Los Altos AP Physics 1Motion Lab
Introduction to Physics – Observing, Measuring, Analyzing & Describing Motion
Physicists observe and analyze nature in an attempt to understand natural phenomenon and to predict the behavior of matter and energy in the universe. The primary language physicists use in their analysis is mathematics. The reason your education in mathematics has focused on arithmetic, geometry, algebra, trigonometry and soon calculus is to prepare you to study physics. Like a creative writing class in a verbal language, this class will teach you to write the story of natural phenomenon in the language of mathematics.
This week long activity is designed to help you get into the spirit of thinking and communicating like a physicist. Use my example as a guide and analyze the motion of the air hockey puck with the fastest speed. The full resolution image for better analysis is located on our class website:
You should use a separate sheet of paper to complete this exercise. Notice the following qualities of my example and include them in yours:
Diagram – A sketch or picture of the situation you are observing. In my example, I used an actual image taken with a camera. I could have drawn a similar diagram. Write descriptions and known conditions on the diagram. The goal is to communicate to another physicist what you observed and what facts you know.
Measured Data Table – An organized list of what I observed and measured in the original units they were measured in. The table was created with vertical lines between columns and horizontal lines between rows. The top or header of each column describes both the meaning of the column and the units of measure. I did my best to estimate each distance measurement to within a few tenths of an inch. I included the uncertainty of my measurement to tell other physicists how precise my measurements were.
Calculated Results Table –An organized list of ordered pairs created from converting measured data into the international standard (mks) metric unit system: Length – Meters (M), Mass – Kilograms (Kg) & Time – Seconds (S). I purposely organized my results to form ordered pairs for easy graphing. I considered time to be the independent variable and Distance to be the dependent variable; Distance as a function of Time compared to the algebraic general form of Y as a function of X. When I converted the number of flashes to time and the number of inches to meters I used significant figure rounding rules.
Graph – The graphical space covered nearly half the area on the page. The coordinate axes are made from vertical and horizontal lines. Each axis is labeled with both a description and the MKS units of measure. Each axis is scaled using the domain and range of the ordered pair data to be plotted. I always try to use about 90% of my graphical space to display data. In this example, the domain of time span between zero and just below six tenths of a second. I placed tick marks at eight equal intervals and chose a scale of 0.080 s for each tick mark. The distance data ranged between zero and one and a half meters. I placed tick marks at ten equal intervals and chose a scale of 0.150 m for each tick mark. There are a variety of techniques to figure out what scale to use, I simply count be ones, twos, tenths or thirds until my data fits within my graphs space. Maximum value divided by number of tick marks works too.
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We will discuss the analysis and title portions of this activity on Tuesday, in class.
Analysis – The reason physicists like to graphically represent data is because we can visually see predictable mathematical patterns that exist between quantities that we observe and measure. In this example there is a linear relationship that exists between distance and time. The constant slope of the mathematical “trend line” that runs through the data is a measurement of the puck’s constant speed sliding across the table. Once a trend line is drawn continuously through the data points, two points near the ends of the line (not data points) will be identified and the slope between them will be calculated. The two points should be indicated with different markers than data and their coordinates should be clearly labeled as ordered pairs. The calculation for the slope should not appear on the graph, only the result should appear. The slope should be rounded using sigfigs with units and include a brief description of its meaning.
Title–The title should clearly communicate the results of the graphical analysis. It should state what kind of mathematical relationship is present (linear, inverse, quadratic, exponential…) and that the meaning of the slope, intercept, or other coefficients mean. The title should also include the numerical result + units. The title should not state DISTANCE VS. TIME or GRAPH OF DATA. Agood title for this graph would be: There is a linear relationship between the distance the puck traveled and time. The slope of the best fitting trend line is 2.4 m/s, which is a measure of the puck’s speed.