## Relative Velocity Lab

by Professor Rich Born

### Introduction

Here is a physical science lab for junior high students that brings out the S, T, E, and M in STEM -- S for the science of relative velocity, T for the technology of sensors, E for engineering an experiment design, and M for the mathematics used in analyzing data. How can all of this be accomplished? Simply interface PocketLab Voyager with a pair of "intelino smart train" engines. Designed for all ages, intelino is intuitive with its app, has built-in sensors to provide an interactive experience for the user, and is easily programmed with color snaps that allow the user to control intelino's actions. In this lesson, your students are challenged to design an experiment to study relative velocity with the help of PocketLab Voyager's IR rangefinder.

### The Relative Velocity Typical Lab Setup

Figure 1 shows a typical setup for the relative velocity lab. There are two intelino train smart engines. Your students need to imagine that they are aboard the blue engine (A) on the left. This engine has PocketLab Voyager mounted to the top using a 3M damage-free strip. Voyager's rangefinder is pointing toward a piece of white card stock on the yellow engine (B) at the right. The 8½" x 11" piece of card stock has been folded in half to provide rigidity and is held by a 3D printed holder mounted to the engine with a damage-free strip. The STL file for the card stock holder can be downloaded below:

In the example shown in Figure 1, both engines are moving to the right. Voyager's rangefinder IR beam reflects off the card stock. As a result, the distance it measures is always the distance from the blue engine to the yellow engine, regardless of the speed of either engine as set by the intelino app. With this setup, the slope of the distance versus time graph produced by the PocketLab app represents the velocity of the yellow engine (B) relative to the blue engine (A). If the slope is zero, then the two engines remain separated by the same distance while traveling. If the slope is positive, then the separation of the two engines increases with time. If the slope is negative, then their separation decreases with time.

Figure 1 - Typical relative velocity lab setup

### Challenge #1: Engine B Traveling Faster than Engine A

"Design an intelino/Voyager experiment using only straight track that will allow determining the speed of engine B relative to engine A, where the intelino app speed of A is 30 cm/s and the speed of B is 40 cm/s. Both engines start out at 30 cm/s moving to the right on the track, but engine B's intelino speed quickly changes to 40 cm/s. Once the two trains are started from the intelino apps, no more interaction with the app is allowed. The engines must come to a stop on their own without leaving the track. The engines are controlled by intelino apps running on two devices, while the PocketLab app is controlled by a third device. You will need to make use of custom color snap commands in the intelino "Snap Editor". You should determine the requested relative speed by analyzing Voyager's rangefinder data."

### A Typical Solution to Challenge #1

Figure 2 shows the track layout that was designed by the author of this lesson. The two engines start on the far left and move in the direction shown by the blue arrow. The initial speeds for both engines are set to "slow" (30 cm/s) from the intelino autopilot mode. Both engines are started at the same time by pressing the "slow" buttons on each intelino app simultaneously. When engine B encounters the white/magenta/red custom action, its speed is set to 40 cm/s. However, when engine A encounters this custom action, engine A ignores it as the sequence white/magenta/red is left undefined for engine A. Similarly, when engine B encounters the white/magenta/blue sequence, it is ignored as this color sequence is left undefined for engine B. When engine A reaches the white/magenta/blue sequence, however, engine A pauses since this sequence has been defined for engine A to represent a pause. Finally, when engine B reaches the white/magenta/yellow custom action on the far right, it pauses since the action for this sequence has been defined as a pause. We have met the challenge requirement that neither engine leaves the track. Clearly, this is a great way to challenge your students in logic and reasoning. Creating custom commands when two intelino engines are running on the same track requires more care than when only one engine is running the track.

Figure 2 - Example track layout for challenge #1

### Video of Challenge #1

The short video below shows an action run of the example track layout for challenge #1. Notice how engine B increases its speed upon reaching the first color action snap. Also, when engine B reaches the end of the track and stops, there is a sudden change in the slope of the distance versus time graph. At this point in time, the relative velocity changes its sign from positive to negative. From an observer in A's reference frame, engine B suddenly appears to be moving toward engine A. This could be avoided by moving the white/magenta/blue custom color action snaps further to the left in the set up so that both engines stop at the same time. What would happen if this set of snaps was moved too far to the left?

### Data Analysis for Challenge #1

Figure 3 shows an Excel graph created from rangefinder data recorded from the PocketLab app. Annotations on the graph clarify the things that are happening in the author's solution to challenge #1. The slope of the graph from roughly 7 to 9 seconds turns out to be about 10 cm/s. This means that engine B is moving away from engine A at that speed. This is as we would expect since A is moving at the intelino speed of 30 cm/s and B is moving at the intelino speed of 40 cm/s (40-30=10). After engine B has stopped but A continues moving, the slope is -27 cm/s, meaning that from the point of view (reference frame) of an observer on A, B is moving toward A at a rate of 27 cm/s. This is close to the 30 cm/s intelino speed of engine A.

Figure 3 - Challenge #1 data analysis

### Challenge #2: Trains Heading Toward Each Other

"Design an intelino/Voyager experiment using only four straight tracks that will allow determining the speed of engine B relative to engine A, where the two trains have speeds of 30 cm/s and are moving toward each other. Once the two trains are started from the intelino apps, no more interaction with the app is allowed. The engines must come to a stop on their own without colliding. The engines are controlled by intelino apps running on two devices, while the PocketLab app is controlled by a third device. You should determine the requested relative speed by analyzing Voyager's rangefinder data. "

### A Typical Solution to Challenge #2

Figure 4 shows the setup for this challenge that was used by the author of this lesson. PocketLab is on intelino engine A with its IR rangefinder facing the white card that has been attached to engine B. The two engines are moving toward one another as shown by the white arrows in the figure. Both engines are started at the same time using the slow speed (30 cm/s) in the intelino "autopilot" mode. The default (white-red-blue) "end route" action snap commands keep the engines from colliding with each other. The snaps are placed the same distance from their respective engines. Doing this makes the engines stop at the same time.

Figure 4 - Typical setup for challenge #2

### Video of Challenge #2

The short video below shows an action run of the example track layout for challenge #2. Notice that the engines start at the same time. They also reach their end route color snap commands at the same time since the distance and speed are the same for both engines.

### Data Analysis for Challenge #2

Figure 5 shows an Excel graph created from rangefinder data recorded from the PocketLab app. Annotations on the graph clarify the things that are happening in the author's solution to challenge #2. The slope of the graph from roughly 3 to 3.5 seconds turns out to be about -54 cm/s. This means that from the point of view of an observer on A, engine B is moving toward engine A at a relative speed of 54 cm/s. This is as we would expect since A is moving at an intelino speed of 30 cm/s and B is moving at an intelino speed of 30 cm/s . Moving toward each other, the speed would add and give us a relative speed of 60 cm/s. Compared to our relative speed calculation of 54/cm/s, we find a difference of only 10%.

Figure 3 - Challenge #2 data analysis