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UT Arlington PHYS 1443 - Lecture Notes

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Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu1PHYS 1443 – Section 001Lecture #2Wednesday, May 31, 2006Dr. Jaehoon Yu• Brief history of physics• Standards and units• Dimensional Analysis• Fundamentals• One Dimensional Motion: Average Velocity; Acceleration; Motion under constant acceleration; Free Fall• Motion in Two Dimensions: Vector Properties and Operations; Motion under constant acceleration; Projectile MotionWednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu2Announcements• Reading assignment #1: Read and follow through all sections in appendices A and B by Thursday, June 1• There will be a quiz on tomorrow, Thursday, June 1, on this reading assignment.Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu3Brief History of Physics•AD 18thcentury:– Newton’s Classical Mechanics: A theory of mechanics based on observations and measurements•AD 19thCentury:– Electricity, Magnetism, and Thermodynamics• Late AD 19thand early 20thcentury (Modern Physics Era)– Einstein’s theory of relativity: Generalized theory of space, time, and energy (mechanics)– Quantum Mechanics: Theory of atomic phenomena• Physics has come very far, very fast, and is still progressing, yet we’ve got a long way to go – What is matter made of?– How do matters get mass?– How and why do matters interact with each other?– How is universe created?Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu4Needs for Standards and Units• Three basic quantities for physical measurements– Length, Mass, and Time• Need a language that everyone can understand each other– Consistency is crucial for physical measurements– The same quantity measured by one must be comprehendible and reproducible by others– Practical matters contribute• A system of unit called SISI (System International) was established in 1960– Length in meters (m)– Mass in kilo-grams (kg)– Time in seconds (s)Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu5Definition of Base UnitsOne second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 (C133) atom.1 s (Time)It is equal to the mass of the international prototype of the kilogram, made of platinum-iridium in International Bureau of Weights and Measure in France. 1 kg (Mass) = 1000 gOne meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.1 m (Length) = 100 cmDefinitionsSI Units•There are prefixes that scales the units larger or smaller for convenience (see pg. 7)•Units for other quantities, such as Kelvins for temperature, for easiness of useWednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu6Prefixes, expressions and their meanings• deci (d): 10-1• centi (c): 10-2• milli (m): 10-3• micro (µ): 10-6• nano (n): 10-9•pico(p): 10-12• femto (f): 10-15• atto (a): 10-18• deca (da): 101• hecto (h): 102• kilo (k): 103• mega (M): 106•giga(G): 109•tera(T): 1012• peta (P): 1015•exa(E): 1018Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu7International Standard Institutes• International Bureau of Weights and Measure http://www.bipm.fr/– Base unit definitions: http://www.bipm.fr/enus/3_SI/base_units.html– Unit Conversions: http://www.bipm.fr/enus/3_SI/• US National Institute of Standards and Technology (NIST) http://www.nist.gov/Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu8How do we convert quantities from one unit to another?Unit 1 = Unit 2Conversion factor Xseconds36001 hrHere….MoreAnd manyminutes601 hrkm3.03x10-41 ftM0.3031 ftcm30.31 ftkm2.54x10-51 inchm0.02541 inchcm2.541 inchWednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu9Examples 1.3 and 1.4 for Unit Conversions• Ex 1.3: A silicon chip has an area of 1.25in2. Express this in cm2. 21.25 in =22cm 06.8cm 45.6 25.1 =×=⎟⎟⎠⎞⎜⎜⎝⎛×=222in 1cm 45.6in 25.1•Ex 1.4: Where the posted speed limit is 65 miles per hour (mi/h or mph), what is this speed (a) in meters per second (m/s) and (b) kilometers per hour (km/h)? 1 mi= 65 mi/h =65 mi/h =(a)(b)21.25 in×What do we need to know?22.54 cm1 in⎛⎞⎜⎟⎝⎠()5280 ft1609 m 1.609 km =12 in1 ft⎛⎞⎜⎟⎝⎠2.54 cm1 in⎛⎞⎜⎟⎝⎠1 m100cm⎛⎞=⎜⎟⎝⎠()65 mi29.1 m/s 1609 m1 mi⎛⎞⎜⎟⎝⎠1 1 h⎛⎞⎜⎟⎝⎠1 h3600 s⎛⎞=⎜⎟⎝⎠()65 mi104 km/h 1.609 km1 mi⎛⎞⎜⎟⎝⎠1 1 h⎛⎞=⎜⎟⎝⎠Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu10Estimates & Order-of-Magnitude Calculations • Estimate = Approximation– Useful for rough calculations to determine the necessity of higher precision– Usually done under certain assumptions– Might require modification of assumptions, if higher precision is necessary• Order of magnitude estimate: Estimates done to the precision of 10s or exponents of 10s;– Three orders of magnitude: 103=1,000– Round up for Order of magnitude estimate; 8x107~ 108– Similar terms: “Ball-park-figures”, “guesstimates”, etcWednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu11Example 1.8()222RdhR +≈+222dhRh−≈22222 RdhhRR +≈++Estimate the radius of the Earth using triangulation as shown in the picture when d=4.4km and h=1.5m.Rd=4.4kmR+hPythagorian theoremSolving for R()()224400 1.521.5 6500mmmkm−=×=Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu12Uncertainties• Physical measurements have limited precision, however good they are, due to:– Number of measurements – Quality of instruments (meter stick vs micro-meter)– Experience of the person doing measurements–Etc• In many cases, uncertainties are more important and difficult to estimate than the central (or mean) valuesStat.{{Syst.Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon Yu13Significant Figures• Significant figures denote the precision of the measured values– Significant figures: non-zero numbers or zeros that are not place-holders• 34 has two significant digits, 34.2 has 3, 0.001 has one because the 0’s before 1 are place holders, 34.100 has 5, because the 0’s after 1 indicates that the numbers in these digits are indeed 0’s.• When there are many 0’s, use scientific notation: – 31400000=3.14x107– 0.00012=1.2x10-4Wednesday, May 31, 2006PHYS 1443-001, Summer 2006Dr. Jaehoon


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