1.2 measurement in experiments. learning objectives list basic si units and quantities they describe...
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1.2 Measurement in Experiments
Learning Objectives
List basic SI units and quantities they describe
Convert measurements to scientific notation
Distinguish between accuracy & precision
Use significant figures in measurements & calculations
Numbers as Measurements
In science, numbers represent measurements
Numbers involve three thingsMagnitude how much?Dimensions length, mass,
timeUnits of what?
The SI system
The standard measurement system for science
Base unitsBasic units that are not a combination
of some other units Derived units
Are combinations of base units
Base UnitsPhysical Quantity
(Dimension)
Unit Abbreviation
Mass Kilogram kg
Length Meter m
Time Second s
Electric current Ampere A
Temperature Kelvin K
Luminous intensity
Candela cd
Amount of substance
Mole mol
Derived units
Derived units are combinations of base units
Base Unit Derived Unit
m (length) m3 (volume)
kg (mass)
m (length)
s (time)
N (newton) for force
1N = 1 kg∙m
s2
Prefixes indicate orders of magnitude (powers of 10)
Power Prefix Abbrev Power Prefix Abbrev
10 -18 atto- a 10 -1 deci- d
10 -15 femto- f 10 1 deka- da
10 -12 pico- p 10 3 kilo- k
10 -9 nano- n 10 6 mega- M
10 -6 micro- μ 10 9 giga- G
10 -3 milli- m 10 12 tera- T
10 -2 centi- c 10 15 peta- P
Converting Prefixes & Units
The main idea: multiply the given unit by a conversion factor yielding the desired unit
Conversion factor: a ratio of two units that is an equivalent to 1.
Example: convert millimeters to meters1 mm x 10-3 m = 1 x 10-3 m
1 mm
Practice 1A, #1-5
Converting units of area and units of volume
How many cm2 are in 1 m2? How many cm3 are in 1 m3? How many in3 are in 1 L?
Scientific Method
http://www.sciencebuddies.org/science-fair-projects/overview_scientific_method2.gif
A way of thinking and problem solving
A group of related processes and activities
Scientific Method: Important Terms
Law vs. Theory Fact / Observation Hypothesis Experiment
Accuracy & Precision
AccuracyNearness of a measurement to the
true value Precision
Degree of exactness or refinement of a measurement
Repeatability of a measurement
Precision
describes the limit of exactness of a measuring instrument
Significant figures reflect certainty of a measurementAre figures that are known because
they are measured
Significant Figures
Represent numbers known with certainty plus one final estimated digit
Reflect the precision of an instrument or measurement
Must be reported properly Require special handling in
calculations
Rules to determine significant digits
1. All non-zeros ARE
2. All zeros between non-zeros ARE
3. Zeros in front of non-zeros ARE NOT
4. Final zeros to right of decimal ARE
5. Final zeros without a decimal ARE NOT
How many significant figures?
50.3 20.001 3.0025 3426 0.892 210 0.0008 6.58 x 103
57.00 1.534 x 10-4
2.000000 2.00 x 107
1000 5000. 20. 30
Rules of calculating with significant figures
1. When adding & subtracting, final answer must have fewest decimal places present in the calculation.
2. When multiplying & dividing, final answer must have fewest significant digits present in the calculation.
3. Number of figures in a constant are ignored wrt sig figs.
1.3 Language of Physics
Physical quantities often relate to one another in a mathematical way
Data is collected in a table form Data is graphed
to show relationship of independent & dependent variables
When time is a variable it is usually the independent (x) variable
Manipulated & responding variables
Data Table and Graph
Determining k through displacement
x (m)Force
(N)mass
(kg)
0.00 0.00 0.00
0.01 0.49 0.05
0.03 0.98 0.10
0.06 1.47 0.15
0.09 1.96 0.20
Hooke's Law
0.00
0.50
1.00
1.50
2.00
2.50
0.00 0.02 0.04 0.06 0.08 0.10
Displacement (m)
Forc
e (N
)
Equations
Equations indicate relationships of variables
2)(2
1tatvx
tavvt
xv
i
if
Evaluating Physics Equations: Dimensional Analysis
Can give you clues how to solve a problem Can help check many types of problems
because… Dimensions can be treated as algebraic
quantities Example: derive a formula for speed Example: How long would it take a car to
travel 725 km at a speed of 88 km/h?
Order of Magnitude Estimates Physics often uses very large and very
small numbers Using powers of ten as estimates of the
numbers can help estimate and check your answers
Example: from the previous problem,
hhkm
km
speed
disttime 10
10
10
/88
7252
3