Introduction to Relative Velocity
Airplanes can experience head winds or tail winds that affect their flight time. Similarly, motorboats on a river experience ground velocities that are dependent on whether they are traveling upstream or downstream. Both of these phenomena are associated with a physics concept known as relative velocity--the main topic of this lab.
Relative Velocity Lab Setup
This lab combines PocketLab Voyager, Ozobot, and a LEGO powered cart in a way that makes it easy for students to learn about relative velocity. Figure 1 shows the basic setup for this lab. A powered cart is constructed from LEGO parts and motor. This cart moves at a constant speed when turned on. A piece of basswood is attached to the top of the LEGO cart using 3M Command mounting strips. A piece of adding machine tape is taped to the top of the basswood. A straight line is drawn on the tape. This line provides a path on which Ozobot, a tiny line-following robot, can travel. Voyager is mounted to the top of Ozobot using a small piece of clay. The IR rangefinder on the orange side of Ozobot faces a piece of white cardboard on the far left of the experiment setup. Throughout the experiment, the rangefinder records Ozobot's position relative to the stationary cardboard.
Figure 2 shows the four suggested experiment runs associated with this lab. The purpose of Run #1 is to determine the speed of the cart alone relative to the wall. The purpose of Run #2 is to determine the speed of Ozobot alone relative to the wall. In Run #3, we simulate Ozobot traveling downstream as for a boat, or with a tail wind as for an airplane. In Run #4, we simulate Ozobot traveling upstream as for a boat, or with a head wind as for an airplane. The cart acts as the water current on a river, or as the wind on an airplane. Ozobot acts as the boat or as the airplane.
The OzoBlockly Program for Ozobot
Figure 3 shows the OzoBlockly program that needs to be loaded into Ozobot for this lab. Ozobot's top light will be red for three seconds prior to any movement by Ozobot. The line-following speed for Ozobot is set to the maximum allowable for Ozobot. Nominally, this is 85 mm/s, but the lab will have the student measure the actual speed for better precision. When Ozobot reaches the end of the line drawn on the tape, it will shut down. This should prevent Ozobot and the attached Voyager from falling off of the basswood.
Figure 4 shows a graph of position vs. time for each of the four runs. Data from the four separate csv files produced by the PocketLab app have been combined on this single graph for clarity. The pertinent data for each run has been adjusted so that all runs start arbitrarily at time zero. The coeffcient of x in the linear trendline analyses in Excel provide the velocity in m/s for each of the four runs.
The table of Figure 5 summarizes the results that are displayed in the graph. The table verifies two things regarding the relative velocity:
- For the boat going downstream or the airplane with a tailwind, the relative velocity is equal to the sum of the separate velocities.
- For the boat going upstream or the airplane with a headwind, the relative velocity is equal to the difference in the separate velocities.
For any teachers who want to do this investigation in the classroom, a pdf file with an empty table accompanies this lesson. Please feel free to make copies as needed for your students.