    you dont want a material to return to its original shape , e.g. drawing copper into wires or gold into gold foil 
  90. draw a stress-strain graph of a brittle material 
    the graph starts with a straight line through the origin . so brittle materials obey Hooke's law . However , when the stress reaches a certain point , the material snaps - it doesn't deform plastically 
  91. examples of brittle materials 
    • a chocolate bar is an example of a brittle material - you can break chunks of chocolate off the bar without the whole thing changing shape
    • ceramics (glass and pottery) are brittle too - they tend to shatter  
  92. the structure of brittle materials 
    • atoms in ceramics are bonded in a giant rigid structure . the strong bonds between the atoms make them stiff , while the rigid structure means that ceramics are very brittle . 
  93. when stress is applied to a brittle material any
    tiny cracks at the metals surface are made bigger and bigger until the material breaks completely . this is called brittle fracture . the cracks in brittle materials are able to grow because these materials have a rigid structure . other materials , like most metals aren't brittle because the atoms within them can move to prevent any cracks getting bigger