Topic 1: Measurement and uncertainties
1.1 – MEASUREMENTS IN PHYSICS
Physics has some of the most famous names in science.
▪ If a poll were to be taken on who is the most famous
scientist, many people would choose…
Albert Einstein
A PHYSICIST
▪ other people might choose…
A PHYSICIST
Isaac Newton
The physics we will study was pioneered by the following four individuals:
▪ Other greats will be introduced when the time comes.
Galileo
Newton
Maxwell
Einstein
Kinematics
Dynamics
Classical Physics
Calculus
Electrodynamics
Relativity
Physics is the study of forces, and matter’s reaction to them.
▪ All of the sciences have examples of force:
▪ In biology, we have the bighorn sheep:
F12
F21
W2
W1
f1
f2
Fn2
Fn1
Kilo Newtons
▪ In chemistry, we have the popping balloon
Dakota H-Bomb – 1 million tons of TNT
In physics, we have the biggest forces of all:
Meteor Crater - Arizona
100 Dakota H-Bombs
Physics is the study of the very small.
▪ And the very large.
▪ And everything in
between.
Barred Spiral Galaxy NGC 1300
About 2 ×1021 meters in diameter
The little spring is meant to indicate that the quarks inside a nucleon are held together by a force we call gluon exchange.
WHAT is PHYSICS?
The study of matter, energy, and the interactions between them
… in other words, everything!
“Physics investigates the essential nature of the world, and biology describes a local bump. Psychology … describes a bump on a bump.”
Willard Van Orman Quine,
American philosopher (1908 – 2000)
Remarkably, we have found that these laws can be expressed in terms of mathematical equations.
Physics is the study of the fundamental laws of nature.
Branches of physics
Side Note
“No amount of experimentation can ever prove me
right; a single experiment can prove me wrong”
-- Albert Einstein
No theory is here to stay forever.
Side Note
In nearly all everyday situations, Einstein’s theory gives predictions almost the same as Newton’s.
Main distinction is in extreme case of very high speed
(close to the speed of light)
Science of very fast:
● Special theory of relativity – Albert Einstein.
The new theory gave us much more:
Our view of the world is affected with that theory.
– Our concepts of space and time underwent a huge change
– mass and energy as a single entity ( E = mc2 ).
Quantum mechanics is the science of the very small:
on the scale of atoms and subatomic particles.
Stands for Système international d'unités. It is standard body of measurements, the modern form of the metric system adopted in 1960.
▪The SI system is pretty much the world standard in units.
Why use SI units?
▪ universal
▪ easy (metric system)
SI Units
▪ The fundamental units in the SI system are…
Length | meter (m) |
Mass | kilogram (kg) |
Time | second (s) |
Electric Current (I) | ampere (A) |
Temperature | kelvin (K) |
Amount of matter | mole |
Intensity of light/Luminosity | candela (cd) |
▪ You will also use the gram. In Chemistry. In physics we use the kilogram (SI unit).
Length – 1 meter (1m) is the distance traveled by the light in a vacuum during
a time of 1/299,792,458 second.
Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium
alloy cylinder kept at the International Bureau of
Weights and Measures at Sevres, France
1 kg is basic unit of mass, not, I repeat, not 1g !!!!!!!!!!
SI Units
Time – 1 second (1s) is defined as 9,192,631,770 times the period of one
oscillation of radiation from the cesium atom.
▪ The International Prototype of the Kilogram was sanctioned in 1889. Its form is a cylinder with diameter and height of about 39 mm. It is made of an alloy of 90 % platinum and 10 % iridium. The IPK has been conserved at the BIPM since 1889, initially with two official copies. Over the years, one official copy was replaced and four have been added.
▪ One meter is about a yard or three feet.
▪ One kilogram of mass has weight of 9.8 N
on earth or about 2.2 pounds in USA -☺.
EX: Which one of the following is fundamental unit?
A. Coulomb B. Ohm C. Volt D. Ampere
▪ The body that has designed the IB course is called the IBO, short for International Baccalaureate Organization, headquartered in Geneva, Switzerland and Wales, England.
▪ The IBO expects you to memorize the fundamental units.
The ampere is equivalent to one coulomb (roughly 6.241×1018 electrons) per second
One Ampere is defined as that current flowing in each of two infinitely‑long parallel wires of negligible cross‑sectional area separated by a distance of one metre in a vacuum that results in a force of exactly 2 x 10‑7 N per metre of length of each wire.
Learning Intentions
Fundamental and derived SI units
▪ In the sciences, you must be able to convert from one set of units
(and prefixes) to another.
EX: Suppose the rate of a car is 36 kmh-1, and it travels for 4 seconds.
What is the distance traveled in that time by the car?
▪ distance: s = vt.
s = 0.04 km
= 211.2 ft FORBIDEN
Dimensional analysis
▪ You can use units to prove that equations are invalid.
EX: Decide if the formulas are dimensionally consistent. The information you need is that v is measured in m/s, a is in m/s2, x is in m and t is in s.
