< 8) Often you will want to compare two values. One way to do this is to calculate % discrepancy. < |value - value % discrepancy = 100% best value < where the best value is whichever value you think is more reliable: e.g., a literature value, your result, the average of two values (if your numbers are close and you have no reason to believe one is more reliable), the initial value (if you are comparing an initial and final value), etc. < < % discrepancies are generally given to 1-2 significant figures. < < What is the % discrepancy between the following two values? < aexperimental = 5.6 m/s + 2.1% and atheoretical 5.4 m/s + 1% < Show the calculation here: < 9) Two values agree if the % discrepancy between them is less than or equal to the sum of the % uncertainties of the values you're comparing. < < State whether the following 2 values agree and show your work: < < aexperimental = 5.6 m/s + 2.1% and atheoretical = 5.4 m/s + 1% WolframAlpha gravitational acceleration in Kelowna, BC| computational knowledge engine. Web Apps =Examples Random Assuming "gravitational acceleration" is referring to gravity | Use the input as a formula instead Input interpretation: gravitational acceleration Kelowna, British Columbia Gravitational field strength for Kelowna, Canada: total field 9.81307 m/s (meters per second squared) Show non-metric units Although g values are measured and therefore do have uncertainty, the % uncertainty is so small that it can be safely considered to be 0%. < Acceleration due to gravity, g = % for the location of The source of this value is Drawing Graphs by Hand Finely scaled graph paper (1mm) is required to get adequate precision from your graphs. < + Your graph must always occupy at least half of the graph paper in each direction. If your graph is confined to a smaller region, then the precision of any results taken from the graph will be limited. Stretch out the scaling and/or start the axes from values other than zero if that helps spread your graphed relationship over a larger portion of the graph area. t Scale the axes by values that are easy to work with whenever possible (e.g., multiples of 1's, 2's, 5's, etc. rather than 3's, 7's, etc.). Draw in the axes as solid lines. Not every division needs to be labeled, but make tick marks along the axes for the ones that you do label. < Label the axes clearly with quantity name, symbol, units and uncertainty value (if the uncertainty is constant for all of the data along that axis). < Plot the data points as small sharp dots using a sharp pencil. To account for the estimated experimental uncertainty of the data, draw in uncertainty bars (more often called "error bars") for each data point. These should be drawn to scale, showing how large the uncertainties on the x- and y-axes are for each data point (see diagram below). < t Note that the two uncertainty bars form an uncertainty box. According to the measurement uncertainties chosen, the data point lies anywhere inside that box. y-axis data:+ 2.2 0.6 < +0.6 x-axis data: -0.6 6.3 0.4 < 6.0 < 6.5 3 - 0.4+ + 0.4+ 2 < uncertainty box= Draw in the "best fit" line (or curve). Use pencil for best-fit lines or curves. If the data suggests a linear relationship, then use a ruler to draw in your best estimate of the linear regression line (e.g., the line which has the minimum sum of the distances from the points to the line). If the data suggests a curve, then use a flexible ruler or French curve to help draw in a smooth (if your hand is steady, then sketching in the curve by hand is also acceptable). Never join point- to-point and do not "force the graph through the origin." t Give the graph a descriptive title related to the experiment. Do not simply name the variables being graphed. The title should add information, not just duplicate what is already clear. 6) If we want to produce a linear graph of x and t measurements, then we can plot x on the y-axis and t on the x-axis. The reason this will be linear can be seen from the comparison of the relationship between the variables to the general equation of a straight line, term by term, as follows: < + x = vot + at 2 OR x = (2a)+ + vit. + b In other words, if t is plotted on the x-axis and x is plotted on the y-axis, then the relationship is in the form of a linear relationship with the slope m = a and the y-intercept b = vot (Note: we expect b = 0 if the object is falling from rest since vo = 0). < If you were to calculate t for a measurement of t, how would you calculate the uncertainty of t from the % uncertainty of t? (Recall that when you multiply 2 values, you add the % uncertainties.) < t If t = 0.1202 s 3%, then t = s %. t From the x vs t graph, what will the slope m be equal to (in terms of acceleration a)? t From the x vs t graph, how can you calculate a from the slope m of the graph? t t 7) Sometimes there is a previously determined value for a quantity being experimentally determined. There are many good ways to find these values, but using a reliable source is required. If you're unsure of the credibility of a source, don't use it. Always give the source of values you cite. One credible source for the purposes of this course is an online database/software called Wolfram Alpha. < Look up a value for the acceleration due to gravity g for your location using Wolfram Alpha. Example for Kelowna: g = 9.81307 m/s