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?

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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!

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Derived units are combinations of the base units.

Ex: speed is measured in meters per second or m/s

SI Prefixes

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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 UnitsEx: convert 10 m to cm

1. Draw a big T

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2. Put your starting number in the top left and its same unit in the bottom right

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How to: Converting Units3. Write the unit that you want in the top right

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4. Add numbers to your conversion factor to make it =1. (how many cm in a m or vice versa)

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How to: Converting Units5. Multiply through and cross out units that cancel out.

*** You can do these conversions in multiple steps***

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Practice Problems1. How many megahertz is 750kilohertz?

2. Convert 5021cm to km.

3. How many seconds are in a leap year?

4. Convert the speed 5.30m/s to km/h.

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.

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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

1. Move decimal so only 1 nonzero # is to the left of the decimal

2. Count how many spaces you moved the decimal- if you moved right the exponent is negative and if you moved left it is positive

3. Get rid of any nonsignificant digits (more on this later)

4. Write the number multiplied by 10 to the power of however many spaces you moved in step 2

Practice Problems

1. Write 4 numbers that are not in scientific notation. Pass them to your neighbor and have him put them into proper scientific notation.

2. Do the opposite- write 4 umbers in scientific notation and have your neighbor write them out in full decimal form.

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

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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

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Percentage Uncertainty

• Ratio of uncertainty to measured value

• So if your answer is 8.88+ 0.1cm…..

• Percentage uncertainty= 0.1cm/8.88cmx100%

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

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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 digs that you started with

– Multiply/divide: perform operation and then round to lowest sig digs that you started with

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

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Nonlinear relationships

• Quadratic- when one variable depends on the square of another- y=ax2+bx+c

• Inverse- when y variable depends on 1/x

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Practice: graphs

• Practice problems p. 18 #24- see handout