170 likes | 332 Views
Chapter 1.2. Measurements and Uncertainties. 1.2.1 SI Units. 7 fundamental SI units m length kg mass s second A electric current K Temperature Cd intensity of light. 1.2.2 Derived SI Units. Derived SI Units- combinations of the fundamental SI units
E N D
Chapter 1.2 Measurements and Uncertainties
1.2.1 SI Units • 7 fundamental SI units • m length • kg mass • s second • A electric current • K Temperature • Cd intensity of light
1.2.2 Derived SI Units • Derived SI Units- combinations of the fundamental SI units • N, J, W, Pa, Hz, C, V, T, Wb, Bq • Example 1:
1.2.3 Convert units to SI • Examples 2 (conversion):
1.2.4 Know Common SI Prefixes • Question 3: • Accepted SI units: ms-2 not m/s2 • 1.2.5 Values must be stated in scientific notation • Example: 5.0 x 10-16 nm with appropriate prefixes
1.2.6 Uncertainty and error in measurement • Random errors= if readings of a measurement are above and below the true value with equal probability then errors are random. • Examples: changes in experimental conditions, such as temperature, pressure, humidity • Different person reading instrument • Malfunction of the apparatus
Systematic error= due to the system or apparatus being used. • Examples: observer consistently making the same mistakes -apparatus calibrated incorrectly • Random errors can be reduced by repeating measurement many times and taking the average but not systematic errors.
1.2.7 • Precise= getting same answer over and over • Accurate= getting equally close to the answer you want. • Example: Dart Board 4 Graph Possibilities • A measurement may have great precision yet may be inaccurate.
1.2.8 • Measurements are accurate if systematic error is small. They are precise if random error is small. • Random errors can be reduced by taking many readings (measurements) and taking the average.
1.2.9 Significant Figures • Give measurements with numbers that can be guaranteed (measurement of a paper) • Should reflect precision of the value or input data to a calculation • Multiplication and division number of significant figures in a result should not exceed the least precise value upon which it depends.
Example: assume reading error is half smallest division on instrument on a ruler. Interval is 1mm; half is .5mm • Measurement would be 14.54 +/- .05cm
Uncertainties in calculated results 1.2.10 • Absolute uncertainty= error in measured time to show uncertainty. Drop a ball= uncertainty due to reaction time. • Example: Measured time= 1.0s, uncertainty= +/- .1 s • Uncertainty can also be shown as a fraction or a percentage. • +/- .1s or 1/10 or 10%
1.2.11 Determine Uncertainties in Results • Example pg. 34 Tsokos • To determine maximum uncertainties: • addition/subtraction= absolute uncertainties may be added • Mult/division/exponential= percentage uncertainties may be added • Trig fxns/other fxns= mean of highest/lowest possible answers may be calculated to determine uncertainty.
1.2.11 Determine Uncertainties in results • Can throw out outliers • Square root= percentage uncertainty is halved • Uncertainties in graphs - Excel example of how to calculate and draw error bars on graphs
1.2.12 • Uncertainty values must always be shown at the top of data tables as +/- sensible values • Represented as error bars on graph (only need to be considered when uncertainty in one or both plotted quantities is significant) • Do not have to have error bars for trig or log fxns. • Question 4: How to draw minimum and maximum gradients
Excel Example with Error Bars • Best fit line must pass through error bars. If it doesn’t, point must be labeled as an outlier. • To determine uncertainty in gradient and intercept of straight line graph, error bars only need to be added to the first and last data points.
Significant Figures Handout • Review significant figures and do several examples