Physics 1 Lab report

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Aerodynamic Drag Forces and Falling Objects

Equipment: coffee filters, metal spheres, foam cushion 2 m stick, timer, micrometer, tape The force of gravity that acts on an object only depends on the mass of the object, not its size (volume) or shape. Forces related to fluid flow like lift and frictional drag depend on the shape of the object, the properties of the fluid the object moves through (e.g. air) and speed. Both gravity and drag act on falling objects and the resulting motion depends on both forces. When both forces balance, a falling object will move with a constant speed called a terminal speed. By studying the factors that affect the terminal speed of an object we can learn about the drag force that acts on the object. Activity I: Terminal Speed a. Obtain a metal sphere and a coffee filter. Have someone in your group hold a 2 m stick vertically while someone else drops each object from the top of the stick. Place a cushion on the floor to catch the falling object (especially needed for the sphere). Describe the speed of each object. Does it appear to be speeding up or moving at a constant speed? b. Study the motion of the coffee filter closely and determine a distance interval over which you can safely conclude (based on your observations, not measurements yet) that the speed is constant. The filter is said to have reached terminal speed or terminal velocity at the point where it stops accelerating and its velocity remains constant. How could you demonstrate that the speed is constant over the interval? Describe a procedure and discuss it with the instructor. After you talk to the instructor carry out the procedure and list your data below. Discuss your results.

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Activity II: Does the Terminal Speed Depend on Surface Area? a. Determine the cross-sectional ("into the wind") surface area of the filter assuming it is circular in shape. Use the same distance units as you used for your speed measurements. Open Filter Area:_____________ b. Design a procedure that could be used to vary the "into the wind" surface area and determine a numerical value at each step using the measurement you made in part a. That is, how could you do this without making length measurements at each step? Describe the procedure. c. Conduct an experiment to determine if and how the terminal speed of the filter depends on surface area. Several factors need to be considered: (1) Your measurements need to be confined to the distance interval over which you can safely conclude that the filter is falling at a constant speed. You can do this by observation. You don't have to keep demonstrating it as in Activity I. (2) Timing measurements introduce errors based on reaction time. Averaging several measurements is a way to reduce the effect of the errors if they are random. (3) You need to get a good range of data to conclude anything. Discuss your procedure with the instructor and then proceed. Create a data table (or tables) to record your measurements. d. Represent your data on a graph. At this point confine your interpretation of the trend (if any) in the graph within general categories. For example: Is there a dependence? If so, is the dependence direct or inverse, linear or nonlinear. If you wish to add a trend sketch it. Don't get into fitting any functions yet. We don’t know enough. Discuss your conclusions.

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Activity III: Does Terminal Speed Depend on Volume? a) In the previous activity was the volume of the filter (the volume occupied by the paper) varying or staying the same? Discuss. b) Use a micrometer to determine the thickness of the filter. Use this measurement combined with the area measurement in Activity II to determine the volume of the filter. Thickness_____________ Volume_____________ c. Let's assume all the coffee filters we have are identical. How could you vary the volume of the falling "filter" while keeping its surface area the same? Describe a procedure. Can you keep the mass of the falling filter fixed while varying the volume? Discuss. d. Design and carry out a procedure to determine if and how the volume of a falling filter affects the terminal speed. All of the considerations of your previous experiment need to be factored into the procedure. List your data below. e. As in Activity II represent your data on a graph. At this point confine your interpretation of the graph within general categories. For example: Is there a dependence? If so, is the dependence direct or inverse, linear or nonlinear. If you wish to add a trend sketch it. Don't get into fitting any functions yet. We don’t know enough. Discuss your conclusions.

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Activity IV: Surface Area to Volume Ratio a. In general, but only based on your experiments, describe the factors that affect the terminal speed of a falling filter. b. Here's a way to combine the multiple factors you have considered so far into a single

variable. Compute the surface area to volume ratio (

�

= S V

) for each data point from

Activity II and III. Note S is the "into the wind" area and V is the volume occupied by the paper. Discuss this with the instructor if you have questions. List these values in a table below with the corresponding terminal speed measurements. Note: This ratio has units. c. Does the terminal speed appear to vary with the S to V ratio? If so, how? Is a pattern present. Plot a graph and discuss. d. Sketch or fit a smooth trend to the data. If you use software, use Graphical Analysis. Consider only simple two parameter1 functions such as a power function, y=Ax^B, or a

1 When performing a best fit to data you are optimizing the values that describe a smooth function to minimize the differences between the function and the data. Linear functions are defined by two constants or parameters: the slope and intercept. Power functions are

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line y=mx+b. Limiting yourself to two parameter functions is a conservative approach that does not lend too much weight to scatter in the data or outliers. If you use a power function choose an integer or rational power (e.g. 1 , 1/2 ,2 etc.) and use the manual fit option in Graphical Analysis. e. Plot a second graph using the V to S ratio as the independent variable. f. Sketch or fit a smooth trend to this data following the same approach you followed in d. g. These questions are based on the assumption that one of the relationships between terminal speed and either of the surface and volume ratios is direct. For the direct relationship: Is it linear? If so, can you also say it is proportional (linear through the origin)? Discuss. This is not a yes or no answer. Please talk about your data. Is it nonlinear? If so, describe the relationship (i.e. the trend). Now consider the relationship between terminal speed and the other ratio. What relationship would you expect, given the direct relationship you found between terminal speed and the inverse of this other ratio? Discuss. Is this evident in your data? (Note: this may require an additional best fit analysis. Attach additional graphs to your report if needed.)

similar: one parameter multiplies the base and the other is the power to which the base is raised. See Introductory Materials, Section 2.