Post on 04-Jan-2016
The Metric The Metric SystemSystem
UNITS OF UNITS OF MEASUREMENTMEASUREMENT
Use Use SI unitsSI units — based on the metric — based on the metric systemsystem
Length Length
MassMass
VolumeVolume
TimeTime
TemperatureTemperature
meter, mmeter, m
kilogram, kgkilogram, kg
seconds, sseconds, s
Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K
liter, Lliter, L
Mass vs. WeightMass vs. WeightMass: Amount
of matter (grams, measured with a BALANCE)
Weight: Force exerted by the mass, only present with gravity
Can you hear Can you hear me now?me now?
Uncertainty in MeasurementUncertainty in Measurement
2 Reasons: ◦instruments aren’t flawless ◦measuring involves estimation (last digit)
Reliability of measurements can be checked 2 ways:◦Precision: same result obtained over and over
again◦Accuracy: how close the obtained value is to
the accepted value
Metric PrefixesMetric Prefixes
EqualitiesEqualities
State the same measurement in two State the same measurement in two different unitsdifferent units
lengthlength
10.0 in.10.0 in.
25.4 cm25.4 cm
DENSITYDENSITY
Density mass (g)volume (cm3)
Density mass (g)volume (cm3)
Mercury
13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33
Aluminum
2.7 g/cm2.7 g/cm33
Platinum
Solving CalculationsSolving Calculations
StrategyStrategy1. Get dimensions in common units.1. Get dimensions in common units.
2.2. Calculate volume in cubic Calculate volume in cubic centimeters.centimeters.
3. Calculate the density.3. Calculate the density.
ProblemProblem A piece of copper has a A piece of copper has a mass of 57.54 g. It is 9.36 cm long, mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cmCalculate density (g/cm33).).
Density mass (g)volume (cm3)
Density mass (g)volume (cm3)
Volume DisplacementVolume Displacement
A solid displaces a matching volume of A solid displaces a matching volume of water when the solid is placed in water.water when the solid is placed in water.
33 mL33 mL25 mL 25 mL
Temperature ScalesTemperature ScalesFahrenheitFahrenheitCelsiusCelsiusKelvinKelvin
Anders Celsius1701-1744
Lord Kelvin(William Thomson)1824-1907
Temperature ScalesTemperature Scales
Notice that 1 kelvin = 1 degree Celsius1 kelvin = 1 degree Celsius
Boiling point Boiling point of waterof water
Freezing point Freezing point of waterof water
CelsiusCelsius
100 ˚C100 ˚C
0 ˚C0 ˚C
100˚C100˚C
KelvinKelvin
373 K373 K
273 K273 K
100 K100 K
FahrenheitFahrenheit
32 ˚F32 ˚F
212 ˚F212 ˚F
180˚F180˚F
Calculations Using Calculations Using TemperatureTemperature
Generally require temp’s in Generally require temp’s in kelvinskelvins
T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K
Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K
Generally require temp’s in Generally require temp’s in kelvinskelvins
T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K
Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K
Dimensional Dimensional AnalysisAnalysis
Conversion FactorsConversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm 2.54 cm 1 in.
How many minutes are in 2.5 hoursHow many minutes are in 2.5 hours??
Conversion factor
2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min 1 hr1 hr
cancel
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up,
and the UNITS are calculated as well as the numbers!
English and Metric English and Metric ConversionsConversions
If you know ONE conversion for each type of measurement, you can convert anything!
You will need to know and use these conversions:◦Mass: 454 grams = 1 pound◦Length: 2.54 cm = 1 inch◦Volume: 0.946 L = 1 quart
Steps to Problem SolvingSteps to Problem Solving
1. Read problem2. Identify data 3. Make a unit plan from the initial unit to
the desired unit4. Select conversion factors5. Change initial unit to desired unit6. Cancel units and check7. Do math on calculator 8. Give an answer using significant figures
Simplified Problem Solving Simplified Problem Solving StrategyStrategy
Where do we want to go?
What do we know?
How do we get there?
Does it make sense?