Ted Corley, Miriam Fuhrman and Susan Wyckoff
BACKGROUND
This experiment is especially useful for reinforcing the differences between accelerated motion and constant speed, and their graphical representations in motion graphs. The white board presentations by groups at the end of class provide an important means for students to articulate their understanding of different kinds of motion in terms of graphs. Although the main emphasis of this experiment is on the interpretation of motion graphs, students should also come away with an understanding that accelerated motion requires an applied force, and constant velocity can occur only when the net force on an object is zero (i.e. there is no force or balanced forces acting on an object).
TEACHING TIPS
The purpose of the Hurdles homework is for students to understand a real-life context for the use of distance vs. time graphs. Be sure to allow time for the groups to discuss exactly how the race unfolds. Encourage students to improvise creative interpretations of the graphs into their "announcer's description" of the race. You may have to assist them with scaling the graph axes to gather data points. The purpose of sketching the velocity vs. time graphs for each of the distance vs. time graphs, is to facilitate students' understanding of moving between the two representations of motion. The classroom discussion should end with the correct velocity vs. time graphs known to the students, so that they begin the lab with the correct motion graphs (distance vs. time and velocity vs. time pairs).
Each group should have all of the materials listed in the Student Guide available before beginning the experiment.
The styrofoam plate taped to the fan cart provides a "reflector" for the sonic pulses from the motion detector. The plate improves the data quality by minimizing the possibility that the sonic pulses will reflect from extraneous objects during the experiment. Occasionally the motion detector will even pick up the ramp, if the detector is not elevated a few centimeters above the ramp. Also remember that objects closer than 0.5 meters cannot be sensed by the motion detector.
Students may need to read and follow the guide on using a TI-83 and CBL. A "nice" setting for the PHYSICS program parameters is fifteen .2 second intervals for a total of 3 seconds of data collection. Students need to arrive at some reasonable numbers in order to be able to interpret the data
The "ends" of the data lists may need to be deleted. Students should be urged to discuss with the instructor their justification for discarding the end points of their data sets. They should not be permitted of course to keep the "good" points and discard the "outliers".
If students insist on "perfect graphs," exiting the program "PHYSICS" and changing the window or plotting the meaningful data points is necessary.
After a group starts to appear comfortable with the equipment, you may need to ask, "Is there any other way you can arrange the fan cart that would give you the same graph?" There are usually two or more ways to generate each of the d(t) graphs. If the students have already used the motion detector to study the gravitational acceleration of falling objects, comparisons between the cart accelerated by the fan and an object in free-fall would promote a good class discussion. Although the fan carts are designed to be frictionless, they may not be. Deviations from frictionless motion will be manifested by deviations from parabolic distance vs. time graphs, and straight line velocity vs time graphs. Note that air resistance in the case of free-fall has the same effect as friction in the case of the fan cart.
If you see students giving the car an initial velocity, you should raise the question of how they think their motion graphs are affected with and without the initial speed.
A good way to handle the white boarding at the end of the experiment is to assign a different distance vs. time and velocity vs. time graph for each group to explain. Students should be able to think of more than one way that the motion of the fan cart can be set-up to match the given graphs. The white board presentations are good ways for the instructor to know how conversant students are with motion graphs and the concepts of force, acceleration, velocity and Newton's second law.
PHYSICS AND MATHEMATICS TERMS
acceleration
distance/displacement
force
frictionless
function of time
mass
velocity
v(t)
THINKING SKILLS
reasoning
making sense of data
verbal communication
written communication
relationships among displacement, time, velocity, acceleration, force, mass
SAMPLE TEST QUESTIONS
For each of the following questions (1-5), choose the distance (displacement) versus time graph on the next page that best describes the motion in each situation.
1. You throw a ball straight up in the air. It travels upward and then downward. Which graph best describes the motion of the ball? (d is measured as distance from your hand, t starts when the ball leaves your hand)
Options: I,III, VI, VIII, IX
2. A frictionless cart is on a level track. You push it (one small push) down the track hard enough to hit the hard rubber bumper at the far end of the track (d is measured from where you gave the initial push, t starts when the cart leaves your hand)
Options: II, IV,V,VIII, IX
3. A frictionless cart rolls down a ramp. (d is measured from the top ofthe ramp)
Options: I, III, IV, V, VIII
4. A car traveling down a straight, level road in the desert with the cruise control at 75 mph. (d is measured from a mile marker ahead of the car)
Option: II, III, IV, VI, X
5. A satellite is in a geosynchronous orbit, 125 miles above Phoenix. (d is measured from the ground to the satellite)
Options: I, III, IV, VI, IX
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