Circuit misconceptions, and an advance copy of a quiz

On a problem set last week, I gave students the simple circuit shown to the right.  I asked what would happen to various parts of the circuit when I decreased R₂.  One of the questions in particular said, "What will happen to the current flowing from the battery when the value of R₂  is decreased?"

The most common answer:  

"The current will not change, because it's the same battery, so it will always provide the same current." 

Silly students, a battery provides a constant VOLTAGE, not a constant current -- but that's a common misconception in the first week of circuits.

The second most common answer:

"The current will not change, because R₂ is the farthest resistor from the battery, and so the current hasn't reached R₂ yet.

Silly student with a common misconception again.  The "distance from the battery" should never be used to justify anything associated with circuitry, because "distance" from a battery is irrelevant.

I decided to use a quiz to bust these misconceptions.  I've often announced the topic of a quiz the night before, in the hopes that students will target some studying.  This time, I actually sent out the quiz below via email, along with a quick note that discussing the questions in advance was encouraged.  

Did it work?  Yes, in that I've pretty much eliminated the misconceptions I've listed (for now -- I'll have to try again in a couple of months during our review time).  Sure, a few students did poorly, because either they (a) didn't prepare at all, or (b) convinced themselves or their friends that the current of a battery is always constant.  Either way, this exercise was useful!  For the students in category (b), they will never make this mistake again.  Someone in category (a) hangs his head in shame when his classmates tells him, "Jeez, Will, Mr. Jacobs gave us this exact copy ahead of time, it was easy points!"

Coming Soon: I handed out tomorrow's quiz tonight (and USIYPT 2012 results)

Folks, I've been at the US Invitational Young Physicists Tournament in Oak Ridge, Tennessee.  It was a well-attended event with the highest level of physics in the tournament's 5-year history.  Attending were:

Rye Country Day School, NY

Woodberry Forest School, VA

The Harker School, CA

Vistamar School, CA

Oak Ridge High School, TN

Shenzhen Middle School, China

Calverton School, MD

The standings after the preliminary rounds put (in order) Woodberry, Harker, Rye, and Vistamar in the semifinals.  Woodberry and Rye advanced; Rye's Andrew Mollerus and Michael Thomas defeated Woodberry's Peter Chen and Damien Chang in a taut, tense final physics fight.  Congratulations to Rye on their first USIYPT championship.

So, um, I lived and breathed physics fights for days, and I'm still adjusting back to the school routine.  My pile of work is testing the compressive strength of paper.  So, you'll get the next real post soon.  Teaser:  I graded a homework that included many common conceptual mistakes, including the "fact" that a battery must always provide constant current.  I wrote a quiz to help bust the misconception, and I actually emailed that quiz to the class folder tonight in advance of the actual quiz tomorrow.  I'll explain why I did that, I'll show you the quiz, and I'll explain whether the gambit did or did not work.

GCJ

Laboratory quiz question: pressure in a static column

A primary laboratory skill, one that is frequently tested on the AP exams, is determination of the physical meaning of the slope and intercept of a linear graph.  My own approach to such a question is to solve the relevant equation for the vertical axis of the graph, then to identify the variable representing the horizontal axis.  Anything multiplying this variable is the slope of the best-fit line; anything added to this term is the y-intercept.  We religiously go through this process of identifying the slope and intercept of a straight-line graph in every laboratory activity.

However, just doing laboratory work isn't enough to develop this skill.  In a 90 minute lab period or a lab report, a large subset of students will parrot their friends' answers or my suggestions without sufficient understanding.

So then, how do I check for "sufficient" understanding?  I give quiz and test questions that ask directly about the physical meaning of graphs that the class hasn't seen before.  For example, a recent "justify your answer" question showed a graph of weight on the vertical axis, and mass on the horizontal; what is the physical meaning of the slope of that graph?

It was instructive to read the justifications.  Most folks got that the slope is g, the gravitational field.  The stronger students recognized the relevant equation weight = mg; since weight is on the vertical and mass on the horizontal, whatever is multiplying m must be the slope.

The weaker students, though, got the correct answer reasoning from the units of the axes.  The vertical axis, they said, "was" newtons.  The horizontal axis "was" kilograms.  Since we've shown that g has units N/kg, the slope must be g.

