## The Gravity of the Situation

### Linda Knowles

#### Description

Students drop a ball and record its position using a CBL and a TI89 graphing calculator. The data collected will then be transferred to an EXCEL spreadsheet and a quadratic curve of best fit will be generated and compared to expected results.

#### Objectives

Solves real-world problems involving rated measures ( miles per hour, feet per second).

Interprets data that has been collected, organized, and displayed in charts, tables, plots.

Designs and performs real-world statistical experiments that involve more than one variable, then analyzes results and reports findings.

#### Materials

-Pencil
-Paper
-Graphing Calculator (TI89)
-CBL with motion probe
-Computer with Microsoft EXCEL Spreadsheet
-Soccer ball

#### Preparations

1. Locate a TI89 graphing calculator, a CBL (Calculator Based Lab) with motion probe, and a soccer ball for each group.
2. Secure use of the computer lab with access to EXCEL spreadsheet.

#### Procedures

Prior knowledge required: Students must be able use an EXCEL spreadsheet and the physics program on a TI89 graphing calculator. They must also know that an equation for the position of an object in freefall towards the earth is s(t) = -.5gt2 + v0 t + s0 (s is in meters, g=9.8 m/s2 , t is in seconds, v0 is initial velocity at t=0 and s0 is initial position at t=0).

1. Review on the board or overhead the formula s(t) = -.5gt2 + v0 t + s0 . Remind them that in our experiment that we are dropping the soccer ball so our initial velocity v0 is zero. Since time is measured in seconds, position is measured in meters and g=9.8 m/s2, the expected graph in our experiment is s(t) = -4.9t2 + s0 . s(t) is the position or in this case the height the soccer ball is above the ground at a certain time (t).

2. Place students in groups of three.

3. Pass out to each group a TI89, CBL and a soccer ball.

4. Connect the CBL with the motion probe to the TI89 graphing calculator.

5. Activate the physics program on the TI89.

6. Use for “Time between samples”: .02 seconds
Use for “Number of samples”: 40
Notice that these settings allow for a total of .8 seconds for the length of this experiment. (This should allow for enough time since the time it takes for a ball to drop from a height of 2 meters to the ground is about .6 seconds.)

7. One student in the group will activate the CBL (located on the floor) and immediately another student (who is holding the ball away from his body and as high up as comfortable) will drop the ball. The third student in the group will catch the ball as it nears the motion detector. The student catching the ball will keep his hands out of the way of the motion detector as much as possible before the catch.

8. Look at the graph of the data. Trace along the curve using left and right arrows and notice that the readings on the CBL become inaccurate when the height of the ball is less than .5 meters.

9. Circulate around the room to help each group as needed.

10. Take students to the computer lab with the data from the graphing calculator.

11. Enter the data on an EXCEL spreadsheet. Time (seconds) in the first column and height (position) in the second column. Be sure to exclude any pre-freefall data or data when y values become less than .5 meters.

12. Graph the data and generate the quadratic curve of best fit.

13. On the same coordinate system, graph the equation s(t) = -4.9t2 + s0 . Remember that s0 will be the height of the ball before it was dropped. (For an example of what this is supposed to look like when completed, see File Document #1)

14. You may wish to repeat the experiment twice more, letting students switch roles.

15. Take up the papers from each group and evaluate them by the rubric at the bottom of File Document #1.

#### Assessments

Each student will be evaluated on the group paper following the rubric included. Students will be expected to complete all parts of the assignement in an organized manner.

#### Attached Files

Document one contains an example problem and also contains a rubric for grading.     File Extension: pdf