Plan Unit systems base units derived units Mass
Plan • Unit systems (base units / derived units) • Mass, Weight, Volume, Density • Calculations with units (dimensional analysis) 1
* *Current would seem to be a derived quantity: charge / time (C/s) 2
All other quantities are related to (derived from) these “fundamental” ones • Volume = length 3 cm 3 (= m. L) • Density = mass/volume g/m. L • Concentration = amount/volume mol/L 3
Mass, Weight, Volume, Density • Mass is basically: – the amount of “fundamental stuff” (i. e. , protons, neutrons, etc. ) present in an object or sample. • Mass is independent of where the object/sample is located. • Mass is also the quantity that determines how hard it is to change the motion of an object. – It is harder to accelerate [or decelerate!!] a truck than it is a subcompact because there is more mass in the truck than in the car. 4
Mass, Weight, Volume, Density (continued) • Weight, on the other hand, is a reflection of – the gravitational force or “pull” (of a planet or moon, for example) on something that has mass. • A bowling ball will weigh less on the moon than it does on the earth, even though the object’s mass is the same. – This is because the force of gravity depends on the mass of both objects. The moon has less mass than the earth, so its "pull" is less strong on a given object. 5
Mass, Weight, Volume, Density (continued) • Volume (of a sample) is – the amount of space occupied by the “stuff” (in that sample). • Volume is not a measure of an "amount of matter". It is a measure of "space“. – 1000 cm 3 of Styrofoam has a lot less mass in it than does 1000 cm 3 of lead, but these two samples occupy the same amount of space. 6
Mass, Weight, Volume, Density (continued) • Density (of an object or sample) reflects – how much mass is present in a given volume (of the object or sample) • Density is a measure of the "compactness" of matter. – A high value of density means "very compact" matter (a lot of mass in a given amount of space). A low value means "very spread out" matter. – Popcorn kernel before popping is more dense than the “fluffy” piece of popcorn that remains afterwards (mass gets “spread out” upon popping). 7
Mass, Weight, Volume, Density (continued) • Density determines whether a substance “sinks” or “floats” in a liquid (once it is submerged) – If dsub > dliq substance sinks – If dsub < dliq substance floats • Velocity of object doesn’t matter • Neither does surface area or surface tension (that can affect something whether something on the surface of a liquid submerges; discussed later) 8
Caution: Mass Density! • Consider these two samples of matter: – 1) a cruise ship – 2) a cup of water • Which has the greater mass? • Which has the greater density? • How can the massive ship have a density that is smaller than the cup of water? – It’s volume is also larger than the cup of water, by an even greater factor than the mass 9
Caution: Mass Density! mcup of water Vcup of water dwater vs. m ship V vs. m V ship Ship has greater mass & greater V than water… …but V is “more” bigger (increases by a greater factor). d is smaller, ship floats canon ball Ball also has greater mass & greater V than water… …but V is “less” bigger (increases by a smaller factor). d is greater, ball sinks 10
Mass, Weight, Volume, Density (final qualitative comments) • “amount of matter” “amount of space” (mass) (volume) • How do you experimentally assess? – Volume can be determined by “liquid displacement” • & can be estimated [roughly] by sight – Mass can be determined with a balance. • & can be estimated [roughly] by “feel” – Density is usually calculated rather than measured directly • & can be estimated [roughly] by “sight” and “feel” 11
Demo/Exercise(s) • Can’t assess mass “visually” – Try “feeling”, but sometimes brain is fooled! • Can (if shapes same) assess volume visually • Water displacement can be used to measure volume (if non-absorbent, and substance sinks in water!) 12
Basic Calculations involving Physical Quantities (& Dimensional Analysis [DA]) • SI system of units (next slide) • Unit conversions • Other calculations 13
*Can be used with any SI unit of measurement **The 8 prefixes with an arrow indicate those you are responsible for on Exam 1 a 14
Assertions • Units are treated like a algebraic variables during calculations • It is often useful to turn “equivalences” into “conversion factors” (fractions) to do many calculations. • “this for that” concept • Procedure called “Dimensional Analysis” (or “factor label”) 15
Dimensional Analysis uses “conversion factors” • 1 kg = 1000 g – Note: You can do the math with the numbers and combine the units, without loss of info: • 1000 g/kg or (1/1000) kg/g = 0. 001 kg/g • 2. 2046 lb = 1 kg • / means “per” 16
Conversions can be done by starting with one qty and multiplying by one or more “factors” • If you are looking for an “amount”, start with an “amount”; if you are looking for a “this for that”, start with a “this for that” • See board (next slide) • Be careful to construct factors properly – Can’t just “make them up” to fit your needs!!! • The factors are “what they are” (determined by equivalences) 17
Basic Calculations involving Physical Quantities (& Dimensional Analysis [DA]) • Unit conversion calculations – What is the mass of a 154 lb person expressed in grams? • 1 kg = 1000 g (this is an exact qty; discussed later) • 2. 205 lb = 1 kg (this is not an exact qty) Many approaches. How would you do it? (Some use explicit proportions; in US, most use DA) Online resource with examples: http: //www. alysion. org/dimensional/fun. htm (NOTE: I have some issues with some the work on this site, but overall, the examples themselves are good ones) 18
Equivalences within a system are typically exact (defined) (e. g. , 1 L = 1000 m. L). Those between systems are usually NOT exact. Exceptions should be indicated as here, with “exact”. The “ 1” in any equivalence is always exact; any uncertainty in an inexact equivalence is found in the quantity that is not “ 1”. → (See Table at the back (or front? ) of Tro for more equivalences) 19
Example • Convert 45 pm into km • One way (not shortest, but generalizable!) – Write equivalences: • 1 pm = 10 -12 m; 1 km = 1000 m – Convert from pm to m (the “base” unit) first • Use/create appropriate conversion factor – Then convert from m to km • Use/create appropriate conversion factor – SEE BOARD 20
2 nd Example (w/ squares and cubes) • For long (multistep) conversion calculations, use the “dimensional analysis” approach to guide you, BUT NEVER STOP THINKING! • Be careful with squares and cubes: – Instructions for a fertilizer suggest applying 0. 206 kg/m 2. Convert into lb/ft 2 • 2. 205 lb = 1 kg; 2. 54 cm = 1 in (exact) • See board and/or next slide for setup and solution 21
Convert 0. 206 kg/m 2 into lb/ft 2 2. 205 lb = 1 kg; 2. 54 cm = 1 in (exact) I’ll convert kg to lb in the numerator first; then convert m 2 to ft 2 in denom. Note: lb/ft 2 is a “this for that”, so started with a “this for that” (kg/m 2) 22
Dimensional Analysis • Useful tool, but very easy to stop thinking…DON’T! – See Ppt 03 slide; you already know about “amounts” and “this for thats”! – For single step calculations in particular, think about the “big guys” and “little guys” and reason first (use DA to check work) • See board, next Ppt for idea and examples 23
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