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Unit 1 Introduction
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Measurement
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To make a measurement, we must... know what we are trying to measure have some standard with which to compare must have some method of making this comparison
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SI Units French scientists adopted the metric system in 1795. Major Benefit: Units are related by __________________. There are seven base units. We will be concerned with only five for now.
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Fundamental SI Units for Physics length time _________________________ mass _________________________ Light (Candela)
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How might you define a second? Class discussion
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Time
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“The ____________ between two occurrences.” The SI unit of time is the second. Originally defined as 1/86 400th of the average length of a day. Redefined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine level of the fundamental state of the atom of Cesium-133 isotope.
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Length
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“The ______________ between two points.” The SI unit of length is the meter. Originally defined as 1/10 000 000 of the distance between the North Pole and the equator through Paris, France. Redefined as 1 650 763.73 times the wavelength of the orange-red Krypton 86 isotope at 1.013 bar and 15 oC. Currently defined as the distance light travels through a vacuum in 1/299 792 458th of a second.
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Temperature
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“A measure of the ______ of a substance.” Heat is a form of energy which is the result of molecular motion. Temperature scales: Kelvin (Absolute scale) (SI UNIT) Celsius Fahrenheit
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Mass
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“A measure of the __________in an object.” The SI unit of mass is the kilogram. Originally defined as the mass of 1 Liter of water at 3.98 oC. Now defined as the mass of a piece of metal kept at the International Bureau of Weights and Measures in Sevres, France.
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Which weighs more, a ton of feathers or a ton of lead?
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Mass vs. Weight “A measure of the amount of __________ in an object.” Does not change from place to place. SI unit is the kilogram. “A measure of the ______________ force between objects.” Changes from place to place. SI unit is the Newton.
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Quantity
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“The ____________ of substance one has.” In the scientific community, substances are referred to in moles (SI unit). One mole is 6.02 x 1023 particles (Avogadro's #). 12 g of Carbon-12
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The Mole A mole of _________ would spread over the surface of the earth, and produce a layer about 50 miles thick. A mole of _______, spread over the United States, would produce a layer 3 inches deep. A mole of dollars could not be spent at the rate of a billion dollars a day over a _________ years. This shows you just how big a mole is. This number is so large that it is usually only represented in scientific notation
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Scientific Notation A method of expressing _________________ as powers of ten. Mostly useful when expressing rather large or small numbers/quantities. Example: 2.03x102 = _______________ 0.0678 = _______________
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Advantages of Scientific Notation Easily able to express very large or small numbers. Number of molecules in 18 mL of water 602 000 000 000 000 000 000 000 The mass of an electron 0.000 000 000 000 000 000 000 000 000 000 911 kg
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Converting between decimals & scientific notation #Direction to move decimal # of places Positive or negative 100Left2+10 2 10Left1+10 1 1n/a0010 0.1Right1-10 -1.01Right2-10 -2
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Converting Between Scientific Notation & Decimals #Direction to move decimal # of places Smaller or greater than “1” 1.0x10 3 right3greater1000 1.0x10 2 right2greater100 1.0x10 0 n/a0 1 1.0x10 -2 left2smaller.01.01 1.0x10 -3 left3smaller.001
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To express a Decimal Number in S.N. (#.##X10#) Example: 605 = 605.0 We always move the decimal so that we have only ONE digit to the _______ of the decimal. 605.0 = 6.05 (we had to move the decimal two places) For every place holder the decimal moves, you +/- 1 from the exponent/power on the “10.” 6.05x10 2
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Multiplying two #’s expressed in scientific notation. Multiply the digits. ___________________________ If necessary, re-write in proper scientific notation. Check the number of significant digits.
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Dividing two #’s expressed in scientific notation. _________________________ Subtract the exponents. If necessary, re-write in proper scientific notation. Check the number of significant digits.
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Prefixes We use prefixes as a __________________ way of expressing large multiples of 10. For instance we use the prefix kilo- to represent 1000 or 10 3
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Prefix Table http://kaffee.netfirms.com/Science/images/SI.Prefixes.Chart.gif
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Prefix Responsibility http://kaffee.netfirms.com/Science/images/SI.Prefixes.Chart.gif
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Derived Units “Units which are the result of combinations of two or more fundamental units.”
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Derived Units What are some other units that are not base units, but units that we see on a regular basis? Examples: – Newton (N)kg * m/s 2 – Joules (J)N * m – Density ( ρ ) g/cm 3
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Measurement Reliability
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Accuracy and Precision ______________: “How closely a measurement is to the true correct value for the quantity.” _______________: “How closely a set of measurements are to each other.”
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Accurate or Precise?
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Significant Digits/Figures The reliable digits in a measurement based on the accuracy of the measuring instrument.
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Rule of Thumb Whenever making a measurement, you are permitted one “guessed” digit. The guessed digit is the last significant digit in a number.
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Significant Digit Demonstration Graduated Cylinder and Beaker
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Rules to determine the number of significant digits. Non-zero numbers are significant. 123 cm Zeros between two significant digits are significant. 103 cm Final zeros after a decimal point are significant. 10.70 in. Zeros used solely for spacing the decimal point are not significant. 186 000 miles/sec. 0.00000186 miles/sec
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During Addition and Subtraction Your answer should be rounded off to the decimal place value as the measurement with the guessed digit in the _____________ decimal place.
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Add the following values. 100.01 cm + 3.0 cm
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Add the following values. 241 cm + 64,300 cm
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During Multiplication and Division The final answer should have the same number of significant digits as the measurement having the smallest number of significant digits.
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Multiply the following values. 44 m x 2 m
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Rules for Rounding Numbers If the digit to the immediate right of the last significant figure is less than five, do not change the last significant figure. 2.532 _____________
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Rules for Rounding Numbers If the digit to the immediate right of the last significant figure is greater than ________, round up the last significant figure. 2.536 ______________
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Rules for Rounding Numbers If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure. 2.535 1 _______________
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Rules for Rounding Numbers If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up. 2.535 0 _______________ 2.525 0 _______________
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Percent Error – Two common versions
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Percent Error Example problem Determine the percent error for the density of Al found experimentally to be equal to 2.60 g/cm 3 if the actual density is 2.70 g/cm 3.
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Parallax The apparent shift in objects when viewed from different _____________. Can be used to discern the distance of the object(s) being observed.
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Dimensional Analysis
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“A problem solving method that focuses on the units that are used to describe matter.” Simply put, it is the analysis of the units in a problem to see if the math was done right.
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Dimensional Analysis Example Problem: A person is traveling 70.0 mph for 10.0 seconds. How far did they travel in feet?
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Conversion Factor “A ratio of equivalent values used to express the same quantity in different units; is always equal to 1 and changes the units of a quantity without changing its value.”
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Dimensional Analysis How many inches are in 2.7 feet?
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Question It is possible to use dimensional analysis to convert between units? Since 1 m = 1000 mm, how many mm are there in 3.45 m?
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Example How many cm 3 are in 3.2 m 3 ?
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Example In Canada, a car travels along Highway 401 at a speed of 100.0 km/h. What is the car’s speed in m/s?
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Scientific Process Review
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REVIEW… Data Representation Types of Graphs What constitutes a good graph? Independent vs. Dependent Variables
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Variables Independent (x-axis) – the variable(s) being manipulated by the scientist. Dependent (y-axis) – the variable(s) that are the observed result of the independent variables being manipulated by the scientist. Note: You will not always have a clear independent and dependent variable. Usually this happens when you are dealing with rates (units per given time). In this case time always goes on the x-axis.
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