(a) v = at2 (b) v2 = 3ax (c) x = at2
Inconsistent Consistent Consistent
▪ The process of substituting units into formulas to check for
consistency is called dimensional analysis.
▪ DA can be used only to show the invalidity of a formula.
Both (b) and (c) are consistent but neither is correct.
They should be: v2 = 2ax and x = (1/2)at2.
numbers don’t have units
Fundamental and derived SI units
Unit for any quantity that is measured or calculated in physics (generally science) is combinations of seven basic /fundamental units.
Derived units are combinations of 7 basic ones.
▪ Speed - measured in meters per second (m s-1).
▪ Acceleration - measured in meters per second per second (m s-2).
▪ Mass density - measured in kilograms per meter3 (kg m-3).
Swine flu virus: diameter of 10 to 300 nanometers (nanometer is equal to one billionth of a meter)��0.0000000000001m becomes 1.0 x 10-13m
Scientific notation and prefixes
Scientific notation and prefixes
Very large and very small numbers: either scientific notation or prefixes should be used
Power of 10 Prefix Name Symbol
10 -12 pico p
10 -9 nano n
10 -6 micro µ
10 -3 milli m
10 -2 centi c
10 3 kilo k
10 6 mega M
10 9 giga G
10 12 tera T
13 700 000 000 = 1.37 × 1010 years = 13.7 billion years
EX:
scientific notation prefix
2. electron mass = 0.000 000 000 000 000 000 000 000 000 000 91 kg
= 9.1 × 10-31 kilograms
Recall that normalized scientific notation requires the expression of a number as a power of 10 multiplied by a factor between 1 and 10. Thus 1.2×103 is 1200, and 12×102 is also 1200, but 1.2×103 is in normalized scientific notation whereas 12×102 is not. Express 61200 in normalized scientific notation.
-53 ks
9.72 Gs
7.51 ns
4.321768 ks
200 ms
EXAMPLE: http://en.wikipedia.org/wiki/Scientific_notation#Normalized_notation
0.00354 m
= 3.54 x 10-3 m
= 3.54 mm
Scientific notation and prefixes
individually:
= 3.004 X 10-5
= 4.56 X 10-2
= 1.045004 X 106
= 9.34 X 103
= 0.0010053
= 53020
Smaller units
every step is 10± 1 power
They are grouped into steps 10± 3
femto pico nano micro mili kilo mega giga tera
f p n μ m k M G T
base unit
1
Larger units
10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012
centi (c) deci (d)
10-2 10-1
NEXT: Unit conversions involving SI unit prefixes
form smaller unit to larger unit →
expect smaller number
= 1
or
Chemistry
from larger unit to smaller unit →
expect bigger number
or
Chemistry
= 1
EX:
EX:
The wavelenagth of green light is 500 nm. How many meters is this?
I have 906 gigabyte hard drive on my computer.
How many bytes of data will it hold?
4.3 x 104 ns = ? µs
5.2 x 108 ms = ? ks
EX:
EX:
EX:
EX:
EX:
DID YOU KNOW?
A dime is 1.0 mm thick.
A quarter is 2.5 cm in diameter.
The average height of an adult man is 1.8 m.
Diameter of a red blood cell ≈ 8 μm
Diameter of atomic nucleus ≈ 5 fm
Diameter of the atom ≈ 100 pm =100 000 fm
If an atom were as big as a football field nucleus would be about the size of a pea in the centre.
Conclusion: you and I and all matter consists of almost entirely empty space.
Diameter of Earth ≈ 13 Mm
Diameter of sun ≈ 1.4 Gm
Diameter of Milky Way ≈ 9500 Tm
visible universe is thought to be around 1025 m
Scale of the Universe
EX:
7.2 m3 → mm3
75 g/cm2 → kg/m2
100 mm3 → m3
72 km/h → m/s
20 m/s → km/h
EX:
EX:
EX:
EX:
EX:
Done with
units (fundamental and derived)
scientific notation
prefixes
Forward to …..
Accuracy is the closeness of agreement between a measured value
and a true or accepted value
Precision is the degree of exactness (or refinement) of a measurement
(results from limitations of measuring device used).
No measurement can be "exact". You can never, NEVER get exact value experimentally
Uncertainty and error in measurement
Error in measurement is expected because of the imperfect nature of our measuring devices.
The inevitable uncertainty is inherent in all measurements.
It is not to be confused with a mistake or blunder
What is the length of the line?
Significant figures
EX:
▪ A ruler is an analog measuring device.
▪ So is a voltmeter with a needle.
0
1
certain digit:
1
certain digit:
2
uncertain digit:
7 or 8
estimate
SIGNIFICANT FIGURES are all certain (reliably known) digits + one uncertain (estimate)
1.28 units
tenths place
09.4
00.0
▪ On the other hand, if measuring with digital
measuring device, one doesn’t know if the last digit
is the result of rounding up, or rounding down
or it is the measured digit.
SIGNIFICANT FIGURES are all certain
(reliably known) digits + one uncertain (last one)
tenths place
09.4
0.
