Transcript km/h --> m/s

General Physics (PHYS101)
Golibjon Berdiyorov
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Syllabus and teaching strategy
Lecturer:
Golibjon Berdiyorov, Room 148 Physics Building
Phone: 860-3869/2283
e-mail: [email protected]
www.cmt.ua.ac.be/golib/PHYS101
Office Hours:
Sunday-Thursday: 8.00-10.00
Lectures:
Sunday: 3.20pm-4.10pm (6/125) 25-27
Tuesday: 3.20pm-4.10pm (6/125) 25-27
Thursday: 3.20pm-4.10pm (6/125) 25-27
Recitation:
Monday: 1.10pm-2.00pm (6/209) 25
3.20pm-4.10pm (6/165) 26
4.20pm-5.10pm (6/201) 27
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Assessment: Grading
DN grade:
• 3 or more unexcused absences in the LAB
• 12 unexcused absences in lecture+recitation
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Format for Active Learning
Warm up for lectures:
Read the text(use a highlighter, if
you prefer)
Understanding physics (lectures):
Answer questions in class
Bring lecture notes, textbook…
Challenge yourself (homework):
Homework
Play with physics (lab):
Discover with hands-on experience
Practice, practice and practice!!!
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Lecture 01
(Chap. 1, Sec. 1-3)
Units, Changing units, Significant figures
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Measurements
• Physics is based on measurement of physical quantities
1 nanometre =1.0 × 10-9 m
1 light year =9.4×1015 m
• Examples are: length, mass, time, electric current,
magnetic field, temperature, pressure ...
• All physical quantities have dimensions: dimensions are
basic types of quantities that can be measured or
computed.
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Base dimensions
• These quantities are the basic dimensions:
Length
[L]
Mass
[M]
Time
[T]
• Other physical quantities are defined in terms of
these base quantities:
- [velocity] = [length]/[time] = [L]/[T]
- [volume]=[length]3=[L]3
- [density]=[mass]/[volume]=[M]/[L]3
- [force] = [mass][length] /[time]2 = [M][L]/[T]2
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Units for physical quantities
• A unit is a standard amount of a dimensional quantity.
• Units can be chosen for convenience:
• Science [L]:
1 angstrom =1.0 × 10-10 metres
1 light year =9.4605284 × 1015 metres
• US customary [L]:
1 ft = 0.3048 m
1 mile = 1.6 km
12 inches in a foot, three feet in a yard
• A single unified system of units makes life easier!
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International System of Units
(metric system)
Basic SI Units
• Length
• Time
• Mass
•
•
•
•
•
Electrical current
Temperature
Luminous intensity
Amount of substance
meter
seconds
kilogram
ampere
Kelvin
candela
mole
m
s
kg
A
K
cd
mol
These are the only units necessary to describe any
quantity.
Si derived units
Length
Time
Mass
[L]
[T]
[M]
m
s
kg
• [Area] = m2 square meter
• [Volume] = m3 cubic meter
• [Density] = kg/m3 kilogram per cubic meter
• [Speed] = m/s meter per second
• [Acceleration] = m/s2 meter per second squared
• [Force]: N (Newton) = kg m/s2
• [Frequency]: Hz (Hertz) = s-1
• [Pressure]: Pa (Pascal) = N/m2
• [Energy]: J (Joule) = N m
• [Power]: W (Watt) = J/s
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Conversion of Units
•
•
One can measure the same quantity in different units. For
instance distance can be measured in miles, kilometres,
meters etc. Velocity can be measured in km/hour, m/s etc.
If physical quantities are measured in different units, then they
should be converted to the same units.
10 m/s = 36 km/h
vman-ground= 5km/h + 10 m/s = 15?? -No
vman-ground= 5 km/h + 36 km/h = 41 km/h
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Conversion of Units: Chain-link method
Example 1: Express 3 min in seconds?
1min = 60 s
1=
60s
1 min
=
1 min
60s
Conversion Factor?
60 s
3min = 3min x 1 = 3min x
= 180 s
1 min
Example 2: How many centimeters are there in 5.30 inches?
1 in = 2.54 cm
1=
2.54 cm
1 in
2.54 cm
5.30 in = 5.30 in x 1 = 5.30 in x
= 13.5 cm
1 in
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Conversion of Units
Example 3: Express 200 km/h in miles/s?
1 km = 0.6 miles
1h = 60 min = 60 x 60 s = 3600 s
200 km/h= 200 x 0.6 miles/3600 s = 0.03 miles/s
Example 4: Express 200 km/h in m/s?