I've got to force these weaker students to get away from the crutch of using units to determine a slope's meaning.  While such an approach is better than nothing, often the units of the slope won't obviously match any known quantity; or, a factor of 1/2 or 2π will be missed.  It's not like the method I'm proposing (of first writing the relevant equation) is too difficult for anyone.*

* The correct method does require remembering or looking up the correct equation, though, which is sometimes an obstacle; but that's a separate issue.

Below is a quiz that will help practice the skill of identifying the physical meaning of a slope.  Note that, by this point in the year, if we just graphed GAUGE pressure vs. depth, most of my class would have little trouble seeing that the slope is ρg.  The addition of the Po term in the equation for pressure in a static column causes difficulty.

1.    In the laboratory, you are given a tall graduated cylinder full of fluid, along with a pressure probe which reads absolute pressure.  You submerge the pressure probe in the fluid and record the reading in the probe P at various depths d below the surface.  The pressure at the surface is 1.01 x 10⁵ Pa.

A graph is made of P on the vertical axis and d on the horizontal axis.

(a)    Is the graph linear, or curved? 

o  Linear

o  Curved

(b)   If the graph is linear, explain how the density of the fluid r could be determined from the best-fit line.  If the graph is curved, explain what quantities could be graphed in order to produce a linear graph from which the fluid density r could be determined.

Two Masses and a Pulley, and a New Misconception

The badly sketched picture to the right shows a classic mechanics problem.  Two equal masses are connected by a string over a pulley.  In this case, the table is frictionless.

Typically, a student is asked to determine the tension in the rope and the acceleration of the masses.  Great -- that's (mg)/2 and g/2.*  This problem is richer, though, than a mere calculation might suggest.  Take a look at a quiz I gave the other day:

* The quick way to get this is to consider both objects as a single system.  The net force on that system is the weight of the hanging mass, mg; the mass of the system is 2m.  By Newton's second law, a = g/2.

1.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  The system is released from rest.

     

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

2.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  This time, the top block is given an initial velocity to the left and released. 

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

Ideally, 1(a) is answered with a kinematic approach -- the hanging mass is speeding up and moving down, so acceleration is also down.  For 1(b), I've defined "free fall" as the situation in which no forces besides weight are acting.  Since a tension acts upward on the hanging mass, the mass is not in free fall and the acceleration is less than g.*  And in 1(c), acceleration is downward, so net force must also be down.  That means down forces greater than up forces, so the tension is less than the weight.

* Okay, sure, if the upward tension is twice the block's weight, the acceleration could be g, upward.  That's highly unlikely in hanging-block-and-pulley problems.  

Of course, question 2 is identical to question 1!  The hanging mass is moving up but slowing down, so acceleration must still be downward.  (Or, one could argue that the block on the table still experiences only one horizontal force, that of tension, so its acceleration must be to the right; the blocks must move as a unit, so the hanging block has downward acceleration.)  Once it's established that acceleration is still down, questions 2(b) and 2(c) follow as in 1(b) and 1(c).

By far the most common misconception here is that the net force must be in the direction of movement.  A student will commonly get question one reasonably correct, but then say "the block is moving upward, so up forces must be bigger than down forces."  This question is just one more salvo in my arsenal aimed at that piece of nonsense.  

Another typical misconception is that in question 1, since the hanging block is falling near earth, its acceleration must be g.  That's taken care of with a request to state the definition of free fall and a sheepish look from the student.

And, a common mistake is to justify (a) and (c) with circular reasoning:  The acceleration is downward because the weight is greater than the tension; the tension is less than the weight because the acceleration is downward.  This student doesn't earn full credit, but I'm not worried so much about his comprehension. 

I discovered a new misconception today, though.  One of my brighter students said acceleration was equal to g, and he stated the definition of free fall accurately.  He asked, "since the surface is frictionless, the block on the table doesn't require any force to move.  So why won't the rope will be slack, the tension zero, and gravity the only force on the hanging block?"

At first I was flummoxed.  I set up two carts on my track, and showed him that the string was in fact not slack.  But why on earth would he think that no friction leads to a slack rope?

In further conversation, I discovered that he was referring back to our class's multiple conversations about how no net force is necessary for motion at constant speed in a straight line.  A mass on a frictionless track, once moving, keeps moving, even without any tension to pull it.  My student wasn't processing that this block on this surface was accelerating, not moving at constant speed.  Once I pointed out how the blocks must move together, and therefore accelerate together, he got it.

