GENERAL PHYSICS 1 Measurements of Uncertainty.pptx

MEASUREMENTS OF UNCERTAINTY

1. GENERAL PHYSICS 1

2. Estimation of Common Physical Quantities Estimation - a guess or calculation about the cost, size, value, etc. of something. If you know that the mass of an adult is 70 kg, you can estimate that the mass of a bag of apples must be less than 70kg.

3. Orders of Magnitude - Orders of magnitude provide a comparative scale to understand how large or small a quantity is. It’s about categorising numbers based on their logarithmic scale , typically powers of ten. A logarithmic scale is a method for graphing and analyzing a large range of values in a compact form. -if one amount is an order of magnitude larger than another, it is ten times larger than the other. If it is two orders of magnitude larger, it is a hundred times larger.

4. - generally used to make very approximate comparisons and reflect very large differences. If two numbers differ by one order of magnitude, one is about ten times larger than the other.

5. Measurements of Uncertainty Uncertainty - refers to the fact that it is impossible to measure any physical quantity with perfect precision. Uncertainty analysis - is the estimate of how far a measured quantity may be from the true value. is the action of analyzing uncertainty to make the best estimate for the true value.   Uncertainty= smallest division/10

6. Accuracy and Precision Accuracy of a data set is dependent on the closeness to a true value. Precision of data set is dependent on the closeness of the measured values to each other. A reliable data is ideally a set that is both precise and accurate.

7. Systematic error is one that is present in every measurement and oftentimes has the same degree of error. ex. Measuring with a defective weighing scale. This type of error can be avoided by making sure that the instruments and methodology are working properly. Random errors are not constant and usually vary from one measurement to another. This type of error significantly affects the precision of a data set.

8. Causes of Error in Doing Physics Laboratory Experiments: Inadequate definition (either systematic or random) – for example, if two students measure the length of a rope, they will possibly get different results because either one may stretch the rope with a different force. - to reduce error is to determine specific conditions that may affect the measurements. 2. Unable to include a factor (systematic) – for example, when measuring free fall, air resistance was not considered. Discuss all aspects that could probably affect the result before doing the experiment. 3. Factors due to the environment (either systematic or random) – errors brought by the environment such as vibrations, temperature, noise, or other conditions.

9. 4. Limited scale of the instrument (random) – for example, a meter stick cannot measure exactly in the smallest scale division. 5. Unable to calibrate or check zero scale of the instrument (systematic) – if possible, always check the calibration of the instrument before taking measurements. 6. Variations in the physical measurement (random) – take several measurements over a whole range that is being explored. 7. Parallax (either systematic or random) – the reading in measurement depends on the experimenter’s alignment of the eye to a pointer in scale. 8. Personal errors – occur from carelessness, poor method, or bias measurement.

10. Approximating Uncertainty for a Single Measurement Ex. A meter stick used to measure the diameter of a tennis ball where the uncertainty was +/- 5mm. If a Vernier caliper is used, the uncertainty can be reduced to +/- 2mm *the plus-minus symbol is used to indicate the range of error or uncertainty associated with a value.

11. Measurement made = (measured value +/- uncertainty) Where the uncertainty indicates the 68% confidence range. Ex. The diameter of the tennis ball = 6.7 +/- 0.2cm

12. Approximating Uncertainty in Repetitive Measurements For example, using a timer, a pendellum has 0.44 seonds period of oscillation. T=0.44 seconds Period 1: 0.46s 2: 0.44s 3: 0.45s 4: 0.44s 5: 0.41 -The best way to analyze the different measured values is by averaging the mean.

13. Measured Width (cm) 1 31.33 2 31.15 3 31.26 4 31.02 5 31.20 Average or mean = sum of measured width/number of observations

14. Standard Deviation Standard Deviation is a mathematical way to characterize the spread of a set of data. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.

15. To determine standard deviation of five measurements, one should: Add all the measurements and divide by five to obtain the average or mean; Subtract the average for each of the five measurements to obtain five deviations; Square the five deviations and add them all; and Divide the result of the sum by (N-1) and get the square root.

16. The importance of standard deviation is if one can have more measurements using the same meter stick, one can expect that the new measurements is within the range of 0.12 cm with an average of 31.19 cm.