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Astronomy 1402 Department of Physics and Geology
Units and Graphing
Equipment Needed Quantity Computer with DataStudio Software 1
Part 1: Background - Units and Graphing
1.1 SI Units (Metric System)
Careful measurements are an important part of science. Two major systems of measurement prevail in the world today: the United States Customary System (USCS, formerly called the British system of units) and the Système International (SI) (also known as the International System or as the Metric System). The SI system is the standard unit system used in the world of science and everywhere else, other that the U.S. and Burma where the USCS system is still in use. The SI system contains basic units for length, mass and time.
SI unit Symbol length Meter m mass Kilogram kg time Second (^) s electric current Ampere A temperature Kelvin K
Table 1.
To represent very large numbers and/or very small numbers, the powers of 10 and their prefixes are quite useful. Since the SI system uses the decimal system, physical quantities can be easily represented by combining metric prefixes with basic SI units. (Example, 6 million 2 hundred thousand grams = 6,200,000 g = 6.2 x 10 6 g = 6.2 Mg)
Table 1.2 Metric Prefixes and Their Value
Prefix Value
Atto- 0.000 000 000 000 000 001 Femto- 0.000 000 000 000 001 Pico- 0.000 000 000 001 trillionths Nano- 0.000 000 001 billionths Micro- 0.000 001 millionths Milli- 0.001 thousandths Centi- 0.01 hundredths Deci- 0.1 tenths UNITY 1 ones Deka- 10 tens Hecto- 100 hundreds Kilo- 1,000 thousands Mega- 1,000,000 millions Giga- 1,000,000,000 billions Tera- 1,000,000,000,000 trillions Peta- 1,000,000,000,000, Exa- 1,000,000,000,000,000,
Table 1.3 Metric Prefixes and Their Value in Powers-of-Ten
Prefix Symbol Power-of-Ten
Atto- at’toe a 10 - Femto- fem’toe f 10 - Pico- pee’ko P 10 - Nano- nan’oe n 10 - Micro- my’kroe μ 10 - Milli- mil’I m 10 - Centi- sen’ti c 10 - Deci- d 10 - UNITY l 100 = Deka- da 10 Hecto- h 102 Kilo- kil’oe k 103 Mega- meg’a M 10 6 Giga- ji’ga G 10 9 Tera- ter’a T 10 12 Peta- pe’ta P 10 15 Exa- ex’a E 1018
The Pythagorean Theorem relates each side of the triangle by
c^2 = a^2 + b^2
and the angle θ is related to the sides of the triangle by the following trigonometric functions:
sin θ = b / c ; θ = arcsin ( b /c)
cos θ = a / c ; θ = arccos ( a / c )
tan θ = b / a ; θ = arctan ( b / a )
1.5 Graphing
In science it is very important to find and understand the relationships between variables. Using tables and graphs are just two ways that we can represent data to clearly show interrelationships.
A graph is simply a picture of the collected data from some experiment or other source. It is a visual presentation in which trends and relationships between data sets may be made clear. There are many different types of graphs. The most common forms of graphs include bar and linear graphs and pie charts. Below you can find examples of these graphs. Depending on the specific purpose of the graph, should be the type of graph you should choose, but some results are best shown by a particular form. Historical data, such as the population of Hidalgo County, might be best shown as a bar graph, while the speed of a car might be better shown as a rectilinear graph. Throughout the semester you will make many linear graphs.
a. Bar Graph b. Pie Graph
c. Linear Graph
A linear graph shows how one quantity varies as a second quantity is changed. These are called the dependent and independent variables. Traditionally the independent variable is plotted along the
( 1 )
horizontal axis (also known as x -axis), called the abscissa, while the dependent variable goes on the vertical axis (also known as y -axis), called the ordinate. The intersection of the two axes is called the origin, and is usually the point of zero value for each variable. The graph itself is the line drawn through (or near) the data points showing the relationship between the two variables in a visual form.
The following is a list of rules for drawing a graph.
- Select a title for the graph which tells what the graph represents.
- Select a scale for each of the axes. These scales should be chosen so that the data can all be plotted on the page and that the graph will fill as much of the page as possible. Selecting the proper scale will make it easier to locate points. The scale must be laid off uniformly along the axes, but each axis can have a different scale.
- Label each axis. Tell what each scale represents, including the units of measurement.
- Carefully plot each of the data points by placing a small dot at the intersection of the ordinate and abscissa corresponding to the values of the variables. Draw a small circle around the dot.
- After all the data has been plotted, join the dots with a smooth curve. This may be a straight line. The curve might not pass through all of the points plotted. We expect some error in our data and the fact that the curve may not pass through all the points may be an indication that there is some error in our data. The curve should come as close to as many points as possible. This is especially required when the data points are to be fit with a straight line. Use a clear ruler (for a straight line) and make the line pass as near as practical to each data point. Do not use just the first and last point; they are no better or worse experimental points than the others.
SAFETY REMINDER
- Follow the directions for using the equipment.
Part 2: Lab Activity – Units and Graphing
The purpose of this laboratory activity is to remember the SI Unit system, practice simple measurements of fundamental physical and astronomical quantities in SI units, and to familiarize yourself with DataStudio software that will be used in other labs in ASTR 1402. You will also perform conversions between units and angular measurements and solve right triangles.
2.1 Graphing
2.1.1 Data Studio Software
Using the data and the procedure below, create a simple linear graph.
x -axis Force (N)^5 10 15 20 25
y -axis Length (cm)^ 3.17 3.56 3.92 4.35 4.74 5.
Computer Setup:
a) Start the DataStudio software b) Once the software starts up a screen similar to the one pictured here will appear. Select Enter Data.
Entering Data Table:
a) Two windows will appear as shown. On the right side of the screen will be the Data Table window and on the left will be the graph area. Using the data table above, enter the x and y pairs to be graphed. You will notice that as you enter the data into the data table, the points will begin to appear on the graph and the scales will automatically adjust to make the graph take up as much space on the window as possible.
b) Click Summary ( ) in the top of the screen. A window will appear on the left of the data table.
c) Add the title to your graph. In the Displays ( )section of the window on the left, click on ‘Graph 1’ and change it to what you want the title of your graph to be (for example “Length vs. Force”).
d) Add the label and units for each axis. In the Data section ( ) of the window on the left, double click on ‘Data’. A new window will open. In this new window select the ‘General’ tab. Change the variable name from ‘X’ to what your label for the x -axis is (for example, “Force”) and under units type in the units for this same axis (for example, “N”). In the drop down menu of the variable name select ‘Y’ and replace ‘Y’ with your label for the y -axis of your graph (for example, “Length”) and under ‘units’ type in the units for this same axis (for example “cm”). e) Click ‘Summary’ in the top of the screen to remove the left window.
Analyzing the Data:
a) Click ‘Fit’ ( ) in the Graph toolbar and select ‘Linear Fit’. This will draw the linear fit line and a text box will appear on the graph with the y intercept and slope automatically calculated by the computer. Record the slope and y intercept in the lab report section. b) Using the slope and y intercept from the computer, find the equation of the line and record it in the lab report section. c) Print a copy of the graph and attach it to the lab report section. d) Explore the options in the graph area to become familiar with the program.
