General Physics 1 - Measurement (Grade 12).pptx

For Grade 12 Gas and STEM

1. General Physics 1

2. fxtas.org/ chrisquarshie91.files.wordpress.com udel.edu burpee.com wallown.com The Measuring Process

3. Measurement Is the process of comparing something with a standard. To carry out measurements, a system of standards and a system of units should be defined.

4. Two system of units have evolved; The Metric system The English system The Metric System has two variations; The mks system the cgs system The English system is otherwise known as the; fps system

5. The fps system considers pound-force as a fundamental quantity. The counterpart of pound-force in the metric system is mass. The International System of Units, abbreviated SI from the French Le Système International d'Unitès , is the modern form of the metric system .

6. It is the system of units that the General Conference on Weighs and Measures has agreed upon and is legally enforced in almost all parts of the world.

7. Physical quantities may either be fundamental or derived. Fundamental quantities are basic quantities which are independent of one another. (Length, mass, time, thermodynamic temperature, electric current, luminous intensity, and amount of substance )

8. Derived quantities are combinations of fundamental quantities. Speed may be defined as distance traveled divided by time. (Acceleration, density, work, and energy )

9. The SI fundamental units are: meter, kilogram, second, kelvin, ampere, candela, and mole. The units for derived quantities are combination of these fundamentals units.

10. Nonstandard Units of Measurement Dimension Unit of Measurement Description Length Tinuro Length of a forefinger Dali Breadth of a finger Dangkal or dama Width of a palm Dipa Distance between the tip of the middle finger of two extended arms Length of a foot talampakan A single stride Hakbang Weight Dakot A handful Kaing A container Salop A conatiner Kaban A container

11. Nonstandard Units of Measurement Dimension Unit of Measurement Description Volume Gusi A jar Salok A scoop

12. Scientific Notation and Unit Conversion

13. Scientific notation is a convenient and widely used method of expressing large and small numbers. Any quantity may be expressed in the form of Nx , where N is any number between 1 and 10 and n is the appropriate power of 10.  

14. 1. The speed of light is approximately 300 000 000 m/s. 2. The mass of a strand of hair is approximately 0.000 000 62 kg. 3. Express a.) 0.000 646 and b.) 5 430 000 in Scientific notation

15. In expressing SI measurements in scientific notation, the SI prefixes are used to denote multiples and submultiples of the SI units.

16. SI Prefix Symbol Multiplier SI Prefix Symbol Multiplier yotta - Y yocto - y zeta- Z zepto - z exa - E alto- a peta - P femto - f tera - T pico - p giga - G nano - n mega- M micro- m kilo- k milli - µ hecto - h centi - c deca - da deci - d SI Prefix Symbol Multiplier SI Prefix Symbol Multiplier yotta - Y yocto - y zeta- Z zepto - z exa - E alto- a peta - P femto - f tera - T pico - p giga - G nano - n mega- M micro- m kilo- k milli - µ hecto - h centi - c deca - da deci - d

17. Quiz Convert 55 km to meters Convert 12 g to kilograms

18. Uncertainty and Error Analysis

19. Measurement always have some degree of uncertainty due to unavoidable errors. Error is the deviation of a measured value from the expected or true value. Uncertainty is a way of expressing the error.

20. Accuracy versus Precision Accuracy refers to the closeness of a measured value to the expected or true value of a physical quantity. On the other hand, precision represents how close or consistent the independent measurement of the same quantity are to one another.

21. Random versus Systematic Errors Random errors , as the name suggests, result from unpredictable or inevitable changes during data measurement. Examples of causes of random errors are electronic noise from an electrical device, slight variation of temperature when the volume of a gas is being measured,

22. and uncontrollable presence of wind when determining the period of a simple pendulum. Random errors affect the precision of measurements. These errors may be reduced by increasing the number of trials of a measurement and averaging out of the results .

23. Systematic Errors , on the other hand, usually come from the measuring instruments or in the design of the experiment itself. These errors limit the accuracy of one’s results.

24. Percent Error versus Percent Difference When there is an expected or true value of a quantity, percentage error is usually calculated.

25. Percent error= x100%  

26. Where - is the true or accepted value x - is the measured value Percent error is usually considered in judging the accuracy of a measurement.  

27. Percent difference is a measure of how far apart the different measured values are from each other, and is therefore an indication of precision.

28. Percent difference=  

29. Where and are two measured values in an experiment.  

30. Problem 1. Two trials were performed in an experiment to determine the latent heat of vaporization ( ) of water at 100 . The values of of water obtained were 532 cal /g and 536 cal /g. Find the percent difference between the two.  

31. Referring to Problem 1, find the percent error for each measurement if the accepted value of of water at 100 is 540 cal /g.  

32. Variance Another way to estimate errors from multiple measurements of a physical quantity is to determine the variance of the set of measurements. The variance measures the squared deviation of each number in the set from the mean.

33. The variance of a set measurement is calculated step-by-step as follows: Take the mean of the set of measurements, = Take the deviation of each measurement from the mean (x- ).  

34. 3. Square each deviation , ( x- ) 4. Get the sum of the squares of each deviation, ∑(x- ) 5. Divide the sum of the squares by the number of measurements in the set, In symbols, variance ( = )  

35. A variance of zero means that all measurements are identical. A small variance indicates that the values are close to one another, which means they are precise.

36. The square root of the variance is the standard deviation . It is a measure of how diverse or spread out are a set of measurements from their average. A small standard deviation means that most of the measurements are close to their average.

37. A large standard deviation means that the measurements are very diverse. The measurement x of a physical quantity in a set of measurements is usually reported as x= ± ó Where is the mean of the set of measurements and ó is the standard deviation of the measurement.  

38. During an experiment in a physics laboratory class, a group of five students was asked to measure the period of a simple pendulum. Their measurement were as follows: 2.3 s, 2.4 s, 2.2 s, 2.5 s, and 2.1 s. D etermine the a. mean, b. variance, c. standard deviation, and d. measured period of the pendulum.

39. In an experiment, 10 trials were done to determine the range of a projectile. The measurements for the range of the projectile in centimeters are as follows: 134.8 133.9 135.1 134.7 135.3 134.9 135.2 134.8 135.5 135.4

40. Absolute and Relative Uncertainties A measurement must be represented by two components: 1. a numerical or measured value with the proper unit that gives the best estimate of the quantity measured and,

41. 2. The degree of uncertainties in the measurement. Uncertainty indicates the range of values within which the measurement is asserted to lie with some level of confidence.

42. The degree of uncertainty may be reported as absolute or relative. Absolute uncertainty has the same unit as the quantity itself.

43. Relative uncertainty or percent uncertainty, on the other hand, is dimensionless and is obtained by dividing the absolute uncertainty by the numerical or measured value.

44. Least Count Absolute uncertainty is usually based on the least count of the measuring device. Least count is the smallest value that can be read from any measuring device.

45. Graphical Analysis Experiments in physics usually involve changing a variable and observing how another variable is affected by this change. The variable that is changed by an experiment is called independent variable.

46. The variable that is affected by the change of the independent variable is called dependent variable.