Note: A video camera trained on the apparatus with output to a large monitor will facilitate students' viewing of the experiment.
1. Adjust speeds such that cart x is the same speed as cart y. Students gather around apparatus. Ask students what will happen if the carts move at the same speed. Discuss answers. Perform run, recording car track with pen and recording data on the computer. Replace paper.
2. Ask students what will happen if one cart moves faster than the other (say, x is faster than y). Discuss various answers. Perform run, recording car track with pen and recording data on the computer. Keep paper in place.
3. Ask students how the picture will change if the situation is reversed (now, the opposite car is faster). Discuss answers. Perform run, recording car track with pen and data on the computer. Replace paper.
4. Ask students what will happen if one car starts before the other. Discuss, perform run, replace paper.
5. Have students suggest "what if" scenarios. Perform sufficient runs and data collections so that each lab group can have a piece of paper with track and data from a run.
6. Give each group data and paper with tracks. Move to analysis phase.
Whole class discussion: Show data table on monitor (time, x, y, r). Ask students to establish what the columns are and exactly what they mean. Ensure articulations are precise and that students agree. Ask students what will happen if the y column is plotted vs. the x column. Discuss with students how x, y, and r should relate (they should come up with the triangular relationship). Move to student centered phase.
1. Using the graphing function of your data collection program, display the x vs. y motion of the box.
2. Using the graph, chose ten points in time and calculate r based on the x and y positions.
3. Plot r vs. t of the box. Compare this graph with your data table for number 2 above.
[Note: The teacher may wish to lead a discussion preceding number four cementing the concepts of 1-3 above and pointing out the features of Vx, Vy, and Vr which will lead to successful completion of number 4 below.]
4. Using the graphing function of your data collection program, display Vx, Vy, and Vr. Work with your group to develop a rule for finding Vr from Vx and Vy.
This graph of x vs y
provides a picture of the boxes track with corresponding
distances recorded. This graph of r vs t
allows students to see and verify x^2 +y^2 = r^2. The idea
is that students will use this concept to develop the
relationship Vx^2 + Vy^2 = Vr^2.
