Physics II workshop_Part_71

Physics II workshop_Part_71 - for which we have no theory...

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144 In the example above, I find 147 mA - 107 mA mA "best" slope = ------------------ = 7.27 ---- 10 V - 4.5 V V 145 mA - 115 mA mA "min" slope = ------------------ = 5.45 ---- 10.5 V - 5.0 V V 152 mA - 106 mA mA "max" slope = ------------------ = 9.20 ---- 10 V - 5.0 V V Uncertainty in slope is 0.5 * (9.20 - 5.45)mA/V = 1.875 mA/V There are at most two significant digits in the slope, based on the uncertainty. So, I would say the graph shows slope = 7.3 +/- 1.9 mA/V Adapted from M. Richmond.
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145 Curve Fitting We are free to make many plots from a given set of data. For instance if we have position (x) as a function of time (t) we can make plots of x versus t, x versus , log(x) versus t, or any number of any choices. If possible, we choose our plot so that it will produce a straight line . A straight line is easy to draw, we can quickly determine slope and intercept of a straight line, and we can quickly detect deviations from the straight line. If we have the guidance of a theory we can choose our plot variables accordingly. If we are using data
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Unformatted text preview: for which we have no theory we can empirically try different plots until we arrive at a straight line. Some common functions are listed in Table 1 along with plots which yield straight lines. Table 1. Different graphs for different functions. This summarizes some of the most common mathematical relations and the graphing techniques needed to find slopes and intercepts. FORM PLOT (to yield a straight line) SLOPE Y-INTERCEPT y = a x + b y versus x on linear graph paper a b y 2 = c x + d y 2 versus x on linear graph paper c d y = a x m log y versus log x on linear paper or y versus x on log-log paper m * log a a (at x = 1) x y = K y versus (1/x) on linear paper K 0 y = a e bx ln y versus x on linear paper or y (on log scale) versus x on semi-log paper b * ln a a * Special techniques are needed when using logarithmic graph paper. These will be discussed in a later section....
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Physics II workshop_Part_71 - for which we have no theory...

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