1 km = 1000 m
1 h = 3600 s
km/h --> m/s :3.6
m/s --> km/h x3.6
200 km/h= 200 x 1000 m/3600 s = 55.56 m/s
Example 5: Express 16 m/s in km/h?
1 m = (1/1000) km
1 s = (1/3600) h
16 m/s= 16 x (1/1000) km/(1/3600) h = 16x3600/1000 km/h=57.6 km/h
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Scientific notations
Scientific notation
Expanded form
1 x 100
1
1 x 101
10
1 x 102
100
1 x 103
1000
1 x 106
1 000 000
1 x 10-1
1/10 or 0.1
1 x 10-3
1 x 10-6
384000 km
0.0000013 m
384000 km=3.84 x 105 km 0.0000013 m=1.3 x 10-6 m
we write them in
1/1000Can
or 0.001
a compact form?
0. 000 001
101 = 1.01 x 102
4321 = 4.321 x 103
1.23 = 1.23 x 100
0.25 = 2.5 x 10-1
0.0007925 = 7.925 x 10-4
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Prefixes and Notation
The following prefixes indicate
multiples of a unit.
Multiplier
Prefix
Symbol
1012
tera
T
109
giga
G
106
mega
M
103
kilo
k
10-3
milli
m
10-6
micro

10-9
nano
n
10-12
pico
p
10-15
femto
f
Rounding
Speed of light: c=299 792 458 m/s
c=2.99 792 458 x 108 m/s
• Overestimation: digits 5 to 9 can be dropped from the
decimal place during the rounding, however, one
should be added to the digit in front of it.
• Underestimation: the following digits can just be
dropped from the decimal place: 0, 1, 2, 3, an 4.
Example 1. Round c to a nearest 1000th. c=2.998 x 108 m/s.
Example 2. Round c to a nearest 10th.
c=3.0 x 108 m/s.
Example 3. Round 273.587 to a nearest integer. 274
Example 4. Round 273.587 to 2 significant figures. 270
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Order of magnitude
• An order of magnitude calculation is a rough estimate
that is accurate to within a factor of about 10.
• It is useful if you want to get a quick rough answer.
• The order of magnitude of a quantity is the power of ten
when quantity is expressed in scientific notation
A=7 600 = 7.6 x 103
The order of magnitude of A is 3
B=3 700 = 3.7 x 103
The order of magnitude of B is 3
A=7 600 ~ 10 000 = 104
B=3 700 ~ 1 000 = 103
The nearest order of magnitude of A is 4
The nearest order of magnitude of B is 3
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Uncertainties in measurements
• All measurements are subject to an uncertainty
• These uncertainties can be due to e.g. limitations in the
measuring tools or fluctuations in the measured quantities.
• The accuracy of the measurements are determined by significant figures.
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Rules for Significant Figures
1. All nonzero figures are significant
359 87678 1245 987889
2. All zeros between nonzeros are significant
205 1003 508009 800009002
3. Zeros at the end are significant if there is a decimal
point before them
4.200 1003.5600 30.003000
4. All other zeros are non-significant
30000 0.0000344
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Rules for Significant Figures
Not significant
Not significant
Significant
zero at the beginning
zero used only to locate
the decimal point
all zeros between nonzero
numbers
0.004004500
Significant
Significant
all nonzeros
zeros at the end of
integers
a number to the right
of the decimal point
Just take care of zeros
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Operations with Significant Figures
• When adding or subtracting, round the results to the
smallest number of decimal places of any term in the sum
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Operations with Significant Figures
• When multiplying or dividing, round the result to the same
accuracy as the least accurate measurements (i.e. the
smallest number of the significant figures)
Example: Calculate the surface area of a plate with
dimensions 4.5 cm by 7.32 cm.
A=4.5 cm x 7.32 cm=32.94 cm2.
A=33 cm2.
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Summary
• Dimensions are basic types of quantities that can be
measured or computed.
• Base dimensions are length, time, and mass.
• A unit is a standard amount of a dimensional quantity.
Summary
• Scientific notations
• Order of magnitude: 10x (x=1,2,3 ..)
• Rounding
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Summary
• Uncertainties in the measurements
• Significant figures
• It is important to control the number of digits or significant
figures in the measurements.
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Express speed of sound (330 m/s) in miles/h
(1 mile = 1609 m)
a) 738 miles/h
b) 730 miles/h
1 shake = 10-8 sec. Find out how many nano
seconds (ns) are there in 1 shake (1ns=10-9s).
a) 1 ns
b) 10 ns
Express the following numbers in scientific notations:
a) 0.015
b) 0.0000002
c) 54800
a) 1.5 x 10-2
b) 2 x 10-7
c) 5.48 x 104