Sinai University Faculty of Engineering Science Department of Basic Science 11/23/2015 1

Chapter 1 Physics and measurements 1.1 Standards of Length, Mass and Time. 1.2 Dimensional analysis 1.3 Conversion of units 1.4 Significant figures 11/23/2015 2

3 1.1 Standards of Length, Mass, and Time In mechanics, the three basic quantities are length, mass, and time. The laws of physics are expressed as mathematical relationships among physical quantities. Ex: v=v 0 +at Most of these quantities are derived quantities, in that they can be expressed as combinations of a small number of basic quantities. E x: speed, v= (distance/time) (m/s)

11/23/ 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 length meter o o Mass kilogram o o Time second o o Temperature the kelvin o o electric current the ampere o o luminous intensity the candela o o the amount of substance the mole

11/23/ 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. 3-However, in October 1983, the meter (m) was redefined as the distance traveled by light in vacuum during a time of 1/ second. 2-In the 1960s and 1970s, the meter was defined as wavelengths of orange-red light emitted from a krypton-86 lamp.

11/23/ Attention, please No Commas in Numbers with Many Digits Examples: is the same as the common American notation of 10, p= is written as

11/23/ Standard of Mass 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 S e vres, France Amount of matter in an object A second mass standard Atomic mass unit, amu= 1/12 mass of C-12 1 amu= kg

Other units of mass British system Pound –mass= kg 11/23/ 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.

11/23/ 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.

11/23/ The standard unit of time The second was defined as Standard day= 24 hours = 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 times the period of vibration of radiation from the cesium atom, Cs-133.

11/23/ Different Units

Derived Units length(m) X width(m)= Area (m 2 ) Distance traversed(m)/unit time(s) =Speed (m/s) Speed(m/s)/unit time(s) = Acceleration (m/s 2 ) Acceleration(m/s 2 )X mass(kg) =Force (N) 11/23/

11/23/ 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. Area [A] = L 2.

11/23/ Dimensional Analysis Dimensional analysis can be used to 1- Derive an equation. 2- Check a specific equation.

11/23/ 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 T 3 -T 2 M+M=2M M*M=M 2 2- the terms on both sides of an equation must have the same dimensions. LTM=LMT T 2 L=LT 2 T 3 =T 3 M.M=M 2 The relationship can be correct only if the dimensions on both sides of the equation are the same.

11/23/ Example In General n=1, m-2n=0, m-2=0 m=2 Left hand side Wright hand side

11/23/ Conversion of Units Example

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11/23/ Significant Figures When certain quantities are measured, the measured values are known only to within the limits of the experimental uncertainty. 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

11/23/ Example T= 21.5, 21,22,22.5 T av = T av =

11/23/ Significant Figures 5.5 cm 6.4 cm Accuracy= 0.1 cm 35 cm 2 (5.6 cm)(6.5 cm) = 36 cm 2. ( 5.4 cm)(6.3 cm) =34 cm 2 Zeros may or may not be significant figures. Those used to position the decimal point in such numbers as 0.03 and are not significant.

11/23/ 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 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. 2.3x significant figure 1.5x10 3 g 2 significant figure 1.50x10 3 g 3 significant figure 1.500x10 3 g 4 significant figure 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 estimated digit

11/23/ For addition and subtraction, For example, , the answer is 128 and not NOT If we compute the sum = , the result has five significant figures, even though one of the terms in the sum, , has only one significant figure. Likewise, if we perform the subtraction = 0.004, the result has only one significant figure even though one term has four significant figures and the other has three.

11/23/ rounding off numbers, 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

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