Graphs

							GRAPHS




                           1
         23 October 2010
      What is the importance of
               graphs?
 Provides clear, easily interpreted visual
  report of an experimental investigation.
 Can show trends and relationships
  between physical quantities which are
  not always immediately obvious from a
  list of figures.




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PHASE 1




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How to draw a graph
 Deciding on what to plot.
 Deciding on orientation of graph.
 Choosing sensible scales for the axes.
 Giving graph a title.
 Labelling axes.
 Plotting points.
 Drawing the ‘best fit’ line.


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   General Rule – Dependent Variable (y –
    axis) versus Independent Variable (x-axis)
    Think about this data for the timing of a famous athlete
    running the first 9 seconds of a hundred metre (100m) race.
    TIME/s            0   1   2    3       4        5   6   7   8   9
    DISTANCE/m        0   5   20 29 38 49 60 70 81 92
    Which one of these quantities seem to be dependent on the
    other?

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   Based on your data, you may need to
    orient your graph as landscape or portrait.
   Use your discretion, taking note of the
    range of values for each physical
    quantity, and the scales you wish to use.




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 Choose scales that you use much of the
  graph paper.
 Scales should always be easy to use and
  the values of the intermediate lines on
  the graph paper easy to calculate.




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   Title your graph as:
     ‘y against x’ or
    ‘y-x graph’ or
    ‘Graph of y against x’

Note: y and x are substitutes for the specific
 names of the physical quantities that you
               are comparing.
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   LABEL both axes with the PHYSICAL
    QUANTITY and with its UNIT e.g.
    Distance/m or Time/s.




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   Accurately mark your points (co-
    ordinates) with RINGED DOTS or
    CROSSES.




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   Determine from the Data table if the line
    should pass through the origin.
   Use a transparent ruler and a sharp pencil
    to draw the line.
   In the case of a curved graph, do not use a
    ruler but draw a smooth curve to show the
    trend.
   The line may not pass through all the points,
    but your aim should be to have points
    scattered symmetrically on both sides of the
    line along the line.
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PHASE 2




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Extracting Information from a Graph

 Extrapolating points.
 Finding the gradient of a graph.
 Finding an intercept on a graph.
 Finding the area under a graph.




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 Extrapolation refers to a process used to
  find the value of a quantity outside its
  tabulated values.
 Once a ‘best-fit line’ is drawn, a number
  of points other than the points from the
  data table can be found.




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 Draw a large triangle against the straight
  line.
 The sides of the triangle represent the
  changes: Δy and Δx.
 It helps to select exact scale graduations
  giving easy-to-read values on the x-axis
  as you will be dividing by the value of Δx.


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   Intercepts are the values obtained where a
    graph cuts an axis.
   The reading from the y-axis intercept is the
    value of the y-variable when the x-variable
    is zero.
   The reading from the x-axis intercept is the
    value of the x-variable when the y-variable
    is zero.
   WARNING – your axes must begin at the
    origin, otherwise where the line cuts will not
    be true intercepts.
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 For straight line graphs, divide the area
  into rectangles and triangles and find
  the area of each.
 For curved graphs count the squares
  and estimate parts of squares making up
  the equivalent of whole squares.
 When you count squares you must
  multiply the no. of squares by the scale
  factor for the value of the total area in
  correct units.
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Question 1




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Question 1 (continued)




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Question 2




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Question 2 (continued)




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        Question 3
Plot a graph of Length/cm against
Depth/cm (your scale should be at least
extend out to 55 cm).

(The data table is on the next slide.)




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Question 3 (continued)
  Length/cm               Depth/cm
     5.0                    20.8
     10.0                   18.5
     14.0                   16.7
     17.0                   15.2
     20.0                   13.8
     23.0                   12.5
     27.0                   10.6
     30.0                    9.3
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            Question 4
   Plot a graph of y/cm against x/cm
    starting at the y scale at ‘y = 30 cm’.

    (The data table is on the next slide.)




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Question 4 (continued)
   x/cm                      y/cm
    13.0                      73.0
    14.5                      53.5
    17.0                      45.4
    20.0                      42.6
    25.0                      43.3
    30.0                      46.5
    40.0                      54.7

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The following items were retrieved from:
Avison, J.H., Neeranjan, D. & Henry, D.
  (2007). Physics for CSEC. Nelson Thornes
  Ltd: Cheltenham/GB.
   graph of displacement against time
   data for the displacement time graph
   graph of velocity against time
   data for the curved velocity against time graph
   y-axis and x-axis intercepts
   question 1 & question 2

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The following items were retrieved from:
Jackson, B. & Whiteley, P. (2003). Logman
  Physics for CXC (2nd ed.). Logman: UK.
   question 3 & question 4




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