Transcript 1.1 Standards of Length, Mass, and Time

Sinai University Faculty of Engineering Science
Department of Basic Science
4/1/2016
1
Chapter 1
Physics and
measurements
1.1 Standards of Length, Mass and Time.
1.2 Dimensional analysis
1.3 Conversion of units
1.4 Significant figures
4/1/2016
2
1.1 Standards of Length,
Mass, and Time
The laws of physics are expressed as mathematical relationships
among physical quantities.
Ex:
v=v0 +at
Most of these quantities are derived quantities, in that they
can be expressed as combinations of a small number of basic
quantities.
Ex: speed, v= (distance/time) (m/s)
In mechanics, the three basic quantities are
length, mass, and time.
4/1/2016
3
SI (Système International),
In 1960, an international committee established a set
of standards for the fundamental quantities of
science. It is called the SI (Systèm International),
o
o
o
o
o
o
o
length
Mass
Time
Temperature
electric current
luminous intensity
the amount of substance
4/1/2016
meter
kilogram
second
the kelvin
the ampere
the candela
the mole
4
Standard of Length
The legal standard of length in France became the
meter
1-As recently as 1960, the length of the meter was defined as
the distance between two lines on a specific platinum–iridium
bar stored under controlled conditions in France.
2-In the 1960s and 1970s, the meter was defined as 1 650
763.73 wavelengths of orange-red light emitted from a
krypton-86 lamp.
3-However, in October 1983, the meter (m) was redefined as the
distance traveled by light in vacuum during a time of 1/299 792 458
second.
4/1/2016
5
Attention, please
No Commas in Numbers with Many Digits
Examples:
1- 10 000 is the same as the common American
notation of 10,000.
2- p= 3.14159265 is written as 3.141 592 65.
4/1/2016
6
Standard of Mass
Amount of matter in an object
The SI unit of mass, the kilogram (kg), is defined as the
mass of a specific platinum–iridium alloy cylinder kept
at the International Bureau of Weights and Measures at
Sevres, France
A second mass standard
Atomic mass unit, amu= 1/12 mass of C-12
1 amu= 1.660 542 02 kg
4/1/2016
7
Other units of mass
British system
Pound –mass= 0.453 6 kg
What is the difference between
mass and weight?
Mass does not depend on height.
Weight depends on the gravitational
pulling force, i.e. acceleration on any
position.
4/1/2016
8
Attention, please
Reasonable Values
Careful thinking about typical values of quantities
is important because when solving problems you
must think about your end result and determine if
it seems reasonable.
If you are calculating the mass of a housefly and
arrive at a value of 100 kg, this is unreasonable
—there is an error somewhere.
4/1/2016
9
The standard unit of time
The second was defined as
Standard day= 24 hours = 86 400 s
The rotation of the Earth is now known to vary
slightly with time, however, and therefore this
motion is not a good one to use for defining a time
standard.
The second (s) is now defined as 9 192 631 770 times the
period of vibration of radiation from the cesium atom,
Cs-133.
4/1/2016
10
Different Units
4/1/2016
11
Derived Units
length(m) X width(m)= Area (m2)
Distance traversed(m)/unit time(s) =Speed (m/s)
Speed(m/s)/unit time(s) = Acceleration (m/s2)
Acceleration(m/s2)X mass(kg) =Force (N)
4/1/2016
12
1.3 Dimensional Analysis
The word dimension has a special meaning in physics.
It denotes the physical nature of a
quantity.
Whether a distance is measured in units of feet or
meters, it is still a distance. We say its dimension is
length
The dimensions of length, mass, and time are L, M, and T,
[ ] to denote the dimensions of a physical quantity.
Velocity [v] = L/T.
4/1/2016
Area [A] = L2.
13
Dimensional Analysis
Dimensional analysis can be used to
1- Derive an equation.
2- Check a specific equation.
4/1/2016
14
Dimensional Analysis
Dimensional analysis makes use of the fact that dimensions can
be treated as
1- algebraic quantities.
quantities can be added or subtracted only if they have
the same dimensions.
Example:
L-L=0 T-L
T3-T2
M+M=2M
M*M=M2
2- the terms on both sides of an equation
must have the same dimensions.
LTM=LMT
T2L=LT2
T3=T3
M.M=M2
The relationship can be correct only if the dimension
on both sides of the equation are the same.
4/1/2016
15
Example
In
General
Left hand side
Wright hand side
n=1, m-2n=0 ,
4/1/2016
m-2=0
m=2
16
1.4 Conversion of Units
1m
100 cm
1=
,
1=
100 cm
1m
0.025 4m
1in
1=
, 1=
1in
0.025 4 m
1in
2.54 cm
1=
,
1=
2.54 cm
1in
Example
4/1/2016
17
4/1/2016
18
1.6 Significant Figures
When certain quantities are measured, the measured values
are known only to within the limits of the
experimental uncertainty.
The value of this uncertainty can depend on various
factors,
1- the quality of the apparatus,
2-the skill of the experimenter,
3- the number of measurements performed.
The number of significant figures in a measurement
can be used to express something about the uncertainty
4/1/2016
19
Example
T= 21.5, 21,22,22.5
Tav= 21.75 + 0.559 016 9
Tav= 21.8 + 0.6
4/1/2016
20
1.6 Significant Figures
Accuracy= 0.1 cm
(5.5  0.1) cm,
 6.4  0.1 cm
6.4 cm
Area = (5.5  0.1) X  6.4  0.1 = 35.22 cm
(5.4
cm)(6.3 cm) =34
cm2
2
5.5 cm
(5.6 cm)(6.5 cm) = 36 cm2.
35 cm2
Zeros may or may not be significant figures.
Those used to position the decimal point in such
numbers as 0.03 and 0.007 5 are not significant.
4/1/2016
21
1.6 Significant Figures
When the zeros come after other digits, however, there is the
possibility of misinterpretation. For example, suppose the mass of
an object is given as 1 500 g. This value is ambiguous because we
do not know whether the last two zeros are being used to locate
the decimal point or whether they represent significant figures in
the measurement. 1.5x103g
2 significant figure
1.50x103g
3 significant figure
1.500x103g
4 significant figure
2.3x10-4
2 significant figure
0.000 23
2 significant figure
In general, a significant figure in a measurement is a reliably known
digit (other than a zero used to locate the decimal point) or the first
22
4/1/2016
estimated
digit
For addition and subtraction,
For example,
123 + 5.35, the answer is 128 and not 128.35. NOT 128.0
If we compute the sum 1.000 1 + 0.000 3 = 1.000 4, the
result has five significant figures, even though one of the
terms in the sum, 0.000 3, has only one significant figure.
Likewise, if we perform the subtraction 1.002- 0.998 =
0.004, the result has only one significant figure even
though one term has four significant figures and the
other
has three.
23
4/1/2016
rounding off numbers,
2.36
2.4
2.35
2.4
265
2.33
2.55
2.3
2.6
2.6
A technique for avoiding error accumulation is to delay rounding of
numbers in a long calculation until you have the final result.
Wait until you are ready to copy the final answer from your calculator
before rounding to the correct number of significant figures.
4/1/2016
24
4/1/2016
25