1.2 Measurement in Experiments
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Transcript 1.2 Measurement in Experiments
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 things
Magnitude
Dimensions
Units
how much?
length, mass, time
of what?
The SI system
The standard measurement system
for science
Formerly called the metric system
Base units
Basic units that are not a combination
of some other units
Derived units
Are combinations of base units
Base Units
Physical 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 meters
1 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?
1 in = 2.54 cm
1 L = 103 mL
1 mL = 1 cm3
Scientific Method
A way of thinking and
problem solving
A group of related
processes and activities
http://www.sciencebuddies.org/science-fairprojects/overview_scientific_method2.gif
Scientific Method: Important
Terms
Law vs. Theory
Fact / Observation
Hypothesis
Experiment
Accuracy & Precision
Accuracy
Nearness 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 measurement
Are figures that are known because
they are measured
Uncertainty in Measurement
No measurement is absolutely correct
All measurements are approximations
Estimated uncertainty
± ½ smallest increment of the
instrument
E.g. a ruler graduated in 0.1 cm units
would be reported as 5.2 ± 0.05 cm
Estimated Uncertainty
Percent Uncertainty
Estimated uncertainty
± smallest increment of measurement
E.g. a ruler graduated in 0.1 cm units would
be reported as 5.2 ± 0.1 cm
Percent uncertainty
= ratio of estimated uncertainty to
measurement
E.g. 0.05/5.2 = 0.96%
Measurement is reported as 5.2 ± 0.96%
Is this diamond yours?
You have a diamond with a mass of
8.17 grams, measured on a scale with
a precision of ± 0.05g
You lend the diamond to a friend, who
returns it. The returned diamond
measures 8.09 g
Is the diamond yours?
Significant Figures
Represent measured numbers and
one final estimated digit
Reflect the precision of an instrument
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
6.
Final zeros to left of decimal
ARE
How many significant figures?
50.3
3.0025
0.892
0.0008
57.00
2.000000
1000
20.
20.001
3426
210
6.58 x 103
1.534 x 10-4
2.00 x 107
5000.
30
Rules of calculating with
significant figures
1.
2.
3.
When adding & subtracting, final
answer must have fewest decimal
places present in the calculation.
When multiplying & dividing, final
answer must have fewest
significant digits present in the
calculation.
Number of figures in a constant are
ignored wrt sig figs.
1.3 Language of Physics
Mathematics is the language of
physics
Data is collected in a table form
Data is graphed to show relationship
of independent & dependent variables
Data Table and Graph
Determining k through
displacement
Hooke's Law
mass
(kg)
2.50
0.00
0.00
0.00
2.00
0.01
0.49
0.05
0.03
0.98
0.10
0.06
1.47
0.15
0.09
1.96
0.20
Force (N)
x (m)
Force
(N)
1.50
1.00
0.50
0.00
0.00
0.02
0.04
0.06
Displacement (m)
0.08
0.10
Equations
Equations indicate
relationships of
variables
x
v
t
v f vi at
1
2
x vi t a(t )
2
Evaluating Physics
Equations
Dimensional analysis can give you clues
how to solve a problem
Dimensional analysis 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,
3
dist
725km 10
tim e
2 10h
speed 88km / h 10