Physics 1 – Aug 25, 2016  P3 Challenge – Do Now (on slips of paper) What is the acceleration of gravity, 9.81 m/s 2 in ft/min 2 ? (Use the 1 in = 2.54 cm bridge to make it a five step conversion.) Textbooks are here!!! If you still need one, come sign one out. 1)Hand in Safety Contract on front bench. 2)Get out 1.1 Worksheet for p1- 2 Homework check.

Objectives  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.  IB 1.2 Uncertainties and errors  Distinguish between random and systematic uncertainties

Agenda  Safety Quiz and Contract  Agenda for IB 1.1 Measurement in physics – Standard operating procedures  Standards  Metric units  Unit conversion  Dimension Analysis  Estimation  Assignment: IB 1.1 Measurement in Physics Practice Sheet, Pages 3-4  IB 1.2 Uncertainties and errors  Types of error  Accuracy and Precision  Data Analysis (ave and std)

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  Three Ways to Convert:  1) Prefix unit to base unit –  Replace prefix symbol with power of 10  Ex: 540 nm = 540 x m  2) Move the decimal place  Often used with 3 orders of magnitude changes.  Ex: 45.6 mL = L  3) 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.

Typical Physics Problem Solving  Assess the physical situation, event or problem. (Read the problem.)  Identify what kinds of quantities are relevant. (List symbol for each variable and provide their measurement if possible.)  Draw a picture and/or diagram to model the problem. (Shows relationships between objects, labels distances. Perhaps a before/after pairing, or progress in time. Free body diagrams are often drawn next to a drawing.  Determine mathematical relationships between variables involved. ( Construct from theory or find relevant Equation.)  Solve problem (Do the algebra.)  Do any needed Unit Conversions (Bring meaning to the answer.)  Perform Error Analysis. (How well do you know the answer?)

Evaluating Results  Two Sources of error  Systematic errors  Random errors  Systematic (should be minimized with careful attention to lab techniques)  Instrumental (Ex: Every piece of measuring glassware has an uncertainty associated with it. Marked on the glassware.)  Procedural (Ex: During a chemical processing, every transfer from one vessel to another creates some additional error)  Tends to influence resulting data to be skewed in one direction

Evaluating Results  Random  Can never remove uncertainty because of the fundamentally random nature of the motion of atoms.  Influence of the observer (uncertainty principle)  Tends to increase uncertainty of a measurement in all directions.  Error vs a mistake

Data Analysis

Standard Deviation Not specifically tested on IB, but a “need to know” for the IA. Don’t use the calculator shortcut until you can do it yourself.

Find average and standard deviation m85.31 m83.91 m84.22 m85.18 m m85.21 m84.97 m84.14 m84.87 m 1)Find the average 2)Find the standard deviation by hand 3)Check your answer with the stat func 1-var calcs on a graphing calculator (larger sample std listed as Sx) 4)Express you best guess rounded to the proper number of sigfigs with its associated uncertainty. Possible data set for stopping distances measured by a computer sensor.

Accuracy and Precision  Accuracy – low % error – how close is the Average to the Expected  Precision – small range – how close are the data to each other

Exit Slip - Assignment  List the steps needed to perform a standard deviation calculation by hand.  What’s Due on Thurs Aug 25? (Pending assignments to complete.)  IB 1.1 Measurement in Physics Practice Sheet, P3-4  What’s Next? (How to prepare for the next day)  Read IB 1.2 p 16-20