Experiment
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Student Activity: Exploring Gravity

 

Overview: We will explore the properties of motion of falling objects, then graph and analyze the results. We will explore regression analysis of data using a graphing calculator. We will investigate the impact of different weights of similar falling objects with respect to gravity.

Objective: To derive an equation that reflects the motion of a falling object.

Terms: Regression analysis, average.

Materials: CBR Motion Detector and cable to connect to a TI83-Plus graphing calculator. The Ranger program on the graphing calculator. A 12 inch ruler or longer. 3 balls of different weight but equal diameter and enough aluminum foil to cover each ball if necessary. (Recommended balls: a soccer ball, a plastic playground ball, and a large Nerf ball.) The weight of each ball. Three Data Collection Charts. Six adhesive strips that will be used to mark off six ten-inch lengths on the wall that will total 60 inches in height. A chair for one student to stand on. A complete set of all materials is needed for each group performing the experiment. Two is the minimum number of students for each group, however 3-4 students per group is recommended.

Procedures: The teacher will provide the weight of each ball used in the activity for the students.

The students will mark off heights of 10", 20", 30", 40", 50", and 60" on the wall starting from the floor and going up the wall. The students will use the ruler and the 6 adhesive strips to mark these heights.

The teacher will demonstrate for the students the procedure for measuring the time it takes the ball to hit the floor with the CBR motion detector and how to transfer the data to the calculator. The teacher will demonstrate and discuss with the students how to find the total drop time of the ball from a specific height by subtracting the time of release from the time of impact. Discuss why an average time is being determined.

Before performing the experiment, the students will make two hypotheses:

    1. The students will predict if the rate of fall will increase or remain the same as the weight of the ball increases.
    2. The students will predict if the rate of fall will increase as the height increases, or will it remain constant or decrease.

The students will drop each ball from each of the six heights five times and determine the average drop time for each ball from each height. Responsibilities of the group:

    1. The first person will drop the ball after 3 seconds are counted off. The person will remain completely still until the CBR stops logging data.
    2. The second person will record the time the ball was dropped and the time of impact with the ground on the Data Collection Chart from the data recorded on the CBR.
    3. The third person will hold the CBR above the ball.
    4. The fourth person will press the ENTER key on the calculator and count off 3 seconds out loud as follows: "One, one thousand, two, one thousand, three, one thousand." This will enable the first person to concentrate on standing very still and just dropping the ball at the appropriate time.

 

The students will record the data on the provided Data Collection Chart, which has the following headings.

                Type of Ball

                Weight of Ball

                Height of drop

                1st drop time

                2nd drop time

                3rd drop time

                4th drop time

                5th drop time

                Average drop time for this height

The students will calculate the average drop time for each ball for each height and record the average drop time on the Data Collection Chart. Calculators may be used to perform these calculations. The students will then list the average drop times in a table on the Data Analysis Chart following the Instructions for Using and Completing the Data Analysis Chart (Part 1). This chart and documentation may be found in the "Data Analysis" section of this web site as well as in the "Documentation" section. (Note that sample test data has been provided for anyone not having the equipment to actually perform the experiment, but who want to do the data analysis.)

The students will evaluate the compiled data on the Data Analysis Chart by answering the following 4 questions in writing on their own paper.

    1. Looking across the average drop times for any given height, is the average drop time approximately the same or does it differ greatly? Remember that the average drop time is recorded in ten-thousandths of a second. If they differ greatly, do you see a pattern that might explain the difference based on the weight of each ball? What does the data show according to your first hypothesis? Was your first hypothesis correct?
    2. The students will plot their test data on 3 separate graphs, using the data from one ball to plot on one graph. Each ball will have a separate graph reflecting the test data for that ball. Include the point 0 inches, 0 seconds as the first point on each graph. The x-axis will be labeled "Height of Drop in Inches" using increments of 10, and the y-axis will be labeled "Average Drop Time in Seconds" using increments of .1 (tenths). Connect the points on each graph with a line or a curved line, which ever is more appropriate.
    3. The students will compare the three graphs and determine if the graphs are similar or if they are different. If they are different, how are they different?
    4. The students will explain in writing why they dropped the ball 5 times from each height and then found the average drop time.

The students will verify their 3 graphs by plotting the data on the graphing calculator using the x-axis as "the height the ball was dropped from" and the y-axis as "the drop time." Instructions for Plotting Data on the Graphing Calculator are included in the "Data Analysis" section of this web site.

At this point the students must have a checkpoint with the teacher to determine (1) if they should continue analysis with their data, or (2) if they should analyze the sample test data provided, or (3) if they should repeat the experiment (although this option is not highly recommended because it takes approximately 3 to 5 hours just to perform the experiment if it is done correctly).

 

The students will now proceed to analyze the data looking for patterns in the table on the Data Analysis Chart by following the Instructions for Using and Completing the Data Analysis Chart (Part 2). The students will answer questions concerning their data and develop an equation to reflect their results. The students will then use the graphing calculator and regression analysis to evaluate their second hypothesis concerning the rate of fall. The students will follow the Instructions for Regression Analysis on the Graphing Calculator provided in the "Data Analysis" section of this web site. The students will answer questions concerning their data and develop an equation to reflect their results of regression analysis. The students will compare their results to the scientific equation reflecting the motion of a falling object. The teacher should give this equation to the students. The constant of the equation is to be expressed in terms of (inches)/(second^2). The completed Data Analysis Chart is to be turned in to the teacher along with a blank Evaluation Sheet.