"Group Quiz" on impulse-momentum

Happy and Sad Balls -- which one produces
more force when dropped onto a force plate?

I can't count the number of articles I read that sanctimoniously preach how physics teachers need to "actively engage learners," involve students in "peer instruction,", provide "inquiry-based interactions", or any other set of edu-buzzwords you can create.  These articles push a fundamentally correct point: that I'll have enormously less success if I merely talk at the white board than if I somehow get the class to involve themselves in the topic at hand.

But as with any other educational method, active engagement only works if it's done right.  The trick is to get students to care about the answer to the question you posed, and about the justification of that answer.  I don't want to read any other literature telling me that active engagement can be effective.  I want to know specifically how other successful physics teachers get their students to actively engage.

I incessantly ask "check your neighbor" questions, in which I give students time to write an answer; I give time for class discussion; and then I survey the class, or call on a random student to summarize his thoughts.  These are generally effective.  However, after a few weeks, the shine has gone off of this novel (to the students) activity.  I can see the beginnings of apathy cross my students' faces... "Oh, again with the neighbor arguing thing.  Gee whiz."

I've got to vary my approach if I'm going to keep class activities fresh and interesting.  I tend to ratchet up the reward for correctly justified answers to my check-your-neighbor questions.  One thought that I've detailed previously is to call on a random student after discussion... if that student can clearly and correctly answer my question, I'll cancel the next day's quiz. 

I generally give a daily quiz at the beginning of class.*  My colleague Paul Vickers modified my daily quiz to an occasional "group quiz," in which he assigned groups of 2-8 students to answer a check-your-neighbor-style question for a quiz grade.  The fact that it's called a "quiz," that the students perceive that their performance will directly affect their grade, keeps everyone focused and on-task.  Yesterday, I tried a new hybrid approach to a check-your-neighbor question.

* Why?  Because students *care* whether they get the answers right, so they pay attention when I go over the quiz better than they would pay attention to the same conversation without the context of a quiz.

The question:  I have a happy ball (one that bounces nearly to the height from which it was dropped) and a sad ball (one that hardly bounces at all).  I drop each ball from the same height onto a force plate.  Both balls have the same mass; both balls are in contact with the scale for approximately the same time.  

Question 1:  Which ball experiences a bigger momentum change?

Question 2:  Which ball causes a larger reading on the force plate?

The method:  I began like a standard check-your-neighbor question.  I wrote the questions on the board, and asked the students to write and justify an answer in their notebook.  After about a minute or two, I asked everyone to argue with his neighbor.  Nothing to see here, really; I did let the discussion go on a bit longer than usual, making sure that those who were still making physics points to each other had a chance to hash out any disagreements.  

Finally, I gave everyone a blank card.  I told them to write and justify the answer to each question as if it were a quiz.  I promised that I would choose a student's card at random to read to the class.  A correct answer with justification on the card would be worth an extra credit point for EVERYONE on that day's quiz.

Oh, boy, did I get careful justifications.  One class's random delegate explained the answer perfectly, earning the credit with no doubt.  The other class's delegate explained beautifully (but incorrectly) that since the balls have the same weight, the force plate must read the same value, and thus both balls will have the same momentum change.  Knowing that many class members had convinced themselves of this mistaken fact, we talked about why the force plate would NOT read the weight of the ball.  

Right or wrong, making the check-your-neighbor question into a quasi-quiz convinced all my students to write clear descriptions of their thoughts.  Even though I only looked at one answer per class, everyone took the writing seriously, and everyone could evaluate for himself the quality of his arguments.  

I may get away with this quasi-group-quiz once or twice more before it becomes just another day of class.  Then I'll have to provide a different sort of incentive for careful, invested participation.  I'm open to ideas -- email me, or post a comment.

GCJ

Multiple Choice quiz: two-body problem in an elevator

Diagram for today's problem, modified from
something in (I think) Serway & Vuille

A couple of nights ago, I assigned a two-body problem in an elevator, from (I think) Serway & Vuille.  Two blocks were hanging from an elevator as shown in the picture; the acceleration in the original problem was upward.  On the homework, I asked (among other things):

• Draw a free body diagram for each object.
• Is the tension in the lower rope greater than, less than, or equal to 35 N?
• Calculate the tension in each rope.
• The ropes have a breaking tension of 85 N.  Calculate the maximum acceleration that will cause a rope to break.
• When a rope is observed to break, explain how the elevator was moving.

