Physics Unit 1 Notes -Measurement
Physics studies the behavior, structure and properties of matter from the subatomic scale to the entire universe. The study of physics encompasses quantum physics, which predicts and explores the world below the atomic level and ranges all the way to cosmology which deals with the origin and structure of the entire universe. As recently as the 1800's Physics, Chemistry and Biology was just science and no distinction was made between them. As the sciences became more specialized we have separated these studies. Physics explores our physical universe and uses mathematics and mathematical models to explain and predict our universe.
As a quantitative science, measurements and calculations involving those measurements are central to this field. That is what we will first need to master.MEASUREMENT:
All science uses measurements in the scientific process. For scientist all over the world a common language is needed so the measurements will be uniform. That system is the Systeme Internationale or the SI system. We refer to it as the metric system. It is far simpler than our English system. The SI is based on powers or multiples of ten. The prefixes prior to the unit itself tell us how many times to multiply the unit times ten. Prefixes you MUST know are
Kilo - 1000 times
Deci - 1/10
Centi - 1/100
Milli - 1/1000
Micro - 1/1,000,000 or 1x10 6 or 1/ millionth
Nano - 1/1,000,000,000 or 1 x 10 9 1 /billionth
Pico - 1/trillionth or 1 x 10 12
For example a "deci meter" means literally "1/10 meter" and a kilogram means 1000 grams. To make it easier to remember connect the prefix to something you are already familiar with.
Deci comes from same root word that decade does we know a decade is 10 years. Centi comes from same root that we get century so 100 is easy to remember. Also Milli comes from millenium so 1000th should be easy also.
UNITS:
Units used to measure a basic quantity are called Fundamental Units. There is no simpler quantity than a fundamental unit . The fundamental units we will use are:
Length - meter
Mass - kilogram (or gram in small quantities)
Time - second
Temperature - Kelvin, although we usually use Celsius. A Celsius and a Kelvin degree are the same size; they just start at different points
Some measurements will combine fundamental units. These are Derived Units, combinations of fundamental units, like meters per second, M/S
When using these units remember there is a major difference between mass and weight. MASS is simply how much matter an object contains. WEIGHT is how much force gravity exerts on that mass.
Mass is constant anywhere in the universe, Weight will vary depending on where you are, even on the Earth.
On Earth we "weigh" an object with scales or on a balance to determine its mass.
Also when working with mass, the kilogram is a relatively large unit so we often use the smaller gram as a unit of mass.
Density is an example of a derived unit. Density measures how much matter is in a given space. The equation for Density is
D = M/V You can see from the equation the units will be a union of two fundamental units, grams and dm3.
When using these measurements we must consider two factors, accuracy and precision.
Precision how closely measured quantities agree with each other. For example we take 3 measurements of length, M1 = 2.475 cm, M2 = 2.473 cm and M3 = 2.476 cm. All are very close thus our measurements are precise.
Accuracy - how closely these measurements agree with an accepted value. If the above measurements were for an object that was 2.900 cm they may have been precise but they were not accurate.
To be precise we must be careful with our instruments. To be accurate we must agree with some standard.
Any measured quantity has a certain amount of uncertainty due to the ability to read the instrument beyond its measured divisions. For example a meter stick can measure to the 1000th of a meter exactly with its mm divisions but when a measurement fall between two mm marks we must estimate its value. In measurements we measure to the limit of the instrument then estimate one digit. The number of reliable digits in a calculation are the "significant figures". When we use digits other than these in our answers we increase uncertainty in the final values because we used uncertain values to arrive at the answer. Significant figures are important in getting valid results in our experiments and calculations. The following rules show how to apply and use significant figures.
SIGNIFICANT FIGURES:
In real life you can not get a perfect measurement. You always read to the limit of your instrument then estimate one more digit. When doing calculations we must take into account this uncertainty. A calculation can't be more precise than its least precise quantity. So the rules for calculations involving significant figures are as follows:
a) Any number that isn't a zero is significant.
3.567 has 4 sig figs
239 has three
b) Zeroes without non zeroes in front of them aren't significant. They are simply place holders.
.005 has only one sig fig
.00303 has three
c) Zeroes between non zeroes are always significant.
306 has three
1005 has four
d) Zeroes at the end of a number are significant only if the number contains a decimal point
200 has only one sig figs
200.01 has five sig figs
200.0 has four sig figs
e) Counting numbers, numbers in equations and conversions are considered to be exact, in other words they have an infinite number of significant figures.
When multiplying or dividing significant figures, express your answer with the same number of significant figures as the number with the fewest significant figures.
When adding or subtracting significant figures, your answer cannot have more numbers to the right of the decimal than any of the original numbers.
Factor Label
When using measurements we often must convert one quantity into another. We may need to change meters to cm or grams to kg. There is a simple method to do this Factor Label
Four steps to factor label
1. Change your given quantity to a fraction by either placing it over one if it is a fundamental unit or over the other unit if it is a derived unit.
2. Extend your divisor bar and place the unit to be canceled on the opposite side of the bar from where it is originally. Place no numbers before it at this time.
3. Place the units you are changing into on the other side of the divisor bar.
4. Now place numbers in front of these units so they will be equal to one. Anything divided by itself equals one so 100cm/1m equals one for example. Multiply and cancel. You have converted these units.
Example : convert 2.44 km into meters
2.44 km 1000m =
1 1 km 2, 440 meters
With this you need never memorize when to multiply and when to divide. The equation works that out for you. You may remember this from Chemistry. It is a powerful tool for our math exercises.
Graphing Data
We often display the results of our calculations pictorially or graphically. Remember when using graphs the independent variable is always placed on the X axis and the variable whose value depends on our manipulations goes on the Y axis.
We will use graphing calculators extensively as well as a Graphical Analysis program on the computers. This program has the ability to accept data and list directly from a TI calculator and graph it as well as analyze the resulting graph.
Graphs can be generated from lists stored in the calculator. In most TI's you find the "list" button then choose the "edit" option to enter data. When you get to this window you can enter the data one item at a time or you can input an equation in the top window of the list and it will fill the entire list for you.
"StatPlot" will allow you to turn a specific graph on. You can graph more than one graph at a time and this feature allows you to turn the graphs off and on.
"zoom" will allow you to fit the graph to the screen.
"Trace" enables you to find the value at a specific point by using the cursor to mark and read the values at that point.
The computer as well as the calculator allows analysis using regression ('calc" option under "lists") which basically places a "best fit" line through the data you are working with.
