Physics 1 – Aug 23, 2016  P3 Challenge – Do Now (on slips of paper) Complete these meter stick equivalences: 1 m = _____________ cm 1 m = _____________ mm 1 km = ____________ m If you are waiting on a textbook, I’ve found a work around: Google “IB physics 6 th edition pdf” and you can access a sample pdf file that has the first 93 pages. We will have new books ready on Thurs. Remember Label: Name, Date and Phys 3 (or P3)

Objectives  Safety  IB 1.1 Measurement in Physics --- Standard Operating Procedures  State the fundamental units of the SI system  Be able to express numbers in scientific notation  Appreciate the order of magnitude of various quantities  Perform simple order-of-magnitude calculations mentally  Express results of calculations to the correct number of significant figures.

Agenda  Safety Quiz and Contract  Agenda for IB 1.1 Measurement in physics – Standard operating procedures  About Numbers  Measuring  Significant figures  Scientific Notation  Calculations with sigfigs  Assignment: Safety Contract Signed by Student and Parent/Guardian.  IB 1.1 Measurement in Physics Practice Sheet, Pages 1-2  Standards  Metric units  Unit conversion  Dimension Analysis  Estimation

Exact and Inexact Numbers (Math vs Science)  Counting items gives an exact number (e.g. 12 apples = exactly 12 apples)  Definitions within a measurement system give exact numbers (e.g. exactly 12 inches = exactly 1 foot, by definition)  Measurements give inexact numbers (e.g. 5.7 m) with some amount of uncertainty.  In science, we don’t use fractions.  Conversion factors between systems of measurements give inexact numbers. (e.g. 1 lb = approximately kg…give or take a bit)

How to measure  Uncertainty depends on the measurement device used and on how it is used to measure.  Identify the smallest gradation marked on the measurement device.  Measure to this level of precision (certain measurement)  Add one more digit as an estimation of the true measurement’s location between the smallest gradation marks. (source of uncertainty)  Try to decide on one of the five statements below. If you can’t decide between two statements, use the odd digit between.  0 right on the line, 2 just above the line, 4 almost halfway, 6 a little more than halfway, 8 nearly to the next line.

Practice

Determining Significant Figures  Significant figures (digits) – the digits that are known with certainty plus one digit whose value has been estimated in a measured value.  How to determine the number of sig figs:  The digits of a measured number indicate the level of precision for the measurement.  All non-zero numbers are significant.  Leading zeros are never significant.  Confined zeros are always significant.  Trailing zeros are significant if and only if a decimal point is present. (Atlantic – Pacific rule) Ambiguous numbers like 300 mL can be made clear by using a decimal point, a line over the last significant digit, or using scientific notation.

Practice identifying sigfigs  40.7 L  m  250. cm  km  g  mm  kg  2000 cm

Scientific Notation  A clear way to report numbers that are either very large or very small, or numbers with an ambiguous number of significant figures  Two parts: Mantissa x 10 exponent  Mantissa, or decimal part, is a number with one non-zero digit to the left of the decimal point that contains all significant digits, and only significant digits  Exponent indicates the decimal place location for the digits.  Exponent = number of places the decimal point must move to be placed to the right of the first significant figure  Large numbers have positive exponents and small numbers have negative exponents.  2000 cm  2.00 x 10 3 cm makes the significance clear. Use Sci Not if you need clarity or you need to use more than 3 zeros.

Multiplication/Division with Significant Figures (also power and roots)  Perform the calculation indicated.  Round your answer to the same number of significant figures as the number with the least number of significant figures that was used in the calculation.  DO NOT report all digits shown in your calculator  Round down for 4 or below.  Round up for 5 and above.  Ex: 1.92 m x m = m 2  (If a large set of data ends in 5’s, rounding up on all fives can introduce an error. In these cases, apply the odd-even rule for the digit just before the 5, Even rounds down, Odd up.)

Addition/Subtraction with Significant Figures  Perform the calculation indicated.  Round your answer to the same number of decimal places as the number with the least precise decimal place that was used in the calculation.  Decimal places (place value) – the number of digits after the decimal point  DO NOT report all digits shown in your calculator  The number of significant figures may increase or decrease.  Hint: Remove any scientific notation, then add/subtract numbers vertically. The place with a significant digit for all numbers is the place to round your answer.  Ex: 0.92 m m = m

Multistep problems with mixed functions  In general, keep extra digits for intermediate results, while at the same time noting which place is significant by underlining that digit.  Ex: ( )  Ex: ( )  Ex: x  Ex: x  Often it is easiest to just not clear your calculator for intermediate results.  Rule of thumb: Follow significance throughout, but don’t round until the end.

Unit Conversions (Factor-Label method)  “Times sign, draw the line, copy the unit.”  Variations on the theme  Multistep conversions  Metric conversions using prefixes  Metric to English conversions  Squared unit conversions  Ratio unit conversions 1 m = 100 cm1 mL = 1 cm 3 = 1 cc 1 m = 1000 mm1 g of water = 1 mL 1000 m = 1 km  applies to L and g also

Multistep conversions  “Times sign, draw the line, copy the unit.”  If you do not know of the equivalence between the measured unit, and the target unit, consider a third unit that has an equivalence with both.  Ex: convert 4.75 miles to inches mile footinch 4.75 miles miles1 = inches foot1 feet inches = inches = 3.01 x 10 5 inches

Metric to English conversions  You need to know at least one conversion between English and metric for each type of quantity. These are the ones I recommend you memorize.  Length: 1 inch = 2.54 cm  Mass: 1.0 pound = 454 g  Volume: 1 quart = L  Ex: What mass in kg corresponds to a 2.7 ton cargo crate? (use scientific notation for your answer)