This problem is one of the best at separating those who are following an appropriate physics problem solving procedure from those who are just trying to plug numbers into some random equation.  The students who used the free body diagrams to write (up forces) - (down forces) = ma got the right answers, and got them quickly. 

On the other hand, the students who didn't carefully write the equations were confused for most of an hour, got the final answers correct because they asked friends for help, but usually earned little credit -- if after collaboration they just wrote "T = ma + 35 N, so T = 40 N" I marked the answer wrong.  Why?  Because I saw no evidence of how they got to that equation, other than listening to a friend without understanding.  Would an English teacher give credit for a one-sentence essay, even if the one sentence is spot-on in its conclusion?  Of course not.  So why on homework should I reward the correct numerical answer when it was essentially derived through magic?

I invited in for extra help the students who didn't follow the correct method.  They now feel much more confident about two-body problems, because they see that all they have to do is write the correct Newton's Second Law equations from the free body diagrams.  But it's still worth a follow up quiz -- either I build significant confidence, or I discover further misconceptions.

Below is today's three-question quiz that I'll give at the opening of class.  (It refers to the diagram above, in which the acceleration is DOWNWARD.  Yeah, I switched the direction of acceleration for the quiz.)  The "distractor" answers in the second question quote some students verbatim.  

Two 3.5 kg blocks hang from ropes in an elevator, as shown above.  The acceleration of the elevator is 1.6 m/s², downward.  While the elevator has this acceleration, the tension in the bottom rope is 29 N.

19. Which of the following best describes how the elevator’s speed is changing?

(A) The elevator is speeding up.

(B)  The elevator is slowing down.

(C)  The elevator is moving at constant speed.

(D) Whether the elevator is speeding up or slowing down cannot be determined.

  

20. Which of the following describes the meaning of an acceleration of 1.60 m/s²?

(A) The elevator gains or loses 1.6 meters per second of speed each second

(B)  The elevator gains or loses 1.6 meters each second

(C)  The elevator travels 1.6 more or fewer meters each second

(D) The elevator travels 1.6 m/s² more or less each second

(E)  The elevator is either speeding up or slowing down by 1.6 meters for every second squared.

  

21.  Now the magnitude of the elevator’s acceleration is doubled to 3.2 m/s², still directed downward.  What is the tension in the bottom rope now?

(A) 41 N

(B)  35 N

(C)  32 N

(D) 24 N

(E)  0 N (i.e. the rope goes slack)

Multiple Choice poll: electric field due to point charges

The poll on the left is based on a picture from Serway.  I've changed it a bit, and not just so the Serway Lawyers don't come after me -- I've made the question more conceptual than mathematical.  Go ahead and vote.  I'll post results next weekend, along with a discussion of the change I made and why I made it.

FYI, my AP class has just begun studying electric fields due to point charges.  This is their first homework problem, with the request for a justification of the answer, of course.

GCJ

Quiz -- elecric fields introduction



Electric Field Pic from thefullwiki.org



I introduce electric fields in an unusual way, one that's not consistent with any textbook. 

Most textbooks start with Coulomb's law for the force between two point charges.  Then, eventually, they define the electric field as the force per unit charge on a "test charge" in the field.  This is of course correct, and consistent with the way many seasoned PhD physicists think of the electric field.  Try explaining this to a 17 year old in his first physics class, though -- you might as well try to explain the infield fly rule to someone who's never seen baseball.*

* The infield fly rule is a closed book to many actual baseball players and coaches, too -- trust me, I'm an umpire.

I've found much more success presenting the concept of the electric FIELD as primary.  We begin with a full day's class on nothing but F=qE and the definition of the electric field.  And F=qE essentially *is* that definition.  F=qE gives the magnitude of the force on a charged particle in an electric field.  This force is in the same direction of the electric field for a positive charge; the force is opposite the electric field for negative charges.

Those ideas seem so, so basic... but it takes nearly a week of practicing before my students figure this out.  What do they do wrong?  Everything. 

* Label a point in space "point P," and say explicitly "There is nothing at point P but empty space, but the electric field at point P is 200 N/C to the right."  Then ask a student point blank:  "Is there a charge at point P?"  "Is point P positive or negative?"  "What is the force on point P?"  Merely getting folks to agree that a position in space does not have mass or charge, and cannot experience a force, is a MAJOR challenge.

