Graphing is an effective way of showing the

Graphing is an effective way of showing the relationship between variables. Page 11 Physics 20/Kennedy/2015 1

Page 11 Use precision graph paper. The lines should be about a mm apart. Don’t use the less precise grid paper where the lines are about a cm apart. Good Poor Precision graph paper will provide better results Lines are further apart providing poorer precision Physics 20/Kennedy/2015 2

Page 11 Data Tables Manipulated Responding Distance (m) Time (s) 10. 0 1. 1 20. 0 2. 1 30. 0 2. 9 Units are placed in column header. Don’t put units with the numbers in chart Controlled variables are items that are not changed Physics 20/Kennedy/2015 3

Graphical Analysis Page 11 Graphs are used to communicate relationships – how one thing affects another. Step Step 1: 2: 3: 4: 5: 6: Select the Axes Select a Scale Plot the Data Draw the Best-fit Line Title (responding versus manipulated) Calculate slope Your graph should be neat and not cluttered. Physics 20/Kennedy/2015 4

Graphical Analysis Page 11 Graphs are used to communicate relationships – how one thing affects another. Step 1: Select the Axes Responding y Manipulated x Time is always on the x-axis Physics 20/Kennedy/2015 5

Step 2: Select a Scale Page 11 Bad Good 3. 0 2. 0 1. 0 The graph should take up at least 2/3 of the graph paper. Physics 20/Kennedy/2015 6

Page 11 Select whichever orientation works best for your graph. Portrait view Landscape view Physics 20/Kennedy/2015 7

Don’t crowd the axis. 6. 0 8. 0 1. 0 3. 0 2. 0 4. 0 5. 0 7. 0 9. 0 10. 0 15. 0 20. 0 25. 0 Poor Good Physics 20/Kennedy/2015 8

When drawing a graph have a: • clear, plastic ruler/straight edge. You need to be able to see the ruler to graph properly. • sharp pencil. Thin lines are more precise and produce better results. Whenever you have to draw a straight line, use a ruler/straight edge. Physics 20/Kennedy/2015 9

Step 3: Plot the Data Page 11 1. Place a dot at the data point 2. Circle the data point Physics 20/Kennedy/2015 10

Step 4: Draw the Best-fit Line Best-fit lines and data points A best fit line should try to get as close as possible to all the points. This will result in as many points above the line as are before the line. A best fit line results in a type of average Do not connect the dots! A good best fit line should: • Have as many dots as possible on the line. • Have as many dots above the line as below • All the dots as close as possible to the line Physics 20/Kennedy/2015 11

Best fit lines Connect the dots – bad! Best fit line – good Use a clear plastic straight edge for best results Physics 20/Kennedy/2015 12

When drawing the best fit line, lift your pencil so as not to draw over the data point Physics 20/Kennedy/2015 13

Lines Connect the dots – bad! Force through zero – bad! Connect first to last – bad! Best fit line – good! Physics 20/Kennedy/2015 14

Extrapolate and interpolate Page 15 Extrapolate is extending the line beyond available data Interpolate is drawing a line between available data Physics 20/Kennedy/2015 15

Stray data points If a data point does not line up well with the rest of the dots then you may reject it as bad data. Draw an x through it or a place a question mark beside it. 40. 0 Mass (g) 30. 0 20. 0 10 20 30 40 50 Volume (m. L) Physics 20/Kennedy/2015 16

Step 5: Title (responding versus manipulated) Example: Distance versus time Distance as a function of time Page 11 Mass of water as a function of Volume 40. 0 Mass (g) 30. 0 20. 0 10 20 30 40 50 Volume (m. L) Physics 20/Kennedy/2015 17

Step 6: Calculate Slope is a measure of steepness of a line and is usually represented by the symbol m. Slope is the same anywhere on the straight line. Physics 20/Kennedy/2015 18

Identify the line having the greater slope. A Steeper, therefore greater slope B Physics 20/Kennedy/2015 19

Negative slope y y Positive slope x x Undefined slope y y Zero slope x x Physics 20/Kennedy/2015 20

When calculating slope: Page 15 • Don’t use data points as slope points • Select two points that are relatively far apart. • Use your clear plastic ruler to carefully mark the two slope points Mass of water as a function of Volume 40. 0 38, 37. 5 Mass (g) 30. 0 20. 0 12. 0, 11. 6 10. 0 10 20 30 40 50 Volume (m. L) Physics 20/Kennedy/2015 21

Calculating Slope = rise run y 2 – y 1 x 2 – x 1 Physics 20/Kennedy/2015 Show all work: 1. formula 2. substitution with units 3. Answer to proper sig digs 22

Selecting and marking slope points: You may select points that are as easy to read (estimate) as possible but make sure your estimate is actually on the graph. • Don’t use the nearest intersection to your best fit line • Take more care and mark slope points on the line. Physics 20/Kennedy/2015 23

If your graph curves you can use a flexible ruler or free-hand the line Distance as a function of Time 4. 0 distance (m) 3. 0 2. 0 1. 0 2. 0 3. 0 time (s) Physics 20/Kennedy/2015 4. 0 5. 0 p. 15 #1 Do 24

the end Physics 20/Kennedy/2015 25