Squared unit conversions  If a unit is raised to a power, often 2 or 3, to perform a conversion, you must raise the entire conversion factor to that power.  Convert 22 cm 2 to in 2 22 cm 2 cm in = 3.4 in 2 2 Ex: 450 mL to dm 3

Ratio unit conversions  Many derived units involve ratios of units. Mi/h, km/hr, m/s 2 …  If a unit on the bottom needs to be converted, “copy the unit” to the top.  Ex: Convert 25 m/s to km/h meter km min m1000 = 90. km/hr min1 km s 60 1 s hr s1 25 m hr1 min 60

Standards  Why need standards?  Consider a world without standards  Good standards  A) Unchanging over time and B) Accessible everywhere  Poor standards  Ex: “yard comes from the Saxon word "gird" meaning the circumference of a person’s waist” (National Institute Of Standards And Technology)  IUPAC (International Union of Pure and Applied Chemistry)  The world authority on chemical nomenclature, terminology, standardized methods for measurement, atomic weights and other critically evaluated data.

English System  Complex relationships between units  Historical standards are anecdotal  Current standards are defined in terms of SI units  Ex: 1 foot = exactly m  “Treaty of the Meter” 1875  Metric Conversion Act of 1975  “Preferred official system” 1988  2016, we’re still teaching English units

English equivalences to know  1 mile = 5280 feet  1 yard = 3 feet  1 foot = 12 inches  1 pound = 16 ounces  1 dozen = 12  1 gallon = 4 quarts

SI (or metric) System  Standard for time  1 second is defined as the duration of 9, 192, 631, 770 periods of the radiation (light) emitted from a certain transition in a cesium-133 atom. (Atomic clock)  Though Cs-133 is not available everywhere, and it is not simple to make this observation, every cs- 133 atom would behave the same way.

SI (or metric) System  Standard for length  1 meter is defined as the distance that light travels in vacuum in 1/299,792,458 s.  Speed of light in a vacuum is a constant.  Available everywhere.  Depends on the standard of time.

SI (or metric) System  Standard for mass  1 kilogram is defined as the mass of a singular cylinder of a platinum alloy that is housed in Sèvres, France, called the IPK (international prototype kilogram)  K 20 (US official prototype) is a third generation copy – each copy of a copy level creates additional error, though very small  Pt chosen because it does not decay over time, so it is a relatively stable standard.  ByI4s-D-Y World’s Roundest Object ByI4s-D-Y IPK K20

SI (metric) System  BASE UNITS (all defined relative to the 3 standards above)  meter for length  kilogram for mass (note: not the gram)  second for time  ampere for electric current  kelvin for temperature  candela for luminous intensity  mole for the amount of substance  DERIVED UNITS  Units for all other quantities besides the base  For each new quantity we will discuss, we will learn about:  Name of the quantity (Ex: Force)  Symbol used to represent the quantity (Ex: F)  Name of unit used to measure the quantity (Ex: Newton)  Symbol for the unit (Ex: N)  The unit expressed in base units (Ex: 1 N = 1 kg m s -2 )

Metric Conversions  PREFIXES  Allows units to be a convenient size for observations  Defined in terms of powers of 10  Common Prefixes to memorize  Ways to Convert:  Prefix unit to base unit –  Replace prefix symbol with power of 10  Ex: 540 nm = 540 x m  Move the decimal place  Often used with 3 orders of magnitude changes.  Ex: 45.6 mL = L  Factor Label methods using:  # in meter stick: 1 m = 10 3 mm  Definition: 1 mm = m PrefixAbbreviationPower of 10 Nano-n10 -9 Micro-  Milli-m10 -3 Centi-c10 -2 Kilo-k10 3

Metric Conversions using prefixes  “Times sign, draw the line, copy the unit.”  The metric prefixes help you write conversion factors with the power of powers of 10!  Conversions to and from meters:  To create equivalences, replace the prefix of a metric unit name with the corresponding power of 10.  Ex: 1 km =10 3 m; 1 pm = mor 1 m = pm  Conversions between other metric units:  Convert to meters first and then to the target unit.  Ex: km to cm

Dimension Analysis  In physics, problems are often solved with the benefit of a formula that relates some number of quantities.  The units for any formula must be consistent.  Be able to verify the units for any formula by expressing all derived units in terms of base units.  Ex: Knowing that Energy (E) is measured in Joules (J = kg m 2 s -2 ), mass (m) is measured in kg, acceleration (a) is measured in m s -2, and distance (d) is measured in m, Verify that E = mad is a valid formula to use to describe the relationships between these variables.

Estimation  Another common skill for any physics problem is to estimate the order of magnitude for your answer so you can judge whether your calculated answer is reasonable or not.  To estimate, Round all quantities to (one sig fig with an order of magnitude)  Perform the needed calculation using your new simple numbers to find a one sigfig order of magnitude estimate of the answer.  Ex: The frequency of visible light is between 430 nm and 770 nm and the speed of light is 3.00 x 10 8 m/s. If the speed = frequency * wavelength, estimate the order of magnitude for the wavelength of visible light.

Today’s Assignment  What’s Due on Thurs Aug 25? (Pending assignments to complete.)  Safety Contract Signed by Student and Parent/Guardian.  IB 1.1 Measurement in Physics Practice Sheet, P1-2  What’s Next? (How to prepare for the next day)  Read IB 1.2 p 7-20