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General Physics (PHYS101) Golibjon Berdiyorov 1 Syllabus and teaching strategy Lecturer: Golibjon Berdiyorov, Room 148 Physics Building Phone: 860-3869/2283 e-mail: [email protected] www.cmt.ua.ac.be/golib/PHYS101 Office Hours: Sunday-Thursday: 8.00-10.00 Lectures: Sunday: 3.20pm-4.10pm (6/125) 25-27 Tuesday: 3.20pm-4.10pm (6/125) 25-27 Thursday: 3.20pm-4.10pm (6/125) 25-27 Recitation: Monday: 1.10pm-2.00pm (6/209) 25 3.20pm-4.10pm (6/165) 26 4.20pm-5.10pm (6/201) 27 2 Assessment: Grading DN grade: • 3 or more unexcused absences in the LAB • 12 unexcused absences in lecture+recitation 3 Format for Active Learning Warm up for lectures: Read the text(use a highlighter, if you prefer) Understanding physics (lectures): Answer questions in class Bring lecture notes, textbook… Challenge yourself (homework): Homework Play with physics (lab): Discover with hands-on experience Practice, practice and practice!!! 4 Lecture 01 (Chap. 1, Sec. 1-3) Units, Changing units, Significant figures 5 Measurements • Physics is based on measurement of physical quantities 1 nanometre =1.0 × 10-9 m 1 light year =9.4×1015 m • Examples are: length, mass, time, electric current, magnetic field, temperature, pressure ... • All physical quantities have dimensions: dimensions are basic types of quantities that can be measured or computed. 6 Base dimensions • These quantities are the basic dimensions: Length [L] Mass [M] Time [T] • Other physical quantities are defined in terms of these base quantities: - [velocity] = [length]/[time] = [L]/[T] - [volume]=[length]3=[L]3 - [density]=[mass]/[volume]=[M]/[L]3 - [force] = [mass][length] /[time]2 = [M][L]/[T]2 7 Units for physical quantities • A unit is a standard amount of a dimensional quantity. • Units can be chosen for convenience: • Science [L]: 1 angstrom =1.0 × 10-10 metres 1 light year =9.4605284 × 1015 metres • US customary [L]: 1 ft = 0.3048 m 1 mile = 1.6 km 12 inches in a foot, three feet in a yard • A single unified system of units makes life easier! 8 International System of Units (metric system) Basic SI Units • Length • Time • Mass • • • • • Electrical current Temperature Luminous intensity Amount of substance meter seconds kilogram ampere Kelvin candela mole m s kg A K cd mol These are the only units necessary to describe any quantity. Si derived units Length Time Mass [L] [T] [M] m s kg • [Area] = m2 square meter • [Volume] = m3 cubic meter • [Density] = kg/m3 kilogram per cubic meter • [Speed] = m/s meter per second • [Acceleration] = m/s2 meter per second squared • [Force]: N (Newton) = kg m/s2 • [Frequency]: Hz (Hertz) = s-1 • [Pressure]: Pa (Pascal) = N/m2 • [Energy]: J (Joule) = N m • [Power]: W (Watt) = J/s 10 Conversion of Units • • One can measure the same quantity in different units. For instance distance can be measured in miles, kilometres, meters etc. Velocity can be measured in km/hour, m/s etc. If physical quantities are measured in different units, then they should be converted to the same units. 10 m/s = 36 km/h vman-ground= 5km/h + 10 m/s = 15?? -No vman-ground= 5 km/h + 36 km/h = 41 km/h 11 Conversion of Units: Chain-link method Example 1: Express 3 min in seconds? 1min = 60 s 1= 60s 1 min = 1 min 60s Conversion Factor? 60 s 3min = 3min x 1 = 3min x = 180 s 1 min Example 2: How many centimeters are there in 5.30 inches? 1 in = 2.54 cm 1= 2.54 cm 1 in 2.54 cm 5.30 in = 5.30 in x 1 = 5.30 in x = 13.5 cm 1 in 12 Conversion of Units Example 3: Express 200 km/h in miles/s? 1 km = 0.6 miles 1h = 60 min = 60 x 60 s = 3600 s 200 km/h= 200 x 0.6 miles/3600 s = 0.03 miles/s Example 4: Express 200 km/h in m/s? 1 km = 1000 m 1 h = 3600 s km/h --> m/s :3.6 m/s --> km/h x3.6 200 km/h= 200 x 1000 m/3600 s = 55.56 m/s Example 5: Express 16 m/s in km/h? 1 m = (1/1000) km 1 s = (1/3600) h 16 m/s= 16 x (1/1000) km/(1/3600) h = 16x3600/1000 km/h=57.6 km/h 13 Scientific notations Scientific notation Expanded form 1 x 100 1 1 x 101 10 1 x 102 100 1 x 103 1000 1 x 106 1 000 000 1 x 10-1 1/10 or 0.1 1 x 10-3 1 x 10-6 384000 km 0.0000013 m 384000 km=3.84 x 105 km 0.0000013 m=1.3 x 10-6 m we write them in 1/1000Can or 0.001 a compact form? 0. 