SCI 403 J.
Marinay
Physics I
Intro:
- physics is a way of thinking based on experiments with numerical results that can be reproduced
by others
- mathematics is the language of science
Measures of Science:
- a measurement is a comparison between an unknown quantity and a standard
- to be considered valid, the measuring device must be compared against a widely held standard
- the standard must be readily available, reproducible and constant over time
- the French developed our current system of measurement in 1795; it is called the metric system
- until this time, communication among scientists was difficult because the units of measurement
were not standardized
- the metric system uses standards of measurement that are divisible by powers of ten
- the Systeme Internationale d'Unites (SI) keeps the standards of length, time, and mass to which
instruments are calibrated
SI & The United States:
- although the US still uses the English system of measurement, Congress officially committed the
country to the metric system many years ago
- in 1875 Congress signed the Treaty of the Meter which bound the US as well as sixteen other
countries to the metric system
- today, the US is one of only three countries to not use the metric system (Liberia and Myanmar
are the other two)
- the inherent ease of use and the economic benefits of switching to the metric system should
eventually help sway the US population to move to the metric system
Units:
- there are seven base units which serve as the foundation of the SI
- there are many derived units which are combinations of the seven base units
- the seven base units are the meter (length), kilogram (mass), second (time), kelvin (temperature),
mole (amt. of substance), ampere (electric current), and candela (luminous
intensity)
SCI 403 J. Marinay
Physics I
- the base units have been measured in different ways over the years; some of those changes are
listed below:
A) Length:
- the meter was first defined as 1/10,000,000 of the distance from the north pole to the equator
- the meter was then defined as the distance between two lines engraved on a platinum/iridium bar
- today, the meter is defined as the distance traveled by light in a vacuum during a time interval of
1/299,792,458s
B) Time:
- the second is defined today as the frequency of one type of radiation emitted by a cesium-133
atom
- a leap second is added every few years as the Earth's rotation slows
C) Mass:
- the standard is a small platinum/iridium metal cylinder kept at a very controlled temperature and
humidity
- the last base unit measured by a physical standard; scientists are trying to find new ways to
measure this base unit
Scientific Notation:
- many of the numerical values of the multipliers are very small or very large; it becomes
cumbersome to write out so many zeros, so we abbreviate them using scientific notation
- to convert a number to scientific notation, change the numerical part of a quantity to a number
between one and ten; this number is then multiplied by a whole number power of ten
- Ex. the number 198,000,000,000 becomes 1.98 1011
- Ex. the number 0.00000000082 becomes 8.2 10 10
SCI 403 J. Marinay
Physics I
Accuracy and Precision:
- experimental results may be classified by:
A) Accuracy - how well the results of an experiment agree with the standard value
B) Precision - degree of exactness of a measurement
- it is possible to make precise measurements with an instrument that are not accurate and vice
versa
Measurement Techniques:
- to assure accuracy and precision, one must correctly read the measuring instrument
- a common problem is parallax; parallax is the apparent shift in the position of an object when it
is viewed from different angles
- Ex. if you read a meter stick from the side, you may incorrectly read the length of an object;
therefore, you need to read it directly above the stick
Significant Digits:
- significant digits are the valid digits in a measurement; the more precise an instrument, the more
significant digits can be measured
- Ex. a meter stick with only decimeters marked will give you a less precise reading than one with
both decimeters, centimeters, and millimeters marked
- to properly read significant digits on an analog (non-digital) instrument, you read it to the smallest
marking and then estimate the last digit to the nearest tenth (0.1) of the smallest marking
Which Digits Are Significant:
- follow these rules for determining which digits are significant
A) Non-zero digits are always significant
Ex. 26.38 mm = 4 sig. digits
Ex. 7.94 mL = 3 sig. digits
B) Any zeros between two significant digits are significant
Ex. 406 g = 3 sig. digits
Ex. 28.09 nm = 4 sig. digits
C) A final zero or trailing zeros in the decimal portion only
are significant
Ex. 0.00500 K = 3 sig. digits
Ex. 0.03040 m/s = 4 sig. digits
- these zeros are not significant
A) Space holding zeros on numbers less than one
Ex. 0.00500 N = 3 sig. digits (red zeros are not sig.)
B) Trailing zeros in a whole number
Ex. 200 km = one sig. digits
Ex. 25,000 A = two sig. digits
SCI 403 J. Marinay
Physics I
Addition/Subtraction with Sig. Digits:
- in any calculation with significant digits, your answer cannot be more precise than the least
precise measurement
- to add or subtract measurements, first perform the operation, then round off the result to
correspond to the least precise value involved
Ex. 24.686 m + 2.343 m + 3.21 m = 30.239 m
3.21 m is the least precise value (accurate to the hundredths of a meter, the other two terms are
accurate to the thousandths); the above answer should be reported with the same amount of
precision; this requires you to round-off the value, 30.239 m, to 30.24 m; you will report the correct
calculated answer as 30.24 m
Multiplication/Division:
- a different method is used to find the correct number of significant digits when multiplying or
dividing measurements; after performing the calculation, note the factor that has the least number
of significant digits; round the product or quotient to this number of digits
Ex. 3.22 cm x 2.1 cm = 6.762 cm2 corrected to 6.8 cm2
Uncertainty When Counting:
- sig. digits are only used in measurements and not with counting
Ex. if you count four pencils, this number has no uncertainty
SCI 403 J. Marinay
Physics I
SCI 403 J. Marinay
Physics I
SCI 403 J. Marinay
Physics I
SCI 403 J. Marinay
Physics I
SCI 403 J. Marinay
Physics I
What is the density of mercury (13.6 g/cm3) in units of kg/m3?
How many atoms of hydrogen can be found in 45 g of ammonia, NH3?
SCI 403 J. Marinay
Physics I
SCI 403 J. Marinay
Physics I
