Dimensions & Unit Conversions August 10-11, 2017 Working in table groups, write down the table below. Then, find 3 different quantities to measure. This means 3 different TYPES of measurements (for example, weight and length are different quantities). Take your measurement in SI units. Write the measurements on your white board, filling in just the first two columns.   Quantity Measurement Dimension Units SI or not? 10 minutes to do, then discuss (5 minutes) Looking for the students to find 3 physical quantities (dimensions): time, length, and mass. Possible misconceptions: they might measure angles, which are not exactly a quantity (they are dimensionless). They measure weight (which is not metric and is a quantity but is a derived quantity)

In Table Groups … Find 3 different quantities to measure. This means 3 different TYPES of measurements (for example, weight and length are different quantities). Take your measurement in SI units. For now, fill in only the first two columns on your GN 

Dimensions & Units All physical quantities have dimensions and are expressed in units. Dimension describes what the physical quantity is Units are how the quantity is measured Example: Speed Speed has the dimensions of Length / Time Speed may be measured by a variety of different units (e.g. mph, km/s, etc.) You can convert between different units of the same physical quantity (e.g. seconds into hours) but CANNOT convert one dimension into another (e.g you can’t convert time into length)

The corresponding basic SI- units are: In the study of mechanics, we will work with physical quantities that can be described in terms of three dimensions: length (L), time (T) , and mass (M). The corresponding basic SI- units are: Length – 1 meter (1m) is the distance traveled by the light in a vacuum during a time of 1/299,792,458 second. Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sevres, France Time – 1 second (1s) is defined as 9,192,631,770 times the period of oscillation of radiation from the cesium atom. These standards (definitions) have obviously evolved over time. Earlier standards were simpler but less reproducible (e.g. a gram was mass of cubic cm of water).

ALL physical dimensions can be expressed in terms of combinations of seven basic dimensions, which can be measured directly. Derived dimensions are combinations of 7 basic ones. Basic Physical Quantity Derived Physical Quantity Basic Dimension Basic SI Unit Derived Dimension Derived SI Unit Distance, height,width Length (L) meter (m) Mass (m) Mass (M) kilogram (kg) Time (t) Time (T) second (s) Electric Current (I) Electric Current (I) ampere (A) Temperature kelvin (K) Amount of matter mole Intensity of light candela (cd) area L2 m2 Volume L3 m3 speed L/T m/s acceleration L/T2 m/s2 force ML/T2 kg.m/s2 newton (N) power M L2/T3 kg.m2/s3 watt (W) density M/ L3 kg/m3 Blue ones are ones we will work with this semester – start learning them, but do not need to memorize by next class

Go back to the measurements you did earlier & fill in the rest of the table Quantity measured Measurement Dimensions Units SI or not?

SI Conversions 5 mL = ____ kL SI PREFIXES 10 -12 pico p 10 -9 nano n 10 -6 micro µ 10 -3 milli m 10 -2 centi c 10 3 kilo k 10 6 mega M 10 9 giga G 10 12 tera T 5 mL = ____ kL 1st step: What do you expect? Will the number in front of kl be bigger or smaller than 5? Smaller! It takes only a tiny fraction of a kl to equal 5 ml. 2nd step: Take the given number and multiply it by conversion factors – a fractions where the top and bottom are equivalent – so that you can cross out the units you don’t want and put in the units you need. You will often need multiple steps. 5mL X 10 −3 𝐿 1 𝑚𝐿 X 1 𝑘𝐿 10 3 𝐿 = 5 X 10-6 kL These are conversion factors. Notice that the top and bottom of each fraction is equivalent, which means that we are just multiplying our original measurement by 1

One more as a class … The wavelength of green light is 500 nm. SI PREFIXES 10 -12 pico p 10 -9 nano n 10 -6 micro µ 10 -3 milli m 10 -2 centi c 10 3 kilo k 10 6 mega M 10 9 giga G 10 12 tera T The wavelength of green light is 500 nm. How many meters is this? 500 𝑛𝑚× 1𝑚 10 9 𝑛𝑚 =500× 10 −9 𝑚=5× 10 −7 𝑚

Practice 1: Basic SI conversions How many liters is 16 𝜇ℓ ? 4.3 x 104 ns = __ µs 5.2 x 108 ms = __ ks 0.09 cm = __ pm 906 gigabytes = __ bytes 16 𝜇ℓ=1.6× 10 −5 ℓ 4.3× 10 4 𝑛𝑠 = 43 µs 5.2× 10 8 𝑚𝑠=520 𝑘𝑠 0.09 𝑐𝑚=9 𝑋 108 pm 906 𝐺𝑏𝑦𝑡𝑒𝑠=9.06 𝑥 1010 bytes Try on your own first (2 minutes silent!). Look back at the examples I did and try to figure out how to apply them to this. Then confer with your partner. Alternate who explains each one. If one can’t get it, other can help. But then the one who is struggling should continue to lead the explanation until they can do it on their own.

More complex conversion problems Example 1: Metric and English 20 m/s → km/h Example 2: Units raised to a power 7.2 m3 → mm3 20 𝑚 𝑠 = 20 𝑚 𝑠 1 𝑘𝑚 10 3 𝑚 3600 𝑠 1 ℎ = 72 km/h You must raise the conversion factor to the same power as the unit. 7.2 𝑚 3 =7.2 𝑚 3 10 3 𝑚𝑚 1 𝑚 3 = 7.2 x 10 9 𝑚𝑚 3

Practice 2: Complex SI conversions 100 mm3 = ___ m3 60. miles per hour = _____ m/s 75 g/cm3 = __________ kg/m3 9.8 m/s2 = _______ km/hr2 Try on your own first (2 minutes silent!). Look back at the examples I did and try to figure out how to apply them to this. Then confer with your partner. Alternate who explains each one. If one can’t get it, other can help. But then the one who is struggling should continue to lead the explanation until they can do it on their own.

Practice 2: Complex SI conversions 100 mm3 = ___ m3 60. miles per hour = _____ m/s =27 m/s 75 g/cm3 = __________ kg/m3 = 750 kg/m2 9.8 m/s2 = _______ km/hr2 = 1.3 X 105km/hr2 = 10-7 m3 Try on your own first (2 minutes silent!). Look back at the examples I did and try to figure out how to apply them to this. Then confer with your partner. Alternate who explains each one. If one can’t get it, other can help. But then the one who is struggling should continue to lead the explanation until they can do it on their own.

Must these calculations involve a conversion Must these calculations involve a conversion? What units would the answers have? a) Yes! You can only add quantities that have the same unit. Possible units: m OR cm OR km 30 m + 32 cm + 5 km 60 g + 25 m 18 kg X 35 𝑚 15 𝑠 b) Trick question! This calculation is impossible. Different quantities (mass and length) cannot be added Discuss as table group for 2 minutes. Then take thumbs up / thumbs down vote. c) No conversion necessary! Different quantities can be multiplied and divided together. Just combine the units at the end: kg*m/s

Be sure to do HW and MEMORIZE the SI prefix table. Closure What were our objectives today and how did we meet them? How did what we do today reflect our statement of inquiry? … our TOK connection? What was our learner profile trait, and how did we demonstrate it? 1st HW Quiz Next Class! Be sure to do HW and MEMORIZE the SI prefix table.