LESSON 1-APPLYING MEASUREMENTS IN PHYSICS.pptx

MEASUREMENT IN STUDYING PHYSICS AND APPLYING CONVERSION

1. APPLYING MEASUREMENTS IN PHYSICS LESSON 1:

2. Convert the following measurements. 01 03 02 04 586 cm = ___m 1375L = ___ kL 4.28 m = ___mm 1396 mg = ___kg

3. Scientific Notation Scientific notation offers a convenient way of expressing very large or very small numbers . A positive number is written as a product of a number between 1 and l0 and a power of 10. For example, 9.63 x 10 7 and 2.3 x 10 -6 are numbers written in scientific notation.

4. Standard notation to scientific notation a. 580,000,000,000m b. 0.000068g Convert each number to scientific notation: a. 5.8 x 10 11 m b. 6.8x10 -5 g

5. Accuracy and Precision Two key aspects of the reliability of measurement outcomes are accuracy and precision. These terms are often used and even defined synonymously. By contrast, these terms are consistently differentiated in the literature of engineering and the “hard sciences”.

6. Accuracy It refers to the closeness of the measurements to the true or accepted value. A new spring balance is likely to be more accurate than an old spring balance that has been used many times.

7. Precision It refers to the closeness of the measurements of the results to each other. A physicist who frequently carries out a complex experiment is likely to have more precise results than someone who is just learning the experiment.

8. Degree of Accuracy and Precision The center of the bull’s-eye represents the accepted value. The closer a dart is to a bull’s-eye, the more accurate the throwing of the dart. The closer the darts are to each other, the more precise the throws.

9. Degree of Accuracy and Precision There are certain factors affecting the precision and accuracy of a measurement. These are a.) measuring device used, b.) manner of measurement, and c.) condition of the environment during measurement.

10. Experimental Errors Measurement errors may be classified as either random or systematic , depending on how the measurement was obtained (an instrument could cause a random error in one situation and a systematic error in another).

11. Random Errors Random errors are like the tiny differences you get when you try to measure something multiple times, even when you're being careful. They happen because: It's hard for us to do the same thing every time we measure. Our measuring tools aren't perfect and have limits to how precise they can be.

12. Random Errors The good news is that we can deal with random errors: We can use math (statistics) to understand how much these errors affect our results. We can reduce their impact by taking lots of measurements and finding the average.

13. Systematic Errors Systematic errors are mistakes that happen in the same way every time you measure something. Unlike random errors, which can go up or down, systematic errors always push your measurements in the same direction - either too high or too low.

14. Systematic Errors They're consistent: If you repeat the experiment, you'll get the same error each time. They're sneaky: These errors are hard to spot because they happen every time in the same way. Causes: They often come from problems with your equipment or the way you're doing the experiment. Can't fix with more tries: Unlike random errors, taking more measurements won't solve the problem. Hard to analyze: You can't use regular statistics to figure them out.

15. Systematic Errors Example: Imagine you're weighing objects on a scale that's not set to zero properly. It always shows 0.1 kg when there's nothing on it. Every measurement you take will be 0.1 kg too heavy.

16. REMEMBER In real experiments, both random and systematic errors can happen at the same time. Good scientists work hard to minimize both types of errors.

17. Common sources of error in physics laboratory experiments are: Incomplete definition (may be systematic or random) — One reason that it is impossible to make exact measurements is that the measurement is not always clearly defined. Failure to account for a factor (usually systematic) — The most challenging part of designing an experiment is trying to control or account for all possible factors except the one independent variable that is being analyzed.

18. Common sources of error in physics laboratory experiments are: Environmental factors (systematic or random) — Be aware of errors introduced by your immediate working environment. Instrument resolution (random) — All instruments have finite precision that limits the ability to resolve small measurement differences.

19. Common sources of error in physics laboratory experiments are: Calibration (systematic) — Whenever possible, the calibration of an instrument should be checked before taking data. Zero offset (systematic) — When making a measurement with a micrometer caliper, electronic balance, or electrical meter, always check the zero reading first.

