# Falling Bodies

### Overview:

In this activity, a computer spreadsheet will be used to analyze the motion of a falling object which is encountering air resistance. You will design a scenario that would require the need to know specific information about the motion characteristics of a falling object; you will develop a procedure for analyzing the object's motion, use a spreadsheet program to conduct the analysis, and report your findings in the form of a word-processed paper.

### Directions:

1. Conduct a brainstorming session in which you imagine a variety of scenarios which involves the motion of a falling object and demands knowledge about its trajectory. Many examples will be presented by the teacher. On a separate sheet of paper, list several more examples which you can think of. Allow your mind to run freely. Consider examples from movies, sporting events, television commercials, historic happenings, and science fiction plots.

2. Pick an idea from the list which you have generated that interests you. On the separate sheet of paper, describe the scenario fully in words. Your description should include:

• a description of the object/scenario which you will investigate.
• a list of information which you know about the object and its trajectory (see note below).
• a list of information which you would like to know about the object's trajectory or a list of what if? questions about the object's trajectory which you would like to answer.

### Outcome Variables

1. Mass of object (kg)
2. Surface area of object (m2)
3. Drag coefficient of fluid through which object travels (0.5 for air)
4. Time increment (determines how frequently spreadsheet will recalculate motion parameters)
5. Initial vertical velocity of object (m/s), including direction (up or down)
6. Initial height of object (m)
1. Time (s)
2. Height (m) or Vertical Position
3. Vertical velocity (m/s)
4. Vertical acceleration (m/s2)
5. Air resistance (N)
6. Force of Gravity (N)

3. On the separate sheet of paper, describe a procedure for your investigation. The actual variables which the spreadsheet requires to perform its calculations are called input variables and the actual variables which the spreadsheet will calculate are called outcome variables; these variables are listed in the table above. Include the following information in the description of the procedure:

• a list of values for all the input variables; if a range of values will be used for one of the variables, then list the range.
• a list of those outcome variables with which you will be concerned and a description of what you will be looking for in these values - i.e., an explanation of how you will know that you have accomplished the purpose of the investigation.

When finished with steps 1-3, submit the separate sheet of paper to the teacher for approval.

4. Develop a theoretical description of the falling motion which you have identified. In several organized pages of writing, indicate your understanding of motion concepts by describing the various principles which govern the motion. Such a description should include information about the forces (including free-body diagrams), the acceleration, the graphical descriptions, the relationships between such features as air resistance and mass, time, speed, etc. The theoretical description should be word processed (including diagrams) and submitted as a rough draft.

5. Use the spreadsheet to investigate your question(s) according to the procedure you described in step 3. Make notes of any relevant findings and save your work frequently on a floppy disk. Once you have generated pertinent information about the object's trajectory, construct a spreadsheet chart of relevant values. (A set of directions for creating spreadsheet charts will be provided.) Once the chart has been constructed, save it on your disk and/or electronically copy and paste it into a word processing document.

6. Use a word processor to create a written description of your study. In your description, be sure to include the following:

• a description of the problem (as in step 2)
• an explanation of the procedure used to conduct the investigation (as in step 3)
• a discussion of the theoretical background (as in step 4)
• the results of your investigation (posibly organized in row/column format) - i.e., a summary of what you determined
• a spreadsheet chart which is electronically copied and pasted into the document; make reference to the chart and thoroughly discuss its meaning
• a description of how important motion parameters (velocity, acceleration, net force, air resistance, etc.) change with time and an explanation of why they do change as they do with time

The following table lists relevant information for various objects which could be (but don't need to be) the focus of your investigation.

### vt (m/s)

Skydiver

75

0.7

60

0.145

.0042

33

0.046

.0014

32

.00048

.000079

14

.000034

.000013

9.0

The drag coefficient, C, is assumed to be 0.5 in each case.

### Due Dates:

The following due dates have been tentatively assigned for the completion of your project.

 Selection and Description of Idea (steps 1-2) 10/9 Formulation of a Procedure (step 3) 10/19 Development of a Theoretical Background (step 4) 10/14 Manipulation of Spreadsheet and Construction of Chart (step 5) 10/17 Submission of Word Processed Report (step 6) 10/20