Plan

• Unit systems (base units / derived units)

• Mass, Weight, Volume, Density

• Calculations with units (dimensional analysis)

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*Current would seem to be a derived quantity: charge / time (C/s)

*

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All other quantities are related to (derived

from) these “fundamental” ones

• Volume = length3 cm3 (= mL)

3

J)( (m/s)kg time

distance x mass Energy 2

2

• Density = mass/volume g/mL

• Concentration = amount/volume mol/L

Mass, Weight, Volume, Density (see handout)

• 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.

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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.

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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 cm3 of Styrofoam has a lot less mass in

it than does 1000 cm3 of lead, but these two samples occupy the same amount of space.

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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).

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Mass, Weight, Volume, Density (continued)

• Density determines whether a substance “sinks” or “floats” in a liquid– If dsub > dliq substance sinks

– If dsub < dliq substance floats• Velocity of object doesn’t matter• Neither does surface area or surface tension

(unless really lightweight; special case; later)

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Mass, Weight, Volume, Density(final qualitative comments)

• “amount of matter” “amount of space”

• 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”

(mass) (volume)

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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!)

10(Try PS1b, Q’s 12-14 now!)

Basic Calculations involving Physical Quantities (& Dimensional Analysis)

• Unit conversion calculations– What is the mass of a 154 lb person

expressed in grams?• 1 kg = 1000 g (this is an exact qty! Why?)• 2.2046 lb = 1 kg

Many approaches. How would you do it?

(on board)

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**Prefixes with an arrow indicate those you are responsible for on Exam 1b

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”)

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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

1000 g 1 kg

1 kg 1000 g or

2.2046 lb 1 kg

1 kg 2.2046 lb or• 2.2046 lb = 1 kg

• / means “per” 14

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 (redo earlier problem)

• 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)

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→ (See BACK INSIDE COVER of Tro for more equivalences)

Equivalences within a system are typically exact (defined) (e.g., 1 L = 1000 mL).

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”.

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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 BOARD17(Try PS1b, Q’s 15-17 now!)

2nd Example

• 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/m2. Convert into lb/ft2

• 2.2046 lb = 1 kg; 2.54 cm = 1 in (exact)• See board and/or next slide for setup and solution

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2.54 2.54 12 12

cm cm in in

in in ft ft

-1

2

2.06 x 10 2.2046 1 1

1 100 100

kg lb m m

m kg cm cm

20.04219 lb/ft 20.0422 lb/ft

Note: lb/ft2 is a “this for that”, so I STARTED with a “this for that” (kg/m2)

19(Try PS1b, Q’s 18-20 now!)

Dimensional Analysis

• Useful tool, but very easy to stop thinking…DON’T!– See Ppt03 slide; you already know about

“amounts” and “this for that’s”!– For single step calculations in particular, think

about the “big guys” and “little guys” and reason first (use D.A. to check work)

• See board, next Ppt slide for idea and examples

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