* Now, put an electron at point P.  Verify with the class that an electron has a negative charge.  Ask about the direction of the electrical force on the electron.  Half the class will get this wrong... even though you just told them the rule about charges and electric fields!  Try it.  This is more complicated than you might think.

* No matter what you do, students will be confused about negative signs.  I tell them again and again: IGNORE NEGATIVE SIGNS when dealing with electric fields.  Neither a field or a force can be intrinsically negative.  Use F=qE to determine the amount of a force or field; then use the rule about negative charges to determine a relevant direction.

* The electric field does not determine the direction of a charge's MOVEMENT.  This is a holdover misconception from mechanics -- force and velocity are independent of one another. 

So on the first night of electric field study, I break my rule about assigning only two AP-level problems per night.  Instead, I assign six plug-and-chug F=qE problems.  All I'm looking for are the basics -- can students state magnitudes and directions of electric fields and forces.  See, that's more than half the battle in electrostatics.  If we can bust these misconceptions, then perhaps the ideas of parallel plates and point charges won't be so impossible.

Below is the quiz I gave after this first night of homework.  You might think this is "too easy" for an AP class -- but no, it's actually on or above their level after the first night of electrostatics.  And, I could give this at the end of the year, and I would not expect anything close to perfection from a class of students who will mostly earn 5s.  Electrostatics is HARD and ABSTRACT.  Anything we can do to simplify, we should do.

GCJ

1. An electric field points right. What is the direction of the electric force on a +3μC charge in this field?

(A) positive

(B) negative

(C) Left

(D) Right

(E) None of the above, the force is zero.

2. An electric field points north. What is the direction of the electric force on an electron in this field?

(A) North

(B) South

(C) positive

(D) negative

(E) None of the above, the force is zero.

3. A 500 N/C electric field points left. What is the electric force on a -2 μC charge in this field?

(A) 1000 μN

(B) 1000 μN left

(C) 1000 μN right

(D) -1000 μN

(E) Zero

Questions 4-5: An electric field points to the right. An electron enters this field while moving to the right.

4. Which way is this electron moving immediately after entering the electric field?

(A) right

(B) left

(C) positive

(D) negative

(E) nowhere, the electron is not moving

5. Which way is this electron forced when it enters the electric field?

(A) right

(B) left

(C) positive

(D) negative

(E) nowhere, the electron is not forced

Questions 6-8: The charge on an electron is 1.6 x 10^-19 C; the mass of a proton is 1.7 x 10^-27 kg. A proton is placed in an upward electric field of 200 N/C.

6. What is the direction of the electric force on the proton?

(A) Up

(B) Down

(C) Positive

(D) Negative

(E) None of the above, the force on the proton is zero.

7. Which is bigger, the electric force or the gravitational force on the proton?

(A) The electric force

(B) The gravitational force

(C) The electric and gravitational forces are about the same.

8. How many times bigger is the bigger force?

(A) 10⁹ times

(B) 10⁶ times

(C) 10³ times

(D) 100 times

Gravitation and Newton's Third Law Quiz

We've just finished covering Universal Gravitation.  Last night, my class did a problem involving a geosynchrous satellite orbiting Jupiter... they were to calculate the altitude of the satellite, and compare that altitude to the radius of Jupiter.

Today's quiz deals with conceptual issues from this problem, and reinforces Newton's Third Law (which we've been hammering for a week now).  I particularly like the last question, the ranking task -- it forces students to think beyond a single force pair.  They must combine their understanding of gravitation AND the Third Law.

Note that this quiz can be given in longer form or as a homework problem, just by adding the phrase "justify your answer" to the end of each question.

Space probe A orbits directly above Jupiter’s red spot, 9000 km above the surface. Identical space probe B sits on the surface of Jupiter.


27. Which probe has the bigger period of revolution?
(A) Probe A
(B) Probe B
(C) Both have the same period

28. Which probe has the bigger speed?
(A) Probe A
(B) Probe B
(C) Both have the same speed


29. Which probe has the bigger acceleration toward the center of Jupiter?
(A) Probe A
(B) Probe B
(C) Both have the same acceleration

30. Rank the magnitudes of the following gravitational forces from greatest to least. If two or more quantities are the same, say so clearly.

