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16 December 2021

Describing a laboratory procedure: speed of a cart at the bottom of a ramp

 Samar, who teaches in Maryland, called my attention to a question in the AP Physics 1 Workbook:  

In order to perform an experiment, two students need to determine the velocity of a cart just as it reaches the bottom of a ramp.  In a few short sentences, describe an experimental setup that they could use to determine the [instantaneous] velocity of the cart at the bottom of the ramp.

This is posed as an extra suggestion to discuss with students, and so doesn't have a solution in the teacher version.  Which of course - experimental physics is a creative endeavor, where right and wrong certainly exist, but where numerous correct approaches are available.  

Nevertheless, it's worth me giving a few examples of how I'd suggest answering the question such that (a) the procedure is correct, (b) the procedure is clearly communicated, and (c) the procedure is described in "just a few short sentences" rather than in a multi-page lab report full of vacuousness.

I've graded more AP experimental questions than anyone else on the planet*, so please trust me when I say that you shouldn't accept any response longer than about 80 words.  Seriously - no matter how thorough, no matter how accurate, a long response is no good!  For one thing, the student just used all sorts of time writing all these words here, when that time could have been more productively used elsewhere - on other problems in an exam, or perhaps at home playing with the family dog.  It's not possible to earn extra credit, or a "plus one!" on an AP exam.  Just answer the question, then stop.  If you "lose" a point for not saying something important, well, the extra five sentences you wrote at the end aren't gonna help.

* I'm probably not kidding. Guinness Book, please contact me!

So, how would I answer?  Here are four ideas off the top of my head.  I'm sure others will chime in with other thoughts!  

1. Put a dual-beam photogate above the cart at the position where the cart leaves the track.  Tape a thin slice of an index card to the top of the cart, such that the card breaks the photogate beam.  Then drop the cart down the ramp, and the photogate will read the instantaneous speed at the bottom.

2. Place a meterstick horizontally at the bottom of the track.  Record the cart's movement on video.  Pause the video in consecutive frames when the cart is at the bottom of the track.  The distance the cart traveled between frames - read on the meterstick - divided by the time for each frame (known from the video camera) is the instantaneous speed.

3. Place a motion detector behind the cart.  Have the detector create a velocity-time graph for the cart's motion down the ramp.  The maximum reading on the vertical axis is the cart's instantaneous speed at the bottom.

4. Use a smartcart that can create a velocity-time graph of the cart's motion down the ramp.  The maximum reading on the vertical axis is the cart's instantaneous speed at the bottom.

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