Transcript Slide 1
Sinai University Faculty of Engineering Science Department of Basic Science W 1-Ch1 1 Chapter 1 Physics and measurements 1.1 Standards of Length, Mass and Time. 1.3 Dimensional analysis 1.4 Conversion of units 1.6 Significant figures W 1-Ch1 2 1.1 Standards of Length, Mass, and Time The laws of physics are expressed as mathematical relationships among physical quantities. Ex: v=v0 +at Most of these quantities are derived quantities, in that they can be expressed as combinations of a small number of basic quantities. Ex: speed, v= (distance/time) (m/s) In mechanics, the three basic quantities are length, mass, and time. W 1-Ch1 3 SI (Système International), In 1960, an international committee established a set of standards for the fundamental quantities of science. It is called the SI (Systèm International), o o o o o o o length Mass Time Temperature electric current luminous intensity the amount of substance W 1-Ch1 meter kilogram second the kelvin the ampere the candela the mole 4 Standard of Length The legal standard of length in France became the meter 1-As recently as 1960, the length of the meter was defined as the distance between two lines on a specific platinum–iridium bar stored under controlled conditions in France. 2-In the 1960s and 1970s, the meter was defined as 1 650 763.73 wavelengths of orange-red light emitted from a krypton-86 lamp. 3-However, in October 1983, the meter (m) was redefined as the distance traveled by light in vacuum during a time of 1/299 792 458 second. W 1-Ch1 5 Attention, please No Commas in Numbers with Many Digits Examples: 1- 10 000 is the same as the common American notation of 10,000. 2- p= 3.14159265 is written as 3.141 592 65. W 1-Ch1 6 Standard of Mass Amount of matter in an object The SI unit of mass, the kilogram (kg), is defined as the mass of a Specific platinum–iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France A second mass standard Atomic mass unit, amu= 1/12 mass of C-12 1 amu= 1.660 542 02 kg W 1-Ch1 7 Other units of mass British system Pound –mass= 0.453 6 kg What is the difference between mass and weight? Mass does not depend on height. Weight depends on the gravitational pulling force, i.e. acceleration on any position. W 1-Ch1 8 Attention, please Reasonable Values Careful thinking about typical values of quantities is important because when solving problems you must think about your end result and determine if it seems reasonable. If you are calculating the mass of a housefly and arrive at a value of 100 kg, this is unreasonable —there is an error somewhere. W 1-Ch1 9 The standard unit of time The second was defined as Standard day= 24 hours = 86 400 s The rotation of the Earth is now known to vary slightly with time, however, and therefore this motion is not a good one to use for defining a time standard. The second (s) is now defined as 9 192 631 770 times the period of vibration of radiation from the cesium atom, Cs-133. W 1-Ch1 10 Different Units W 1-Ch1 11 Derived Units length(m) X width(m)= Area (m2) Distance traversed(m)/unit time(s) =Speed (m/s) Speed(m/s)/unit time(s) = Acceleration (m/s2) Acceleration(m/s2)X mass(kg) =Force (N) W 1-Ch1 12 Assignment Read carefully the examples of derived units in pages 9 W 1-Ch1 13 1.3 Dimensional Analysis The word dimension has a special meaning in physics. It denotes the physical nature of a quantity. Whether a distance is measured in units of feet or meters, it is still a distance. We say its dimension is length The dimensions of length, mass, and time are L, M, and T, [ ] to denote the dimensions of a physical quantity. Velocity [v] = L/T. W 1-Ch1 Area [A] = L2. 14 Dimensional Analysis Dimensional analysis can be used to 1- Derive an equation. 2- Check a specific equation. W 1-Ch1 15 Dimensional Analysis Dimensional analysis makes use of the fact that dimensions can be treated as 1- algebraic quantities. quantities can be added or subtracted only if they have the same dimensions. Example: L-L=0 T-L T3-T2 M+M=2M M*M=M2 2- the terms on both sides of an equation must have the same dimensions. LTM=LMT T2L=LT2 T3=T3 M.M=M2 The relationship can be correct only if the dimension on both sides of the equation are the same. W 1-Ch1 16 Example In General Left hand side Wright hand side n=1, m-2n=0 , W 1-Ch1 m-2=0 m=2 17 W 1-Ch1 18 1.4 Conversion of Units 1m 100 cm 1= , 1= 100 cm 1m 0.025 4m 1in 1= , 1= 1in 0.025 4 m 1in 1= , 2.54 cm 2.54 cm 1= 1in Example W 1-Ch1 19 W 1-Ch1 20 1.6 Significant Figures When certain quantities are measured, the measured values are known only to within the limits of the experimental uncertainty. The value of this uncertainty can depend on various factors, 1- the quality of the apparatus, 2-the skill of the experimenter, 3- the number of measurements performed. The number of significant figures in a measurement can be used to express something about the uncertainty W 1-Ch1 21 Example T= 21.5, 21,22,22.5 Tav= 21.75 + 0.559 016 9 Tav= 21.8 + 0.6 W 1-Ch1 22 1.6 Significant Figures Accuracy= 0.1 cm (5.5 0.1) cm, 6.4 0.1 cm 6.4 cm Area = (5.5 0.1) X 6.4 0.1 = 35.22 cm (5.4 cm)(6.3 cm) =34 cm2 2 5.5 cm (5.6 cm)(6.5 cm) = 36 cm2. 35 cm2 Zeros may or may not be significant figures. Those used to position the decimal point in such numbers as 0.03 and 0.007 5 are not significant. W 1-Ch1 23 1.6 Significant Figures When the zeros come after other digits, however, there is the possibility of misinterpretation. For example, suppose the mass of an object is given as 1 500 g. This value is ambiguous because we do not know whether the last two zeros are being used to locate the decimal point or whether they represent significant figures in the measurement. 1.5x103g 2 significant figure 1.50x103g 3 significant figure 1.500x103g 4 significant figure 2.3x10-4 2 significant figure 0.000 23 2 significant figure In general, a significant figure in a measurement is a reliably known digit (other than a zero used to locate the decimal point) or the first 24 W 1-Ch1 estimated digit For addition and subtraction, For example, 123 + 5.35, the answer is 128 and not 128.35. NOT 128.0 If we compute the sum 1.000 1 + 0.000 3 = 1.000 4, the result has five significant figures, even though one of the terms in the sum, 0.000 3, has only one significant figure. Likewise, if we perform the subtraction 1.002- 0.998 = 0.004, the result has only one significant figure even though one term has four significant figures and the other has three. 25 W 1-Ch1 rounding off numbers, 2.36 2.4 2.35 2.4 2.65 2.6 2.33 2.55 2.3 2.6 A technique for avoiding error accumulation is to delay rounding of numbers in a long calculation until you have the final result. Wait until you are ready to copy the final answer from your calculator before rounding to the correct number of significant figures. W 1-Ch1 26 W 1-Ch1 27 Assignment 1 Solve the following problems 2,4,7,9,15,18,31,3,5,6,10,1 2,16,20,22,26,30 W 1-Ch1 28