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
 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?

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
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
 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
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
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  at
1
2
x  vi t  a(t )
2
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,
3
dist
725km 10
tim e 

 2  10h
speed 88km / h 10