Need a paragraph-response item for AP Physics 1?

Remember the 2013 AP Physics B problem 4 about a modified-Atwood machine?  A ball was placed on top of the block on the top surface.  That ball became a projectile when the top block hit the edge of the table.  After some good calculational parts, part (d) asked a very carefully targeted descriptive question.  The exam stated that increasing the mass of the ball would cause the ball to land closer to the table... then asked, why?

I'd say a good quarter of the responses globally were something along the line of "since the ball is heavier, it falls faster, and so doesn't have time to go as far while it's in the air."  My personal opinion -- NOT shared by the College Board, at least publicly -- is that readers should be allowed to make a student who gives this response retake the entire test, this time in the presence of flesh-eating ants.  My proposal for this particular adjustment to the rubric was not accepted by the table leaders, because it was too late in the process to make substantive changes.

Every physics teacher I know praised the verbal portion of the question.  It did an outstanding job of rewarding students who could *explain* physics rather than merely solve problems.  On the old AP Physics B exam, a verbal-response item had to be targeted carefully such that students could answer in the time allotted.  The new exam provides plenty of time for such questions.  In fact, one entire question will include a phrase such as "justify your answer in a clear, coherent, paragraph-length response."  I rewrote this 2013 AP B problem as a paragraph-response item.  Here is my version of the problem, followed by some commentary.

1.      (7 points, suggested time about 13 minutes)

A ball of mass m is in a cup of negligible mass attached to a block of mass M that is on a table.  A string passing over a light pulley connects the blocks to a 2.5 kg object, as shown above.  The cup is a vertical distance h off of the floor.  All friction is negligible.

 In Trial 1, the system is released from rest, the block accelerates to the right, and after moving a distance x the block collides with a bumper near the end of the table.  The ball continues to move and lands on the floor at a position a distance d horizontally from where it leaves the cup.  In Trial 2, the mass m of the ball in the cup is doubled.  The system is again released from rest.  The block collides with the same bumper, the ball continues to move, and lands on the floor.

 In trial 2, does the heavier ball land a horizontal distance from the table that is greater than, less than, or equal to d?  Justify your answer in a clear, coherent, paragraph-length explanation.

Since the paragraph-response item doesn't ask for calculations, I eliminated most of the numerical values.  (I left the 2.5 kg hanging mass so I didn't have to make up yet another mass variable.)  In thirteen minutes, a student will have plenty of time for reasoning and writing; so I didn't feel the need to reveal that the ball goes a distance less than d.  

We only have one published example of a paragraph-response rubric, so most of us teachers are on our own to guess how these will be scored.  In my rough rubric, I looked for the following seven elements:

* Recognition that it is necessary to consider the ball's speed after traveling the distance x

* Statement that the ball has a smaller speed after the distance x in trial 2

* Then two steps of reasoning supporting a smaller speed, for example:

       + In F=ma, the net force on the system is the same with larger mass, giving smaller a

       + Smaller acceleration means the block speeds up less in trial 2, or reasoning with v² = 2ax

* Statement that the ball goes a distance smaller than d

* Then two steps of reasoning supporting a smaller distance, for example:

       + Kinematic justification that the ball is in the air for the same time either way

       + Linking the horizontal distance to the initial horizontal velocity through x = vt

You might come up with a completely different rubric.  That's fine.  I merely chose several elements of reasoning that I expected to see, which allowed me to award partial credit to those who had a reasonable but incomplete understanding of the problem.

When I gave this item on my trimester exam, I found my seniors knocked it out of the park.  The continual writing practice we've been doing this year paid off big time.  The majority of the class earned full credit.  A few people said the ball would go the same distance either way, but they earned partial credit by correctly explaining the projectile portion of the problem -- they didn't understand the modified Atwood part of the problem.  My 9th graders didn't do as well, because they have a lot more trouble expressing their understanding in words.  They would have performed equivalently or better to the seniors on the original, calculation-heavy 2013 AP Physics B problem.  But the seniors have so much more facility with the written word that they dominated the freshmen on this one.  Of course, that's fodder for a future post.

Please feel free to use this question in your class.  Let me know if you have tweaks, either for the question or for the rubric.  And feel free to send your paragraph-response items!

GCJ