Physics Tools and Standards Each discipline has a language. The language of physics is math! What are the mathematical tools you need to succeed?

Measurements We need a way to standardize measurements Compare to a known quantity Must be constant, repeatable, and agreed upon by all users

Measurements 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?

Measurements 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?

Metric System and SI Units Standard measurements based on powers of 10 SI units standardized and accepted by scientists worldwide All your answers will include the SI unit!

Derived units are combinations of the base units. Ex: speed is measured in meters per second or m/s

SI Prefixes

How To: Converting Units Remember factor-label method? Multiply your quantity in one unit by a conversion factor that =1 to convert to another unit REMEMBER- units are your friend! Keep them involved and you will succeed.

How to: Converting Units Ex: convert 10 m to cm 1. Draw a big T 2. Put your starting number in the top left and its same unit in the bottom right

How to: Converting Units 3. Write the unit that you want in the top right 4. Add numbers to your conversion factor to make it =1. (how many cm in a m or vice versa)

How to: Converting Units 5. Multiply through and cross out units that cancel out. *** You can do these conversions in multiple steps***

Practice Problems p. 7 #5-8

UNITS 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.

Scientific Notation Really big or really small numbers can be a bummer to write and work with You can get either really big numbers by using positive powers like 1 x 105 = 100 000 You can also show really small numbers by using negative powers like 1 x 10-5 = 0.00001 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

The Power of Powers Powers of 10 used in scientific notation mean big differences in the value of a number For example: 106 sec is about 12 days 109 sec is about 32 years 1012 sec is about 32000 years!

How to Read Scientific Notation Now try 2 x 10-9

How to Write Scientific Notation Move decimal so only 1 nonzero # is to the left of the decimal Count how many spaces you moved the decimal- if you moved right the exponent is negative and if you moved left it is positive Get 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

Practice Problems 1. Write the following numbers in scientific notation. 1.156 21.8 0.0068 27.635 0.219 444 2. Write out the following numbers in full with the correct number of zeroes. 8.69x104 9.1x103 8.8x10-1

Scientific 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 -4 To enter a number look for the EE or Exp key

Try 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.

Accuracy and Precision No measurement is perfectly exact!

Precision Degree of exactness Written as +n ex: 40.1+1mm Increase precision by finer divisions of the scale This meter stick has divisions down to the mm so you can be precise to 0.5mm

Accuracy Are your measurements correct? Calibration checks measuring tools against a standard

Significant Digits Valid digits in a measurement Depends on the scale used Using top ruler, we are certain of 2.5 and are guessing 2.55 so 2 sig digs Using the bottom ruler we are certain of 2 and are guessing 2.5 so 1 sig dig

Sig 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

Sig Digs: the rules Nonzero digits always sig Final zeros after a decimal pt always sig Zeros btwn other sigs are always sig Final zeros that are not after a decimal pt are unknown- 3400 could have 2,3,or 4 sig digs Write it in scientific notation to clarify

Working with Sig Digs RESULTS NEVER HAVE MORE SIG DIGS THAN YOU STARTED WITH Do the math first: Add/subtract: perform operation and then round to lowest decimal sig figs that you started with Multiply/divide: perform operation and then round to lowest total sig figs that you started with Write 4 numbers on a piece of paper and trade it with your neighbor- decide how many sig digs

The bottom line on sig digs: Don’t write out everything your calculator displays!!! Your answer should only include the sig digs.

Review You have 2 measurements: A=1.24m and B=0.23cm Which has more sig digs? Which is more precise?

Review You 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? 14.2+.05kg (1/2 of the smallest division of measurement)

Graphs Remember the basics of experiments? Independent variable is manipulated Dependent variables change as a result Graph independent vs dependent

Linear relationships y=mx+b Slope=m= y/ x Remember + slope is up to the right, -slope is down to the right

Nonlinear relationships Quadratic- when one variable depends on the square of another- y=ax2+bx+c Inverse- when y variable depends on 1/x

Practice: graphs Practice problems p. 18 # 24