000 001 101 = 1.01 x 102 4321 = 4.321 x 103 1.23 = 1.23 x 100 0.25 = 2.5 x 10-1 0.0007925 = 7.925 x 10-4 14 Prefixes and Notation The following prefixes indicate multiples of a unit. Multiplier Prefix Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 10-3 milli m 10-6 micro 10-9 nano n 10-12 pico p 10-15 femto f Rounding Speed of light: c=299 792 458 m/s c=2.99 792 458 x 108 m/s • Overestimation: digits 5 to 9 can be dropped from the decimal place during the rounding, however, one should be added to the digit in front of it. • Underestimation: the following digits can just be dropped from the decimal place: 0, 1, 2, 3, an 4. Example 1. Round c to a nearest 1000th. c=2.998 x 108 m/s. Example 2. Round c to a nearest 10th. c=3.0 x 108 m/s. Example 3. Round 273.587 to a nearest integer. 274 Example 4. Round 273.587 to 2 significant figures. 270 16 Order of magnitude • An order of magnitude calculation is a rough estimate that is accurate to within a factor of about 10. • It is useful if you want to get a quick rough answer. • The order of magnitude of a quantity is the power of ten when quantity is expressed in scientific notation A=7 600 = 7.6 x 103 The order of magnitude of A is 3 B=3 700 = 3.7 x 103 The order of magnitude of B is 3 A=7 600 ~ 10 000 = 104 B=3 700 ~ 1 000 = 103 The nearest order of magnitude of A is 4 The nearest order of magnitude of B is 3 17 Uncertainties in measurements • All measurements are subject to an uncertainty • These uncertainties can be due to e.g. limitations in the measuring tools or fluctuations in the measured quantities. • The accuracy of the measurements are determined by significant figures. 18 Rules for Significant Figures 1. All nonzero figures are significant 359 87678 1245 987889 2. All zeros between nonzeros are significant 205 1003 508009 800009002 3. Zeros at the end are significant if there is a decimal point before them 4.200 1003.5600 30.003000 4. All other zeros are non-significant 30000 0.0000344 19 Rules for Significant Figures Not significant Not significant Significant zero at the beginning zero used only to locate the decimal point all zeros between nonzero numbers 0.004004500 Significant Significant all nonzeros zeros at the end of integers a number to the right of the decimal point Just take care of zeros 20 Operations with Significant Figures • When adding or subtracting, round the results to the smallest number of decimal places of any term in the sum 21 Operations with Significant Figures • When multiplying or dividing, round the result to the same accuracy as the least accurate measurements (i.e. the smallest number of the significant figures) Example: Calculate the surface area of a plate with dimensions 4.5 cm by 7.32 cm. A=4.5 cm x 7.32 cm=32.94 cm2. A=33 cm2. 22 Summary • Dimensions are basic types of quantities that can be measured or computed. • Base dimensions are length, time, and mass. • A unit is a standard amount of a dimensional quantity. Summary • Scientific notations • Order of magnitude: 10x (x=1,2,3 ..) • Rounding 24 Summary • Uncertainties in the measurements • Significant figures • It is important to control the number of digits or significant figures in the measurements. 25 Express speed of sound (330 m/s) in miles/h (1 mile = 1609 m) a) 738 miles/h b) 730 miles/h 1 shake = 10-8 sec. Find out how many nano seconds (ns) are there in 1 shake (1ns=10-9s). a) 1 ns b) 10 ns Express the following numbers in scientific notations: a) 0.015 b) 0.0000002 c) 54800 a) 1.5 x 10-2 b) 2 x 10-7 c) 5.48 x 104