They did it - 2015 P1 #3 with PASCO smartcarts by Nadia Lara and Joey Konieczny

Last month I showed how I had set up an AP physics problem in lab using a motion detector.  I suggested that a PASCO smartcart would allow for a higher data collection rate in order to better define the energy vs. position graph.

Well!  Two physics teachers wrote in with their results!  I post both below, with their own words.  Take a look at Nadia's to see how to use the Sparkvue app to get the kinetic energy data to display.  See Joey's for a picture of his setup and how to adjust the D = 0 position.

First is Nadia Lara of St. Agnes Academy in Houston.  Her writing is available at her blog, Need to Know Science.  She says:

I set up the problem you wrote about last month and got the following graph with a 100 Hz sampling rate:

I used the spring attached to the smart car on the second setting. It’s pretty stiff, so the curve is steep and it’s harder to see the quadratic vs. linear relationships, but you can get plenty of data points. Higher sampling rates didn’t work well. A weaker spring would work better. I ended up taping a piece of a balloon on the bottom of the car to get enough friction to slow the car down quickly. 

To get the calculated values, click on Experiment Tools on the bottom right, then choose “Calculated Data” -->

Type in your formulas. Use the orange “Measurements” button to select the measured quantities you want to insert into the equation.

To edit the units associated with a calculated value, place the cursor on the line of the quantity you want to update and click the Properties button. Click the keyboard button next to the units and type in the units you want.

Voila! 

Thanks, Nadia! 

Now Joey Konieczny of Atlanta's Drew Charter School:

I was [bored in a place where it's politically incorrect to admit to boredom], so I pulled up your blog and accepted your challenge.  It took me a few trials to get it right, but below is my setup using the Smart Cart and two snapshots [overlaid on the same graph] from SparkVue showing Kinetic Energy vs. position.  In Trial 5 I pressed record (this sets the zero position for the wheels) and pulled the Smart Cart back only the length of the piston.  You can see from the graph that the Smart Cart thinks that zero position is actually about 15 cm ahead of where I told it zero was.  Trial 7 I "cheated" and moved the cart forward 15 cm (pulling it back a total of 20 cm) and voila!  The Kinetic Energy calculation (y-axis) was pretty easy, and Pasco has a ton of online resources to help figure it out.  

I'm a huge fan of the Smart Carts.  The data they spit out is awesome!

Thank you, Joey! 

So why isn't the projectile changing speed at its peak?

A previous post posits a question, and a student's response.  The response seems okay, because every sentence is in fact correct.  But a logical connection isn't there.  Today I'll explain the error in reasoning, and give the better answer.

See the previous post here.  It discusses how to handle the conversation with the student who knows that they're right, even though they're wrong and you can't quite articulate the error on the spot.  That was my purpose in posting this question, as I had heard quite a bit of debate in the physics teaching zeitgeist about this problem.  I'm only posting the solution separately so as not to distract from the pedagogical message of the first post.

Here's the question:

A projectile is thrown upward at an angle.  At the instant the projectile is at the peak of its flight, is the projectile gaining speed, losing speed, or neither?  Justify your answer.

A student responds, "The path followed by a projectile is a parabola.  At the peak of motion, the slope of that parabola is flat, or zero -  the change in speed is zero.  The projectile neither gains or loses speed."

What's wrong?

The student connects the slope of the projectile's path to its speed.  That's not right.  The slope of a trajectory - the path that an object takes - says nothing about speed, just about the direction of motion at that instant.  [The student may well be confusing the slope of the projectile's path with the slope of a position-time graph, which does indicate velocity.]

What's the better answer?

At that instant, the acceleration is downward, and the velocity is horizontal - thus there's no component of acceleration in or opposite the direction of velocity, so the object cannot speed up or slow down.

Or:

At that instant, the net force on the object is downward, and the instantaneous velocity is horizontal - thus there is no work done by the net force, and so the object's kinetic energy cannot change.

How to address students with incorrect reasoning when you can't identify their exact mistake?

A projectile is thrown upward at an angle.  At the instant the projectile is at the peak of its flight, is the projectile gaining speed, losing speed, or neither?  Justify your answer.

A student responds, "The path followed by a projectile is a parabola.  At the peak of motion, the slope of that parabola is flat, or zero -  the change in speed is zero.  The projectile neither gains or loses speed."

Right or wrong?

Wrong.

"Wait, what?" says the student.  "Everything I said is true.  Where's my mistake?"

Deconstruct the student's response sentence by sentence, and you'll find that yes, everything they said is in fact true:

* The path followed by a projectile is a parabola.  Essentially a fact.  

* At the peak of motion, the slope is zero.  Yes.  Draw a tangent to the trajectory at the top - horizontal line.

* The change in speed is zero.  That is the correct answer, as indicated in the key the teacher read online.

* The projectile neither gains or loses speed.  That's what "change in speed is zero" means.

"So if you can't find my mistake, you can't count it wrong."  [Cue body language of rolled eyes, upraised palms, indicating that the student is dealing with a lesser being, someone on a lower social and intellectual plane.  Their body says, "I can't wait until I have the money and the power to properly avenge myself upon this plebe."]