20. Common sources of error in physics laboratory experiments are: Physical variations (random) — It is always wise to obtain multiple measurements over the widest range possible. Parallax (systematic or random) — This error can occur whenever there is some distance between the measuring scale and the indicator used to obtain a measurement.

21. Common sources of error in physics laboratory experiments are: Instrument drift (systematic) — Most electronic instruments have readings that drift over time. Lag time and hysteresis (systematic) — Some measuring devices require time to reach equilibrium and taking a measurement before the instrument is stable will result in a measurement that is too high or low.

22. Common sources of error in physics laboratory experiments are: Personal errors come from carelessness, poor technique, or bias on the part of the experimenter. The experimenter may measure incorrectly, or may use poor technique in taking a measurement, or may introduce a bias into measurements by expecting (and inadvertently forcing) the results to agree with the expected outcome.

23. Estimating Uncertainty in Repeated Measurements AVERAGE MEAN Average (mean) =  

24. Estimating Uncertainty in Repeated Measurements Example:

25. Estimating Uncertainty in Repeated Measurements One way to express the variation among the measurements is to use the average deviation. This statistic tells us on average (with 50% confidence) how much the individual measurements vary from the mean.

26. Estimating Uncertainty in Repeated Measurements STANDARD DEVIATION is the most common way to characterize the spread of a data set.

27. Identifying Scalars and Vectors Scalars and vectors are two kinds of quantities used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction.

28. SCALAR Scalar is a quantity with magnitude and usually a unit of measure. Example: Symbols Name Example d Distance 30 m v Speed 50 m/s t Time 15 s

29. VECTOR Vector is a quantity with magnitude, direction, and usually a unit of measure. Symbol Name Example d Displacement 30 m North v Velocity 30 m/s west F Force 100 lbs up a acceleration 12 m/s2 down

30. VECTOR We draw a vector from the initial point or origin (called the “tail” of a vector) to the end or terminal point (called the “head” of a vector), marked by an arrowhead. Magnitude is the length of a vector and is always a positive scalar quantity.

31. Adding Vectors Using Pythagorean Theorem Example 1: Daffy walks 35 m East, rests for 20 s and then walks 25 m East. What is Blog’s overall displacement? Solve graphically by drawing a scale diagram.

32. Adding Vectors Using Pythagorean Theorem Place vectors head to tail and measure the resultant vector. Solve algebraically by adding the two magnitudes. We can only do this because the vectors are in the same direction. R= 35 m East + 25 m East = 60 m East

33. Adding Vectors Using Pythagorean Theorem Example 2: Aika walks 35 m [E], rests for 20 s and then walks 25 m [W]. What is Aika’s overall displacement?

34. Adding Vectors Using Pythagorean Theorem Using algebraic solution, we can still add the two magnitudes. We can only do this because the vectors are parallel. We must make one vector negative to indicate opposite direction. R = 35 m East + 25 m West = 35 m East + – 25 m East = 10 m East (Note that 25 m West is the same as – 25 m East)

35. Adding Vectors Using Pythagorean Theorem Example 3: Kai leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Kai's resulting displacement.

36. Adding Vectors Using Pythagorean Theorem Example 3: Kai leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Kai's resulting displacement.

37. Adding Vectors Using Component Method When vectors to be added are not perpendicular, the method of addition by components described below can be used. To add two or more vectors A, B, C, … by the component method, follow this procedure:

38. Adding Vectors Using Component Method When vectors to be added are not perpendicular, the method of addition by components described below can be used. To add two or more vectors A, B, C, … by the component method, follow this procedure:

39. Adding Vectors Using Component Method Sample Problem: An ant crawls on a tabletop. It moves 2 cm East, turns 3 cm 40 o North of East and finally moves 2.5 cm North. What is the ant’s total displacement?

40. Adding Vectors Using Component Method

41. Adding Vectors Using Component Method

42. Adding Vectors Using Component Method

43. Adding Vectors Using Component Method

44. Adding Vectors Using Component Method

45. Adding Vectors Using Component Method

46. Adding Vectors Using Component Method