Scratch as a Simulation Engine - Part 3
For the 3rd post on using Scratch as a Simulation Engine, I’ll be moving back to a High School classroom example. The following is a problem from my daughter’s Physics class:
“Crazy Joe Clayton parks his 57 Chevy close to a cliff overlooking the ocean. The land leading up to the cliff is on an incline of 37 degrees below the horizontal. Joe runs to meet his sweetheart Thelma, but leaves the Chevy in neutral. The car begins to roll down the incline with a constant acceleration of 4.0 m/s2 and travels 50.0 m to the edge of the cliff. The cliff’s edge is 30.0 m above the ocean.
a. Find the time the car is in the air.
b. Find the position of Joe’s car relative to the base of the cliff when it lands in the ocean.”
The problem is a simple 2 dimensional trajectory problem… but with a twist. Brittany does not have enough of a math background to comfortably view this as a single problem! For most High School students, the best way to solve the problem is to break it down into 2 pieces; the car accelerating down the slope to the edge of the cliff and the trajectory problem of the car careening into the ocean. (Actually, maybe everyone would solve the problem as 2 separate steps. If one were trying to impress someone, however, one could solve for the velocity at the end of the first part of the problem as an equation and substitute the equation into the 2nd part of the problem. But would anyone really solve the problem this way? I wonder.)
A screenshot from the Scratch simulation I created for this problem is shown below. The project can be run here. The project file can be downloaded here.
Reset the simulation by clicking on the green flag. Run the first part of the problem by clicking on the car. Run the final part of the simulation by clicking on the car again.
What’s hard about this problem and simulation?
- As in most of the simulations I’ve looked at, the actual math is not too complicated. However, the scaling of the movements of the sprites to match a graphic can be fairly challenging.
- With the problem broken down into 2 parts that can be readily solved, it is necessary to realize the the starting x and y velocities of the 2nd part of the problem are equal to the ending x and y velocities of the first part of the problem. This was not intuitive for Brittany. In fact, she argued pretty forcefully that the starting y velocity of the 2nd part of the problem should equal the ending x velocity of the first part.
Could a simulation like this be used to help students understand Physics in a High School Physics classroom? I’ll consider a few possibilities, and my thoughts on them…
- Assign students to develop a simulation of the problem? - Probably Not!
Although this would be a very constructivist (or constructionist) activity, I believe that assigning the students to develop a simulation of the problem would probably be too tough for all but the most advanced students. And the time it took to build the simulation of this one problem would probably be better spent practicing several more problems. - Use the simulation as an in-class demonstration? - I think so!
The simulation could be used in-class to demonstrate how the problem can be broken down into the 2 separate problems. Further, it could be used to explain the relationships of the x and y velocities as the 2nd part of the simulation begins. These relationships may be easier to explain / understand given the simulation. - Use the simulation as an in-class demonstration of debugging? - Hm, I’m not sure!
If you compare the results of the simulation with the results of working the problem by hand, you’ll find that the answers provided by the simulation are not quite right. These inaccuracies are caused by what I would refer to as quantization limits. The simulation moves based on a clock tick and the accuracy of the simulation is limited due to this. An understanding of this phenomenon might be within the scope of a High School Physics class. However, If I used the simulation as an in-class demonstration as discussed above, I wouldn’t include a discussion of the quantization problem because I think it might interfere with the point of the problem - which is to set up and properly solve the problem. I might consider discussing quantization and accuracy, however, whenever discussing the accuracy of experiments carried out in class (or in the real world). In such a discussion, the simulation might make a useful demonstration.
As always, I’d love to hear what readers think of these ideas. Is the use of Scratch for simulations a useful school activity?