It's tough not to cave in to a smart student making this kind of complaint... when you know in your experience that the student is wrong, but you can't explain the error clearly, and the student is starting to get frustrated at what they perceive as your intransigence.  It's tempting to say, "Okay, you must be right, the key is wrong."  Or, "Well, I see your point.  Since we are both so confused, this must be a bad question.  I'll throw it out."

Don't do that.

But also don't do the "Shut up, I'm the teacher, I'm always right, sit down" routine.  No matter how polite you are, just pursing your lips and firmly ending the argument will be perceived as an over-the-top exercise of authoritay.

What do you say?

"Look, I can't pinpoint the error in your answer right now, but I'm pretty sure it's there.  I need to look carefully not just at each statement, but at the logical connections between each statement.  I'll look at this tonight, and I'll see if I can give you a better explanation tomorrow."

Then if you're still struggling, email a colleague, a mentor, or me.  You'll figure it out.

A couple of teaching points: 

* This kind of argument over physics is healthy and important.  That's how scientists operate - they argue through difficult problems.  However, be sure that the argument stays respectful at all times.  The teacher shouldn't pull out the authority card; but at the same time, the student can't be displaying disrespectful body language.  The argument is not about points or grades.  The argument is about physics.  

* This sort of conversation is exactly why I recommend starting out your AP Physics 1 class with AP Physics B-style calculational questions.  A student generally doesn't argue if the answer key says "20 m/s" but their answer says "12 m/s".  To them, numbers have an authority that mere words do not.  The best way to avoid fights with students about subtle issues with explanations is to first build trust in your competence and fairness using problems with unambiguous numerical answers.  As you build in verbal response questions gradually over the year, the students will get used to discussing physics not points.  They will get used to the idea that they are supposed to answer in writing the first time, not come to you later trying to explain what they really meant.

* The beauty of teaching a full-year class is that there's always time to think overnight.  Nothing is so urgent that it needs an answer right now.  (Contrast that with baseball umpiring, where "let me think for a while about whether you're out or safe" doesn't win friends.)  Take the time.  Very often, you'll discover that the student who was so upset today doesn't really care any more tomorrow - teenagers live in the moment.

* Oh, what exactly is the error in this student's logical connections?  I'll save that for this later post here.

Collect assignments seat-to-seat rather than having students stack them up.

The typical way to collect assignments is to have students pile them in the front of the room.  This takes a frustratingly long time.

Especially if there's stapling to do.  Each student in turn, with a huge line behind them, painstakingly aligns papers just so before gently, gently, gently! applying the staple to just the right spot.  Then they check the staple the same way a six-year-old might self-satisfyingly inspect a booger, before reluctantly ceding the stapler to the next person in line.  And the process repeats.

You don't have the opportunity to shepherd the line or encourage haste, because four students, mouths flapping like baby birds begging for regurgitated fish, compete for your attention.  Three are offering excuses or asking for extensions; one merely has a question requiring an answer - right now! - about whether quantum wave functions influence Confucian philosophy.

At least three in a class of twenty will fail to turn in their assignment without calling for your attention.  Usually this is because they didn't do the assignment; but plenty of times it's because they simply spaced out during collection time.

"Do I have everyone's paper?" you ask.  The three students with delinquent assignments don't answer.  Yes, one is deliberately and passive-aggressively ignoring you, hoping you won't notice.  But one is honestly thinking you're asking about a different paper entirely.  The other one is thinking about sex and so didn't process what you said.

When you finally get around to going through the stack, you see that one person (most likely knowingly) left the second half of the assignment blank; this student and three others failed to put names on their work.

AARRGH!  What can you do?!?

You can't complain about slow stapling, or holler at folks to hurry the process up - you'll sound like an officious, nagging arse.  You can tell the hungry birdies to talk to you later, but they will still try to talk to you now.  You can call out individuals, asking whether they turned in their assignment; but you're using even more time, you might call out the wrong people, and you sound like an officious, nagging arse.  

And you can't wait until later to check who's turned in the work, because as soon as the students leave the room, they've forgotten about whatever they were supposed to turn in.  The assignment doesn't serve its purpose - getting students feedback on their understanding - if the students avoid showing you their understanding in the first place.

When I finally snapped, I decided to collect papers from each student's desk individually... and I've never gone back.

I bring the stapler with me so that *I* do all necessary stapling.  If someone doesn't have the work, I can charge an extension or make immediate arrangements for the student to get the work done at an alternate time.  I can glance at everyone's work as I pick it up, so that a substantially incomplete assignment gets the same treatment as a missing assignment.  

Most importantly, the collection process usually occurs while students are working on a quiz or on some sort of timed, quiet, individual work.  No one wants to tell a long story that invariably ends with "and therefore I don't have the assignment" - no, they want to get back to the quiz, so I just hear "extension, please."  If they forget to put their papers on their desk, they grab from their bookbag quickly and quietly when I come to their desk.  With an established routine and practice I can get a 15-20 person class collected in about two to three minutes.  

Note that this collection method isn't only for homework!  Any written assignment, any at all, can be checked this way.  I once saw master physics teacher Peggy Bertrand walk through the class putting her custom stamp on each student's problem log to mark their progress.  I've collected index cards with "check your neighbor" answers on them, shuffled, and picked one person to explain to the class; by collecting from each student's desk, I can be sure every card has a name and some sort of answer on it.

As always, I don't claim to have The One Right Way to collect assignments.  I'm merely sharing something that's worked for me...