I. the force of Jupiter on space probe A
II. the force of Jupiter on space probe B
III. the force of space probe A on Jupiter
IV. the force of space probe B on Jupiter
V. the force of space probe A on space probe B
VI. the force of space probe B on space probe A


greatest ___ ___ ___ ___ ___ ___ least

Multiple Choice questions may have more value than you think

It is common for teachers in other disciplines to view multiple choice questions as the lazy teacher's way of avoiding grading.  In physics, that could hardly be farther from the truth.

Even physics teachers often think of multiple choice questions merely as a useful way of evaluating student understanding broadly and quickly -- after all, it takes a student only about 1-2 minutes per question to respond, and a teacher 1-2 hundredths of a second to grade by machine.  A multiple choice question can be even more valuable.  Some ways to use multiple choice questions creatively:

* I've detailed many times the "test correction," in which students earn back half credit on a multiple choice item they miss by explaining the answer thoroughly.

* I've also explained my typical "clicker exercise," in which teams of two students each have a chance to respond to a multiple choice item on the classroom response system.  The ensuing discussions of each questions can be more valuable than the best-designed homework question.

* Multiple choice questions can be expanded into free response-style homework question with the addition of three words: "Justify Your Answer."  Just today I decided that my class had had enough AP free response review homework.  So I took three of the tougher magnetism questions off of the recently released 2009 AP multiple choice exam, printed them out on a page, and assigned the justifications for homework.

* Even after a question has been assigned and justified, you can develop a further quiz based on the situation presented.  For example, consider a typical multiple choice question in which two railroad carts bounce of each other.  Originally, students may have had to find the amount of mechanical energy dissipated in the collision.  For some reason, that calculation frequencly causes trouble.  So, after I've demanded a thorough justification, I give a quiz -- same question, only this time the carts stick together after collision.  If the student truly understood the concept and calculation on the original problem, the new one should be no trouble.

Condider the multiple choice question below:

A car collides with a mosquito.  Which experiences more acceleration in the collision?

(A) The car, by a factor of about 10⁶

(B) The mosquito, by a factor of about 10⁶

(C) The car, by a factor of about 10¹

(D) The mosquito, by a factor of about 10¹

(E) Both experience the same acceleration.

When correcting this problem, some students will obediently go through the Fnet=ma calculation, estimate the mass of the car to be a million or so times the mass of the mosquito, and correctly answer B.  But not everyone will truly recognize the underlying principle here: This reasoning depends on Newton's Third Law, which demands that the forces experienced by each object in the collision must be the same.

So I'll ask this follow up question on a quiz:

A car collides with a mosquito. The mosquito sticks to the car after the collision.

(a) Which experiences more acceleration during the collision, the mosquito or the car?

(b) Which experiences more impulse during the collision, the mosquito or the car?

(c) Which experiences more force during the collision, the mosquito or the car?

GCJ

Preparing for the AP exam -- Huge Equations Quiz

AP-level students need to memorize equations.

Why, you ask?  After all, many professors and teachers pooh-pooh rote memorization, citing the reasonable notion that physics is about the correct USE of fundamental principles, not about their instant recall. 

As a practical matter of teaching Advanced Placement physics, the AP multiple choice section does not provide an equation sheet; thus, a student who does not know that the energy of a capacitor is (1/2)CV² will not get a question right on that topic. (I've had it argued to me that it's better for a student just to know "energy is directly proportional to capacitance, and also to the square of the voltage." First of all, I dispute that a first or second year physics student understands what the word "proportional" means. Secondly, isn't it far easier to remember the equation than this long complex sentence?)

Beyond testing issues, I think it is pedagogically sound to insist that students know the equations that underlie the basic principles under study.  Physics problem solving requires making connections between topics, using multiple intellectual skills at the same time.  Students have a much easier time with multi-step problems if they have the confidence born of rote knowledge of the basic equations, if they DON'T have to spend two minutes of a 15 minute problem searching for the correct relationship on an equation sheet or in a textbook.

I make the memorization requirement clear all year in my AP class.  Equation sheets are never provided, except on the free response portions of tests; students are regularly quizzed on their recall of equations.  The "four minute drill," in which the class is prompted to take turns reciting as many equations as possible in four minutes, is a fun and effective rote review tool. 

