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An Introduction to Graphs: how to draw a graph; extracting information for a graph.
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. 23 October 2010 2 PHASE 1 23 October 2010 3 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. 23 October 2010 4 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? 23 October 2010 5 23 October 2010 6 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. 23 October 2010 7 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. 23 October 2010 8 23 October 2010 9 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. 23 October 2010 10 LABEL both axes with the PHYSICAL QUANTITY and with its UNIT e.g. Distance/m or Time/s. 23 October 2010 11 23 October 2010 12 Accurately mark your points (co- ordinates) with RINGED DOTS or CROSSES. 23 October 2010 13 23 October 2010 14 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. 23 October 2010 15 23 October 2010 16 23 October 2010 17 23 October 2010 18 23 October 2010 19 23 October 2010 20 PHASE 2 23 October 2010 21 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. 23 October 2010 22 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. 23 October 2010 23 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. 23 October 2010 24 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. 23 October 2010 25 23 October 2010 26 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. 23 October 2010 27 Question 1 23 October 2010 28 Question 1 (continued) 23 October 2010 29 Question 2 23 October 2010 30 Question 2 (continued) 23 October 2010 31 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.) 23 October 2010 32 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 23 October 2010 33 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.) 23 October 2010 34 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 23 October 2010 35 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 23 October 2010 36 The following items were retrieved from: Jackson, B. & Whiteley, P. (2003). Logman Physics for CXC (2nd ed.). Logman: UK. question 3 & question 4 23 October 2010 37