Presentation on theme: "Physics Tools and Standards"— Presentation transcript:
1Physics Tools and Standards Each discipline has a language.The language of physics is math!What are the mathematical tools you need to succeed?
2Measurements We need a way to standardize measurements Compare to a known quantityMust be constant, repeatable, and agreed upon by all users
3Measurements Constant, repeatable, agreed upon Divide into groups of 3 What is the size of the lab tables?What is the time it takes for a pencil to fall from the 2nd story to the ground?
4Measurements Was your data reproducible? How could you test this? How did you agree upon the standard?Did you use estimates if your measurement was not an exact number of your standard? How did you estimate?How accurate were you? How could you be more accurate?
5Metric System and SI Units Standard measurements based on powers of 10SI units standardized and accepted by scientists worldwideAll your answers will include the SI unit!
6Derived units are combinations of the base units. Ex: speed is measured in meters per second or m/s
9How To: Converting Units Remember factor-label method?Multiply your quantity in one unit by a conversion factor that =1 to convert to another unitREMEMBER- units are your friend! Keep them involved and you will succeed.
10How to: Converting Units Ex: convert 10 m to cm1. Draw a big T2. Put your starting number in the top left and its same unit in the bottom right
11How to: Converting Units 3. Write the unit that you want in the top right4. Add numbers to your conversion factor to make it =1. (how many cm in a m or vice versa)
12How to: Converting Units 5. Multiply through and cross out units that cancel out.*** You can do these conversions in multiple steps***
13Practice Problems How many megahertz is 750kilohertz? Convert 5021cm to km.How many seconds are in a leap year?Convert the speed 5.30m/s to km/h.
14UNITS ARE YOUR FRIEND!!!Treat units as algebraic quantities in your calculations and keep them superglued to their numbers!When you do this and the units of your answer are correct, then your answer should be as well.
16Scientific NotationReally big or really small numbers can be a bummer to write and work withYou can get either really big numbers by using positive powers like 1 x 105 =You can also show really small numbers by using negative powers like 1 x 10-5 =Don’t worry about using your calculator to figure out what these mean- just move the decimal point left (negative exponent) or right (positive exponent) the number of spaces given by the exponent
17The Power of PowersPowers of 10 used in scientific notation mean big differences in the value of a numberFor example:106 sec is about 12 days109 sec is about 32 years1012 sec is about years!
18How to Read Scientific Notation Now try 2 x 10-9
19How to Write Scientific Notation Move decimal so only 1 nonzero # is to the left of the decimalCount how many spaces you moved the decimal- if you moved right the exponent is negative and if you moved left it is positiveGet rid of any nonsignificant digits (more on this later)Write the number multiplied by 10 to the power of however many spaces you moved in step 2
20Practice ProblemsWrite 4 numbers that are not in scientific notation. Pass them to your neighbor and have him put them into proper scientific notation.Do the opposite- write 4 umbers in scientific notation and have your neighbor write them out in full decimal form.
21Scientific Notation and Calculators On your calculator, scientific notation is often shown using the letter “E”So 9.2 x 10-4 would be written 9.2 E -4To enter a number look for the EE or Exp key
22Try it on your calculator To check yourself, multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x 109.
23Accuracy and Precision No measurement is perfectly exact!
24Precision Degree of exactness Written as +n ex: 40.1+1mm Increase precision by finer divisions of the scaleThis meter stick has divisions down to the mm so you can be precise to 0.5mm
25Percentage Uncertainty Ratio of uncertainty to measured valueSo if your answer is cm…..Percentage uncertainty= 0.1cm/8.88cmx100%
26Accuracy Are your measurements correct? Calibration checks measuring tools against a standard
27Significant Digits Valid digits in a measurement Depends on the scale usedUsing top ruler, we are certain of 2.5 and are guessing 2.55 so 2 sig digsUsing the bottom ruler we are certain of 2 and are guessing 2.5 so 1 sig dig
28Sig Digs What if your measurement falls exactly on the line of 2.5mm? Record it as 2.50mm because you are certain to within 0.01mm
29Sig Digs: the rules Nonzero digits always sig Final zeros after a decimal pt always sigZeros btwn other sigs are always sigFinal zeros that are not after a decimal pt are unknown-3400 could have 2,3,or 4 sig digsWrite it in scientific notation to clarify
30Working with Sig DigsRESULTS NEVER HAVE MORE SIG DIGS THAN YOU STARTED WITHDo the math first:Add/subtract: perform operation and then round to lowest decimal sig digs that you started withMultiply/divide: perform operation and then round to lowest sig digs that you started with
31The bottom line on sig digs: Don’t write out everything your calculator displays!!! Your answer should only include the sig digs.
32Review You have 2 measurements: A=1.24m and B=0.23cm Which has more sig digs?Which is more precise?
33ReviewYou put your backpack on a scale and find that it weighs 14.2kg. What is the range of weights implied by this measurement? How would you write that?kg (1/2 of the smallest division of measurement)
34Graphs Remember the basics of experiments? Independent variable is manipulatedDependent variables change as a resultGraph independent vs dependent
35Linear relationships y=mx+b Slope=m= y/ x Remember + slope is up to the right,-slope is down to the right
36Nonlinear relationships Quadratic- when one variable depends on the square of another- y=ax2+bx+cInverse- when y variable depends on 1/x
37Practice: graphsPractice problems p. 18 #24- see handout