Summer School Physics — Forces and Motion

Developed by the Cosmology Research Group, UCB Physics Department, and Emery USD

PART I:
Three Lessons in Physics—Speed, Velocity, and Acceleration
Teacher's Guide

• To effectively teach 8th graders the concepts of displacement, path, speed, velocity, vectors, and acceleration.
• To do this with a hands-on approach emphasizing connections between these concepts and students’ everyday lives.

Estimated Time Requirement:

Day 1: Displacement, Path, Speed
~in the classroom~

1. Teacher hands out copies of a city map to each student. This city, which will be familiar to the students, should be organized into a regular grid pattern.
2. The teacher asks students to mark down a route from point A to point B on the map, say, from the market to the movie theater.
3. The teacher asks students to calculate the distance from A to B in their lab books, using the map’s distance scale. (Note that if the city is truly in a grid pattern, then all groups will get approximately the same distance.)
4. Ask students to estimate how long it would take them to reach point B on their skateboards/scooters or walking/running. Have them write down these estimates in their lab books. They will conclude that the time depends on the speed of their travel. At this point, the teacher should lead a class discussion on speed that answers the questions:
   • What is speed?
   • How is it measured? (Units should be discussed here.)
   • What is its relation with travel time and distance? (Namely, derive the relation, RT = D.)
   • Given this relation, how do we calculate speed from D and T?
5. The teacher introduces the experiment below to the students and then works out an example of how to find speed from elapsed travel time and distance. The example should be worked out on the board, perhaps using planes or train as the mode of travel.


~Outside~


6. Outside, students break up into groups of three to perform the following experiment(s) {each group will need a tape measure, a stopwatch, a TI with the speedometer device, some sidewalk chalk, and a vehicle}:
   Each group measures off a straight interval, say seven meters long, and marks the endpoints with chalk. One member of each group stands at each of these endpoints while the third person gets ready to travel the course. The person at the opposite end of the course has a stopwatch and gets ready. The traveler then speeds up to top speed before passing the person at the beginning of the course. At this moment, the person at the beginning of the course yells, “time!” and the person with the stopwatch begins timing, only to stop when the traveler (who is maintaining constant speed) reaches the finish line. The elapsed time, interval length, and name of the traveler should be recorded. Students may switch roles and conduct the experiment a few times to acquire more data, or to compare different people’s maximum speeds. If time permits, students can also explore the concept of instantaneous speed using the TI speedometer device. This experiment uses the same setup except, when the person at the start line yells, “time!” the person at the finish line, who now has the TI, notes the time as the calculator graphs speed versus time. This experiment will also emphasize the fact that the previous experiment results in an average maximum speed. An accurate drawing of this plot as well as the traveler’s name should be recorded in each group member’s lab book.
7. In their lab books, students record their experimental procedure and then their calculation of how long it will take to get from A to B using the data.
8. For homework, students can be asked to write down their ideas of the common speeds for a variety of objects, for example, planes, snails, trains etc. These might be in the American or the metric system, or both.

1. To motivate the concept of vectors, the teacher demonstrates the independence of the x and y coordinates of a point that travels through a simple path. When the class understands this model, the teacher should add the position vector arrow and then, again, allow the students to observe the independence of coordinates as the point’s position vector moves along the path.
   [If this demonstration cannot be set up using the program Fathom, then time elapsed chalkboard drawings will be fine.]
2. The teacher observes from this demonstration that to specify a vector, it is necessary to specify a magnitude and a direction, and this can be done by giving coordinates.
3. The teacher has the students recall what they did on the previous day by asking to hear some of their speed estimates from the homework (or they can make up these estimates on the spot). This should lead into a class discussion on how it is often necessary to head in directions that are not straight to a final destination in order to get there. The route paths the students marked out on the previous day should be used as proof of this. Finally, the teacher introduces the concept of the velocity vector as a way of keeping track of speed and direction throughout the course of travel.
4. Students are then asked to use these route paths to draw the velocity vectors at regular time intervals throughout their hypothetical route. They should take into consideration obstacles in their paths and the maximum speed they calculated the day before. This will not be too difficult because there are only four possible directions on a grid map, in which the velocity vector can point.
5. If they seem comfortable with the above, students can be asked to do the same thing on a map with a curvy route and velocity marked out at regular time intervals throughout the path. This will, of course, be more difficult.


~Outside~


6. Students divide into groups of five to perform the following experiment {each group will need a tape measure, three stopwatches, some sidewalk chalk, and a vehicle}:
   In each group, students created a connected path composed of three straight segments of not necessarily equal length (but not too short). One student shall stand on each of the four segmentation points of the path. Each of the last three students on the path holds a stopwatch. Just like before, a traveler speeds down the path. Each of the stationary people yells, “time!” to the next stationary person as the traveler passes his or her segmentation point. Note that it is not necessary for the traveler to maintain a constant speed throughout the course. This process will generate a travel time for each of the segments. The students should record the travel times, segment lengths, and an accurate drawing of the path in their notebooks.
7. With these measurements in hand, students will be asked to fully describe the trajectory of their group’s traveler by drawing the traveler’s velocity vector for each segment. [If time permits, the groups could trade lab books and be asked to act out the trajectory described in the other group’s lab books. This will show, that the use of the velocity vector concept is necessary to completely describe the path of a traveler].

1. As a warm-up, students are asked to think of possible ways in which their journey from point A to point B is obstructed or slowed down and then to list these obstacles in their lab books.
2. The teacher leads a class discussion on these delays, which ends with the conclusion that the calculated travel time on Day 1 needs to be revised to consider the fact that they must speed up and slow down all throughout their transit.
3. The teacher explains the concept of acceleration as being a change in speed or direction. (It may be too much to explain how acceleration is also a vector quantity.) This might be facilitated by drawing trajectories on the board (with velocity vectors) and asking student to identify places where acceleration occurs. This will take a while. Then, arguing by its analogy with R*T = D, the teacher introduces the relation A*T = V and discusses with the class how they might go about designing an experiment to find A.
4. Limiting all travel time delays to street intersections, students will be asked to make a hypothetical graph of speed versus path length throughout their travel from A to B. To make this graph, start by marking all the points along the path length axis at which 0 velocity is expected (the intersections). Then mark the line speed = max speed on the other axis. Then use these constraints to draw a reasonable graph. This plot will concretely illustrate the need to consider acceleration.


~Outside~


5. Student divide up into the groups of 6 and conduct the following experiment {each group will need a tape measure, a stopwatch, a TI with the speedometer device, some sidewalk chalk, and a vehicle}:
   The groups mark off a straight path divided into four four-meter long segments. One person stands at each of the segment line, including the start line and the finish line; in total, five students standing along a path at four-meter intervals. Except for the person at the start line, each of them holds a stopwatch. The sixth member of the group, the traveler, gets ready at the starting line. When the person standing next to the start of the path says “Go!” all the people with stopwatches begin timing, and the traveler starts down the course. Each time the traveler reaches the end of a segment, the timer for that segment stops the watch and records the time traveled. When the traveler reaches the end of the path, the timers have their specific times written down. These times and the name of traveler are recorded in each group member’s lab book. Students can then switch roles and conduct the experiment again.
6. In their lab books, students calculate the average speed for the traveler as determined from the starting point to the end of each segment. These speeds should then be graphed in a histogram with speed as the y-axis and displacement from beginning of the course as the x-axis. The different speeds obtained from each time will demonstrate that the traveler has accelerated.

Part 2: Acceleration and Forces