GLX
The upcoming amusement park trip is the perfect opportunity to try out the digital data collection devices current owned by the school. While I have been reluctant to have students take these to the park in the past (mostly because I am nervous about lending these materials!), I am ready to experiment more this year. So what are we talking about here?
To start, the students in this course have been well-trained on the use of data collection devices. Specifically, they have used the “Xplorer GLX” model made by Pasco Scientific. While they don’t have the slick interface that some many devices have now (think: iPhone), they have all of the capabilities needed to change classroom laboratories into relevant experiences, modeling those needed for true science education. The model has two basic parts: the GLX and the sensors. First, the device itself (GLX) is a very versatile machine and can interpret information from any of the sensors that connect to its data ports. The sensors can measure any number of quantities: force, distance, voltage, temperature are examples of this. With the data displayed on the screen in numeric or graphic forms, the students have different options for accessing the meaning of the data.
In thinking about the amusement park assignment there are a few ways in which this could be deployed. The sensor that might be the most useful is the motion sensor. It can display a distance as well as velocity and acceleration quickly and readily on the screen. For students wishing to get a read on these quantities this might be the easiest way. The one caveat is that it has a very limited range and any motion that is more than a couple of meters away would not be read at all. Still, within this distance it might be much easier than trying another method.
The next sensor that could be deployed is the acceleration sensor, which tracks acceleration in the x, y, and z planes as it moves. While this might have been the best way to get this information 10 years ago, they are almost a footnote given that the iPhone has one built into the hardware. Now all a student has to do is download an app that does the same thing.
Other sensors? I will have to ask my students what they think – are any of the other sensors potentially useful in this assignment?
Coaster
I’ve been thinking about the challenge of making measurements at the amusement park. Specifically, many of the assigned problems require an application of kinetic energy (KE = 1/2 mv2), gravitational potential energy (GPE = mgh) and work (W = Fd). The interchange between the three is easy to grasp and the students have practiced this many time in this course. Train at the top of the hill loses GPE and acquires KE, with the exception of the work done by friction.
But how do I measure speed, necessary to calculate KE? Well, there is an easy trick that helps with this and the measurements are very easy to make. Think about distance: how do I access this? Well, think about how easy it is to measure the length of the train. Each is composed of multiple cars that come to a stop while loading and unloading. If I make a quick measurement of the length of a section of the train and then count the number of cars I can find the total length of the train, probably to within 10% of the true length.
In order to find velocity (or speed), what remains is time and every student carries a timer built into a phone device. If I wish to know the velocity at the top of the hill then all I need is to time how long it take for the car to pass a certain point at the top. If I wish to find the speed at the bottom then I choose another location and do the same. Repeating the measurement increases the chances that the measurement will be valid.
Now, what about other distances? If I know the length of a train and I examine (from afar) what percentage of a length of track (or loop) the train occupies then I can reasonably estimate the distance of something that I could never reach.
One final word about mass. What should I do if I get stuck on the mass of a car or train? The easiest was is to assume 1 kg (yes, just 1 kg!) for the problem. Therefore any answer you get would be per kilogram by default. That way any futre research would just multiply the factor found.
Geometry
With the trip to the amusement park only days away, it is prudent to examine how a student might begin to make appropriate measurements. The use of accelerometers while at the amusement park adds to the experience and the enjoyment of students in several ways. It gives the students a direct way to check any calculated values for accelerations and “g” forces that they have made as well as providing an opportunity for students with less sophisticated math backgrounds to quantitatively study the rides. It also provides a creative, hands-on activity for the classroom where students can design, construct and test the devices to be used at the amusement park. Trying to foresee and provide for all of the contingencies to be encountered at the park can lead to several days of class discussion and problem solving sessions.
There are basically two types of accelerometers, vertical and horizontal. Both directions are relative to the seat the rider sits in on the ride, with vertical taken as perpendicular to the seat.
Horizontal Accelerometer: this can be used to measure heights and accelerations by recording only the angle from the vertical.
FBD
- Materials: plastic protractor, string, small rubber stopper with hole, large plastic drinking straw masking tape.
- Calibrating: When holding this device so that the straw is horizontal to the ground, there are two forces acting on the rubber stopper. Gravity and the tension in the string. T can be resolved into its x and y components. The string supplies the force necessary to accelerate the stopper to the left or to the right. The stopper is accelerating in the horizontal direction only.
- Measuring Heights: One of the nice features of the horizontal accelerometer is its double use as a clinometer. By sighting the top of the object through the drinking straw, the angle of inclination can be determined from the protractor by subtracting 90 from the angle indicated by the string. Depending on which base line the student is able to measure, the height of object can be found by using the appropriate formula.
Estimating Distances: how in the world can I estimate the distance?
Estimating distance is not as difficult as it might seem. Basic students might be terrified when told that they don’t have access to a meter stick, tape measure or other device which produces hard numbers. Since students don’t have access to the rides themselves, what are they to do? I think the key is repeating structures of the rides themselves. All that’s really needs to be measured is the length of a single unit of the ride that repeats along the ride. This can be done with measured pacing (knowing one’s own stride and repeating the walk).
Now what do I do?
The final key can be found in the preparation before the field trip. Almost everything can be boiled down to a combination of length and time, with a little help from mass and acceleration estimation. Knowing how to boil down each question into the subsequent parts will transform a hairy problem into a very accessible… well… bald one I guess.
So Much Data!
Attending a baseball game can have everything from lip-biting excitement to numbing boredom. There are many who have no use for its pace or its controversies. And baseball seems to lag behind football and basketball in apparent appeal. Yet baseball absolutely dominates in the way that it generates data. Damn!
I am late in coming to the sabermetric party so none of this is news to anyone paying attention. Yet being a science teacher and a baseball fan converges two passions that find common ground in data collection.
The sheer volume of data is staggering. Every pitch, every pitch speed, every swing, every location of ball in play – every everything is observed and catalogued for analysis. What I enjoy about data is the objective look it brings to the observed.
As written by my favorite writer, among others, the goal of this data is to make sense of large groups of data and not to draw conclusions based upon small sample sizes. This brings me to my focus here: coaching students on the importance of more data as a way of getting at answers. “Is one trial enough?”
I think my response should be, “Only if you think the first at bat is predictive of the next.”
