1. Physics 1 – Aug 22, 2017 P3 Challenge – Do Now (on slips of paper)
Complete these meter stick equivalences:
1 m = _____________ cm
1 m = _____________ mm
1 km = ____________ m
Remember Label: Name, Date, Phys 1, and Period 6

2. 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.

3. Agenda
Safety 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

4. 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)

5. 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.

6. Practice

7. 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.

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

9. 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 10exponent
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 103 cm makes the significance clear.
Use Sci Not if you need clarity or you need to use more than 3 zeros.

10. 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 = m2
(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.)

11. 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

12. 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.

13. 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 cm
1 mL = 1 cm3 = 1 cc
1 m = 1000 mm
1 g of water = 1 mL
1000 m = 1 km
applies to L and g also

14. 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
foot
inch
5280
feet 12
inches
4.75 miles
= inches 1
miles 1
foot
= inches = 3.01 x 105 inches

15. 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)

16. 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 cm2 to in2 2 1 in
22 cm2
= 3.4 in2
2.54 cm
Ex: 450 mL to dm3

17. Ratio unit conversions
Many derived units involve ratios of units. Mi/h, km/hr, m/s2…
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 s
min hr 25 m 1 km 60 s 60
min
= km/hr 1 s
1000 m 1
min 1 hr

18. Standards Why need standards? Good standards Poor 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.

19. 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
2017, we’re still teaching English units

20. 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

21. 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.

22. 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.

23. SI (or metric) System IPK K20 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
IPK
K20

24. SI (metric) System 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 )
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

25. 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 10-9 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 = 103 mm
Definition: 1 mm = 10-3 m
Prefix
Abbreviation
Power of 10
Nano- n
10-9
Micro- 
10-6
Milli- m
10-3
Centi- c
10-2
Kilo- k
103

26. 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 =103 m; 1 pm = m or 1 m = 1012 pm
Conversions between other metric units:
Convert to meters first and then to the target unit.
Ex: km to cm

27. 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 m2 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.

28. 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)
Powers of 10
Cosmic Eye
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 108 m/s. If the speed = frequency * wavelength, estimate the order of magnitude for the wavelength of visible light.

29. 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, P1-4
What’s Next? (How to prepare for the next day)
Read IB 1.2 p 7-20