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### Slow Acceleration Apparatus

posted Jul 29, 2015, 12:02 PM by Mark Schober   [ updated Apr 8, 2016, 8:27 PM ]
So that students develop a real kinesthetic sense of accelerated motion, it is ideal for them to investigate the acceleration of an object that speeds up so gradually that the motion can be tracked by hand. Rex Rice, of Clayton HS in St. Louis, developed an elegant solution using a wood disk with an axle made from two golf tees. The wheel and axle rolls down two conduit pipes, and students can mark the position of the axle at equal time intervals, getting 20 to 30 measurements depending on the incline.

After making hundreds of these -- it's no small task cutting 4" disks out of MDF and drilling centering holes in the end of the golf tees so that they align appropriately -- Chris Doscher suggested to me that we could use CD's for the disks by using a faucet washer to attach them to a metal axle. The metal axles are less ideal because they don't have the self-centering feature of the tapered golf tees and the friction between the steel axle and the steel pipes is low enough that they have a tendency to slide on the pipes. One fix we have added is to run a strip of masking tape down each pipe to give a bit better tooth. However, we sometimes found that the disk's acceleration decreased as the wheel approached a terminal velocity with the tape -- be sure to test it ahead of time! I haven't tried it yet, but I want to spray the axle with a clear lacquer to change the friction characteristics.

#### Slow Acceleration Apparatus Instructions

Click to download a .pdf of the directions to build the apparatus.

The teacher's notes for the Uniformly Accelerated Particle Model on the AMTA site spell out the details, but here is an outline of how you could use this apparatus in an instructional sequence:

1. Introduce the activity in terms of prior explorations in constant velocity. Our goal is to quantitatively describe the motion of an object that has a changing velocity. Students will recognize that they can use the same data collection procedure that they used in the constant velocity lab.

2. Students collect data for the moving disk.

3. Students make a position-time graph. Since it's curved, guide them to the idea of finding velocities at different times of the motion by drawing tangents to the curve and finding the slope.

4. Students make a velocity-time graph. In the discussion, acceleration is quantitatively defined.

5. Students are challenged to make and analyze additional graphs: "Linearize" the position-time graph by making and analyzing a position-time squared graph. Graph velocity vs. position and linearize the graph. By the time the analysis is done, all of the accelerated motion equations have been developed from the data.