“Using Finch to Model Vectors”
Introduction/Motivation:
A variety of mathematical operations can be performed with vectors. The impact of wind on the speed and on the direction of an aircraft, just to name one. Two or more vectors can be added together to determine the result (or resultant). The result (or resultant) of walking 11 km north and 11 km east is a vector directed northeast as shown in the diagram to the right. Since the northward displacement and the eastward displacement are at right angles to each other, the Pythagorean Theorem can be used to determine the resultant (i.e., the hypotenuse of the right triangle.
Materials List:
· Finch Robot
· Bird Brain Robot Server Software
· Measuring tape,
· Ruler
· A 90° angle for reference (card stock will work)
Procedure:
Background:
You should have the understanding of adding vectors, and finding the resultant magnitude and direction. You will work together in teams to evenly distribute tasks as well as develop a plan for conducting the experiment.
Preparation:
You need to make sure that the Bird Brain Robot Server software is available on your computer.
Lab Activity:
1. Make sure the finch in plugged in the USB port and open BirdBrainRobotServer. Then import the vectors.xml file, which is included in the “associated files”.
2. Pick an arbitrary speed for the Finch between 10 and 100, and measure its distance (steps) for a 3 second time interval using the “when space Key Pressed” script in Birdbrain. Do three trials and average your result to get the value to set the “steps” for the “sprite”(per 3 seconds).
3. Set the speed for the left and right wheel to make a 90° turn by using the “when up arrow key pressed” script. (It may take you several tries to get the wheel speeds set to get as close as possible to a 90° turn)
4. Draw the Vector: Set the finch at the starting line marked on the floor and set the script to run a sum of 2 vectors. Keeping proportions in mind for number of steps the sprite takes. If your steps were 15 for 3 second they will have to be set to 20 for 4 seconds, etcetera.
5. Use the tape measure to find the magnitude of your resultant vector. Check this with the result gotten by clicking the displacement script.
6. Write a short explanation for what you believe caused the discrepancies between the measured displacement and the “Sprite Displacement”
7. Time permitting: Find a sum of 3 vectors following the same procedures.
8. Be prepared to share your results with the class.
Assessment
Results/Conclusions
1. How close can you get your physical measurements from the finch to the sprite’s displacement? (What was your percent error?)
2. How does changing the speed of one wheel over the other affect the direction? Which wheel needs to be faster to turn left? Right?
3. Why are you doing three trials to set the speed?
4. What additional formulas would you have to use if you did not set the turn to 90°?
Reference(s):