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```									Ch. 2 – Measuring and Calculating

Problem Solving Techniques
#1 – Identify the known facts. #2 – Define the answer required (find the question)

Based on careful reading of the problem. Understand all symbols, words, and units. Read the problem a second time more carefully. Write down all pieces of information given. Write down the unknown to be determined.

Problem Solving Techniques
#3 – Develop possible solutions. Determine relevant vs. irrelevant info. Write down the possible ways to answer the question. #4 – Analyze solutions and determine the correct one.

Problem Solving Techniques
#5 – Develop the individual steps to arrive at the answer. Helps you to recognize algorithms over time. Algorithm – a pattern for solving a particular type of problem. #6 - Solve the problem.

Problem Solving Techniques
Final Step: #7 – Evaluate the results. Is the answer reasonable?

Check:

what unit do you want? Is it the unit that you have? magnitude – size of answer too big or small?

units –

Let’s Try a Problem


15 members of a school soccer team want to get t-shirts imprinted with the school name. Each shirt costs \$9.00 and each imprint costs \$2.00. To raise money for the shirst, the team members decide to sell candy bars at \$.50 each, of which 20 cents is profit. How many bars must each team member sell? Apply the 7 steps.

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Section 2.2 – Numerical Problem Solving
Quantitative – describing a property using a measurement of a number of units 5g 0.002 s 1.2 in. 400 m 8 apples 30 days Qualitative – describing a property without measurements
 

Dark Cold

- heavy - humid

- wet - turquoise

2.2 - THE INTERNATIONAL SYSTEM (SI)
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System of measurement used by all scientists all over the Earth Uses Base Units (p 29) Modifies bases using Prefixes (p29)
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Prefixes are equal to different quantities Indicates that a unit should be multiplied by the equivalent number

2.2 - THE INTERNATIONAL SYSTEM (SI)
http://www.moe.gov.sg/edumall/tl/digital_resources/physics/images/SI_base_quantities.jpg

2.2 - THE INTERNATIONAL SYSTEM (SI) http://itl.chem.ufl.edu/2045_s00/matter/TB01_005.GIF

Practice


Which is bigger?


kilogram

or

megagram?



centimeter

or

millimeter?

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What is the name of the quantity using prefixes and base units?
 

1000 L 0.001 s

-- 1,000,000 cd -- 0.000 000 001 mol

2.2 - MASS AND WEIGHT


Mass – measure of the quantity of matter


Doesn’t change regardless of location on Earth

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Kilogram – SI standard mass unit Balance – used to determine the mass of an object by comparing an unknown mass to a known mass
“Massing” – using a balance to determine the mass of an object

2.2 - MASS AND WEIGHT


Weight – measure of the force of gravity between two objects


 

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Changes as gravity changes with location on Earth Higher altitude  less gravity – lighter weight Lower altitude  greater gravity – heavier weight Moon  less gravity – weigh less

2.2 - Length, Time and Temperature
Length – the distance of a straight line between two points unit = meter (m) tool = ruler or measuring tape Time – 1/86,400 of a day unit = second tool = clock

(s)

Temperature – the avg. KE of the particles in an object unit = Kelvin (K) tool = thermometer

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2.2 – Temperature and Celsius
Celsius (degree C) – based on freezing and boiling point of water
 

Freezing point of water = 0 C Boiling point of water = 100 C

As something is heated, temp. increases - indicates that KE is increasing

2.2 - ACCURACY AND PRECISION


Accuracy – how close a measurement is to the accepted value

42.3 m = accepted

42.2 m = accurate 23 m = inaccurate 100m = inaccurate

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Precision – how close a set of measurements are to each other
22.6 m, 22.7 m, 22.3m – precise 42.3 m, 42.1m, 42.4m – precise 30 m, 82m, 12 m – not precise

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2.2 - PERCENT ERROR
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Used to compare your value to an accepted value Evaluates the accuracy of your measurement I your measurement – accepted I %Error = ------------------------------------------accepted

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2.2 - SIGNIFICANT DIGITS
 

Indicates exactness of a measurement Rules
 

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Digits other than zero are always significant Final zeros after a decimal point are always significant Zeros between two sig. dig are significant Zeros used solely for spacing the decimal point (placeholders) are not significant.

2.2 - PERCENT ERROR - Sample problem – text p35
“A student determines the atomic mass of Aluminum to be 28.9 amu. If the accepted value is 27.0 amu, what is the percent error?” I 28.9 – 27.0 I ------------------- x 100% = 7.0% error 27.0

2.2 - SIGNIFICANT DIGITS
Counting
     

–

inifinite significant digits.



Examples: \$842.30 – 42 students – 39.7 s – 0.0076 g – 300 m – 230,000.0 –

    

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5 sig.digs inifinite sig.digs 3 sig.digs 2 sig.digs 1 sig.dig 7 sig.digs

2.2 - DERIVED UNITS


Combinations of units to make measurements
EXAMPLES:

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Speed – m/s Volume – cm3 Density = m/V = mass/volume
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unit -- g/ cm3

Changes with temperature because volume changes with temperature.

2.2 - DENSITY
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A standard value that can be used to calculate mass and volume m D = ----V m V = ------D

m= DxV

2.2 – DENSITY - Sample Problem p 39
A piece of beeswax with a volume of 8.50 cm 3 is found to have a mass of 8.06 g. What is the density of the beeswax?

m 8.06g D = --- = --------- = 0.948 g V 8.50cm3 cm3

(note: 3 sig.dig.)

2.2 – DENSITY - Sample Problem p 40


Cobalt is a hard magnetic metal that resembles iron in appearance. It has a density of 8.90 g/cm3. What volume would 17.8 g of cobalt have?

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