Appendix B


Course Support
Lab Contents

Slope Calculations with Worst Fits

Show on the graph where the slope is taken from, by a triangle. Make the triangle as large as possible using two widely separated points on the line that are not from your original data. Do not use your original data to calculate slope. The slope that you are determining is of the line drawn (the data plotted no longer plays a role).

State the graph points used when calculating slope using the point form for calculating slope. Clearly show the calculation of slope for all three lines (best and two worst). Then calculate the uncertainty from the two worst fit slopes.

Figure 6

\[slope ~m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{29v - 15v}{110ma - 50ma}=\frac{14v}{60ma}= 0.23333\frac{v}{ma}\]

\[\text{worst high slope }m_{high}= \frac{y_2 - y_1}{x_2 - x_1}=\frac{31v - 15v}{110ma - 55ma}=\frac{16v}{55ma}= 0.2909\frac{v}{ma}\]

\[\text{worst low slope }m_{low}= \frac{y_2 - y_1}{x_2 - x_1}=\frac{28v - 15v}{110ma - 47ma}=\frac{13v}{63ma}= 0.2063\frac{v}{ma}\]

The final slope uncertainty is \(\Delta m = \frac{1}{2}(m_{high} - m_{low}) =  \frac{1}{2}(0.2909 - 0.2063)\frac{v}{ma} = 0.042 \frac{v}{ma} \)

The final slope is quoted as    \(m = m_{best} \pm \Delta m = (0.233 \pm 0.042)\frac{v}{ma}\)