▪ On the other hand, if measuring with digital
measuring device, one doesn’t know if the last digit
is the result of rounding up, or rounding down
or it is the measured digit.
SIGNIFICANT FIGURES are all certain
(reliably known) digits + one uncertain (last one)
Estimating quantities to an appropriate number of sig. fig.
How long is this line?
It is 1.28 cm (or maybe 1.27 cm) long
▪ The 1 and the 2 are the certain digits.
▪ The 8 (or 7) is the uncertain digit
What is the reading on each of the graduated cylinders?
Which digits are uncertain.
EX:
EX:
(A) (B)
Read to the bottom of the meniscus.
(A) reads 52.8 mL. The 8 is uncertain. (B) Reads 6.62 mL. The 2 is uncertain.
SIGNIFICANT FIGURES are reliably known digits + one uncertain (estimate)
(1) All non-zero digits are significant.
(2) All zeros between non-zero digits are significant.
(3) Filler zeros to the left of an understood decimal place are not significant.
(4) Filler zeros to the right of a decimal place are not significant.
(5) All non-filler zeros to the right of a decimal place are significant.
438 g
26.42 m
0.75 cm
3
4
2
12060 m
900.43 cm
4
5
220 L
60 g
30. cm
2
1
2
0.006 L
0.08 g
1
1
8.0 L
60.40 g
2
4
Significant figures in calculations
∙Multiplication and division – round your answer to the same number of significant digits as the quantity with the fewest number of significant digits.
∙Addition and subtraction – round your answer to the same number of decimal places as the quantity with the fewest number of decimal places.
(1.2 cm)(2 cm) 2.4 cm2 2 cm2
π(2.75 cm)2 7.5625 cm2 7.56 cm2
5.350 m/2.752 s 1.944040698 m/s 1.944 m/s
(0.0075 N)(6 m) 0.045 Nm 0.04 Nm
0.00530 m – 2.10 m -2.0947 m -2.09 m
1.2 cm + 2 cm 3.2 cm 3 cm
2000 m+2.1 m 2002.1 m 2000 m
Find: calculator result: proper result:
Mass of universe 10 50 kg
Diameter of universe 10 25 m
Diameter of galaxy 10 21 m
Age of universe 10 18 s
Speed of light 10 8 m s-1
Diameter of atom 10 -10 m
Diameter of nucleus 10 -15 m
Diameter of quark 10 -18 m
Mass of proton 10 -27 kg
Mass of quark 10 -30 kg
Mass of electron 10 -31 kg
Planck length 10 -35 m
Orders of magnitude
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
EX:
Given that the smallest length in the universe is the Planck length of 10 -35 meters and that the fastest speed in the universe is that of light at 10 8 meters per second, find the smallest time interval in the universe.
▪ speed = d / t
▪ t = 10 -35 / 10 8 = 10 -43 seconds
Find the difference in order of magnitude of the mass of the universe (10 50 kilograms) to the mass of a quark (10 -30 kilograms ).
▪ Make a ratio (fraction) and simplify.
▪ 10 50 kilograms / 10 -30 kilograms = 10 80.
▪ Note that the kilograms cancels leaving a unitless power of ten.
▪ The answer is 80 orders of magnitude.
EX:
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
▪ Diameter of nucleus is 10 -15 m.
▪ Diameter of atom is 10 -10 m.
▪ 10 -15 m / 10 -10 m = 10 -15 – (-10) = 10 -5.
EX:
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
▪ The “92” in 92Sr means 92 nucleons.
▪ The mass of nucleons (protons and neutrons) is of the order of 10 -27 kg.
▪ 92 is of the order of 10 2.
▪ Thus 10 2 × 10 -27 kg = 10 -25 kg.
EX:
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
EX:
∙VEarth = 10 12 km3 = 10 12 × (10 3) 3 = 10 12 + 9 = 10 21 m3.
∙Vsand = 1 mm3 = 10 0 × (10 -3) 3 = 10 0 - 9 = 10 -9 m3.
∙Nsand = VEarth / Vsand = 10 21 / 10 -9 = 10 21 – (-9) = 1030
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
Estimation revisited
∙Another form of estimation is to solve complex problems with the simplest math possible and obtain a ballpark figure as an answer.
∙If at all possible, only powers of ten are used.
EXAMPLE: NY and LA are separated by about 3000 mi and three time zones. What is the circumference of Earth?
∙ Since 3000 mi = 3 TZ, 1000 mi = 1 TZ.
∙ There are 24 h in a day – 24 time zones.
∙ 24 TZ in one circumference, or 24×1000 mi = 24000 mi.
Quoting and comparing ratios, values and approximations to the nearest order of magnitude
The human heart rate is about 75 beats per minute.
This is between 10 1 (10) and 10 2 (100).
∙But 1 hour is 60 min, which is also between 10 1 (10) and 10 2 (100).
∙Then our answer is between 10 1 × 10 1 = 10 2 and 10 2 × 10 2 = 10 4.