Transcript Physics Math Intro 2011 USE

Physics
is the science that studies
PHYSICS
the nature of matter,
energy and their
V. HASSELL
relationships.
STATE THE
5
BASE QUANTITIES AND THEIR
SI UNIT
METRIC SYSTEM
SI
unit of time
second
based on atomic standard
radiation emitted by cesium 133
METRIC SYSTEM
SI
unit of length
meter
wavelength of light emitted by
krypton-86
distance light travels in
1/2999 792 458 second
METRIC SYSTEM
SI
unit of mass
kilogram
the quantity of matter an object
contains
mass of a platinum-iridium
metal cylinder kept near Paris
STANDARD UNITS
Kilo
Hecto
Deka
gramdeci
centi
milli
meter- liter
PREFIXES- FRACTIONS
deci
d
centi c
milli m
 micro u
nano n
pico
p
1/10 or 10 -1
1/100 or 10 -2
1/1000 or 10 -3
10 -6
10 -9
10 -12
PREFIXES- MULTIPLES
Deka
Hecto
Kilo
Mega
Giga
da
h
k
M
G
10 1
10 2
3
10
10 6
10 9
Fundamental
quantities &
units
Derived quantities
are
mass-
kg
length-
meter
time-
combinations
of fundamental
quantities
density=
mass/volume
 Nonzero
digits are
always significant
 All
final zeros after
the decimal point
are significant
 Significant
digits are
all the digits of a
measurement that
are certain plus one
estimated digit.
SIGNIFICANT DIGITS
 Your
answers cannot
be more precise than
the least precise
quantity.
 The sum or
difference of two
values is as precise as
the least precise
value.

Zeros between two
other significant digits
are always significant
 Zeros
used solely for
spacing the decimal
point are not
significant
 In
scientific notation all
digits before the 10 are
significant
 2.510
X 10 8 has
______ significant digits
SIGNIFICANT DIGITS- X OR /
 The
result of any
 Note
the factor with
mathematical
the least number of
operation with
significant digits.
measurements can
 Round
the product or
never be more
quotient to this
precise than the least
number of digits.
precise
measurement.
SCIENTIFIC NOTATION
X 10n
only 1 non-zero digit on the
left of the decimal
the exponent gets larger as
the number gets smaller
M
850 METERS = ___________MM
 smaller
 larger
unit - the # gets larger
unit - the # gets smaller
 number
 move
of places- deci, centi, milli
3 times- larger number
 *smallest
units will have largest
numbers
CONVERSION
850
meters = ___________mm
850,000 mm
or 8.5 X 10 5 mm

OR CONVERSION
850
meters = ___________mm
1 meter = 1 X 1000 mm
850 meters 1 X 1000 mm =
1 meter
850,000 mm
 or 8.5 X 10 5 mm

OR CONVERSION
 850
meters = ___________mm
1 meter = 1 X 10 3 mm
 850 meters 1 X 10 3 mm =
1 meter
 850 X 10 3 = 8.5 X 10 5 mm

ADD & SUBTRACT EXPONENTS

the exponents must be the same

Add
10
the numbers in front of the
ADD & SUBTRACT EXPONENTS
2.1
X 10 3 + 3.2 X 10 3 =
 2.1+ 3.2= 5.3
3
5.3 X 10
ADD & SUBTRACT EXPONENTS
3.2 X 10 - 2.1 X 10 =
3.2-2.1 = 1.1
3
1.1 X 10

3
3
ADD & SUBTRACT
W/DIFFERENT EXPONENTS
 Exponents
must be the same number
(doesn’t matter which one)
 Change
other
one of them to match the
(or in between)
 Continue
10
to add or subtract # before
ADD & SUBTRACT
DIFFERENT EXPONENTS
5.5
55
X 10
+ 2.2 X 10
-3
=
X 10 -3 + 2.2 X 10 -3 =
57.2
5.7
-2
X 10 -3=
X
-2
10
SUBTRACT
5.5
55
X 10 -2 - 2.2 X 10 -3 =
X 10 -3 - 2.2 X 10 -3 =
52.8
X 10 -3 =
5.28
X 10 -2
5.3
X 10 -2
MULTIPLY & DIVIDE
 Multiply
or divide the # before
10 as indicated
 add
exponents in multiplication
subtract exponents in
division
 check
m/sec)
units. (May be m2 or
MULIPLY
5.0
X 10 -2m X 3.0 X 10 -3m =
15.0
X 10 -2 + -3 m2=
15.0
X 10 -5 =
1.5
X 10 -4 m2
DIVIDE
6.6
X 10 -2m / 3.3 X 10 -5s =
2.0
10
2.0
X 10
-2+ 5=
-2 - (-5)
m/s =
3
10
X 10
3m/s =
 2.0
X 10 2m X 3.3 X 10 -5kg
6 X 10 -5s =
=6.6
X 10
2 + (-5)= -3
mkg =
6 X 10 -5s
1.1
X 10 -3 -(-5)= -3+5=2
1.1 X 10 2 mkg/s
All
measurements
are subject of
uncertainties
 All
instruments
are subject to
external
influences.
 Uncertainties
in
measurement
cannot be avoided.
INACCURACIES CAN BE DUE TO
human
error in
reading
(precision)

accuracy of
the devise
PARALLAX
 The
apparent
shift in the
position of an
object when it
is viewed from
various angles
==WHAT

IS ERROR?==
Error is the
difference between
the actual value of a
quantity and the
value obtained in
measurement.

Systematic errors
are errors which
tend to shift all
measurements in a
systematic way so
their mean value is
displaced.
Systematic errors
can be compensated
if the errors are
known.
SOURCES

OF
SYSTEMATIC ERROR
zero error, which cause by an
incorrect position of the zero point

an incorrect calibration of the
measuring instrument.

consistently improper use of
equipment.
PRECISION

The precision of a
measurement
describes how exactly
it was measured

the ability of an
instrument in measuring
a quantity in a
consistent manner with
only a small relative
deviation between
readings
WHAT
IS MEANT BY SENSITIVITY OF A
MEASURING INSTRUMENT ?==

The precision
of an
instrument is
limited by the

smallest
division on the
measurement
Measuring instruments that have
smaller scale parts are more
sensitive.

Sensitive instruments need not
necessarily be accurate.
MICROMETER
SCREW GAUGE

Turn the thimble until the
object is gripped gently
between the anvil and
spindle.

Turn the ratchet knob until
a "click" sound is heard.
This is to prevent exerting
too much pressure on the
object measured.

Take the
reading.
MICROMETER
SCREW GAUGE

Reading of main scale = 5.5mm
Reading of thimble scale = 0.27mm
Actual Reading = 5.5mm + 0.27mm = 5.77mm
ACCURACY
 Accuracy
of a
measurement
describes how
well the result
agrees with a
standard value

The accuracy of a
measurement is
the approximation
of the
measurement to
the actual value
for a certain
quantity
STEPS
TO REDUCE
SYSTEMATIC ERROR

Conducting the experiment

with care.

Repeating the experiment by using
different instruments.

by:lack of sensitivity of the
RANDOM ERROR

instrument: the instrument
Random errors
fail to respond to the small
arise from
change.
unknown and

wind, while the experiment
variations in
condition.
It changes from
one measurement
to the next.
natural errors such as
changes in temperature or
unpredictable

Random error can cause
is in progress.

wrong technique of
measurement.
HOW
TO AVOID RANDOM ERROR

Taking repeat readings

Find the average value of the
reading.
ZERO ERROR

A zero error arises when the measuring
instrument does not start from exactly
zero.

Zero errors are consistently present in
every reading of a measurement.

The zero error can be positive or
negative.
HOW
TO MEASURE THE PRECISION OF A
MEASUREMENT ?==

The precision of a reading can be
indicated by its relative deviation.
The relative deviation is the percentage
of mean deviation for a set of
measurements and it is defined by the
following formula:
REVIEW
Accuracy
is determined by the
preciseness of the measurement
To
check the accuracy of an
instrument you measure a
standard devise to determine
the deviation.
ACCURACY

The accuracy of an instrument is usually off the
same direction in all measurements.
 Ex.
A
scale which indicates a measurement over 0
with nothing being balanced will probably show
a higher than accurate amount for all
measurements.
MURPHY’S LAW
Any
error that can creep
in, it will. It will be in the
direction that will do most
damage to the calculation.
Never
mix units. For
example does 30
pounds added to 20
newtons equal 50?
NO

If the forces do not act along a
straight line you can use the
Graphical method to find the
resultant sum.
Also, you can use the
Pythagorean theorem to
find the resultant sum.
 The Pythagorean theorem
is
2
2
2
A +B =C

If
A = 40 N and B
equals 30 N, what is
the resultant sum
(C)?
1.
2.
3.
4.
5.




A2 + B2 = C2
A=40; B=30
402 + 302 = C2
1600 + 900 = C2
2500 = C2
50 = C
First plug in what you know
Square A and B
Add A and B
Square root the answer