I hammer home the need to memorize with a final, enormous equations quiz a couple of weeks before the exam.  The quiz consists of two parts:  20 prompts to which the student must write the correct equation (i.e. I say "net force" and the student replies "ma"), and 5 equations which the student must describe briefly (i.e. I say "ma" and the student says "net force").  The key is, this quiz is not graded on the square root curve -- 60% is the minimum passing score, and 90% is necessary for an A.  And, crucially, a passing score is required in order to pass the course.  I will have a percentage of the class get less than 60% on the first try -- these folks get to try again (with a slightly different quiz) on Monday.  And probably one or two will have to try again on Tuesday.  I've had seniors need four or five attempts to pass.  That's fine -- since they have to pass in order to graduate, they put in the minimal effort to memorize their equations.  Then they get a few more problems right on the AP exam than they otherwise would. 

If you're interested in using my huge equations quiz, check out the link on Scribd: http://www.scribd.com/doc/30391978/102-Huge-Equations-Quiz

GCJ

A different use of a clicker quiz -- snell's law

Springtime for seniors brings a competition as to who can do the least amount of work.  That's certainly not true for all seniors, but if you listen to any high school faculty this time of year, you'd think that this year's crop of 17 year olds were the passive-aggressive scourge of Satan.  In a previous note, I explain my use of the "exemption" as one prong in my defense against the senior slide.

The gist of the exemption:  Students who put in particularly strong effort on out-of-class assignments earn the right to skip a future assignment of their choice.  The first exemption of the year in general physics is awarded to the student with the highest homework average from the previous trimester.  From here on, exemptions will be given for things like maintaining an A homework average over the course of a full week, writing a perfect quiz when that quiz is based on a homework assignment, or a perfect fundamentals quiz.

The homework problem for today involved refraction in a triangular block of glass.  I've introduced Snell's Law already, and we've done several basic problems with simple geometry.  Today's problem was more complicated, because the normal was NOT straight up and down the page.  Take a look at the diagram to the right, which is slightly editied from a problem in the Glencoe text.  The homework problem did not label the 49 degree angle; instead, it gave θ_i as 45 degrees, and asked to find angles A and B, and θ_exit

I warned everyone ahead of time that angles A and B are NOT 60 degree angles.  That doesn't prevent half the class from making that assumption anyway, but it sets up for success those students who pay attention.

For today's quiz, I gave the diagram shown, with the 49 degree angle.  I asked the six questions at the end of this post, to be answered on the classroom response system (the clickers).

Now, I am careful NOT to use the clickers for quiz purposes through most of the year.  At first, I absolutely do not want students seeing how their peers did.  I don't want boasting about good scores, I don't want the sour-grapes rationalization that inevitably follows when someone gets a 25%.  Over the course of the year, 1/4 on a multiple choice quiz is a drop in the bucket.  My guys can deal with that.  What they CAN'T deal with at first is the idea that the average score on the quiz might only be 50%. 

In the spring, though, I use the clickers because I WANT score distributions to be public.  Everyone needs to see that yes, people are getting 6 correct answers on this quiz.  The clickers' instant feedback allows me to pinpoint the folks who missed a straightforward question, and make sure they know why they got it wrong.  And most importantly... when the quiz is over, I can IMMEDIATELY and publicly award an exemption to everyone who got a perfect score. 

GCJ



1. What is the angle of incidence at the left edge, labeled θ_i in the diagram?

2. What is the angle of refraction at the left edge, labeled r in the diagram?

3. What is angle A?

4. What is angle B?

5. What is the angle of incidence at the right edge?

6. What is θ_exit?

 

Double Slit -- convert all distance quantities to meters

We're beginning double-slit problems right now. This is not a difficult topic, especially for AP physics B students who have spent all year learning how to learn physics. They generally pick up quickly what the variables in dsinθ=mλ mean.  They have a bit of trouble with a deep understanding of m.  At first, I just get them to see that m = 0 at the central maximum, m = 0.5 at the first dark spot, m = 1 at the first bright spot, etc.  Once they have facility with getting physically reasonable answers out of the relevant equation, we talk about m as the number of wavelengths in the path difference between two waves.  The meaning of m is the only true conceptual challenge in double slits.

Getting correct answers out of dsinθ=mλ can sometimes be a chore, though.  It's easy to think that such a straightforward calculation doesn't require careful thought; and students hopefully have been trained by now that plugging into the calculator is of minor importance compared to a conceptual understanding of the topic at hand. Nevertheless, I usually need to remind the class that all distance quantities in this equation, or in its small-θ companion x = mλL/d, must be in METERS.

Here's today's quiz.  Note that I ask for no problem solving or calculation; I just make sure everyone knows what the variables mean, and how to convert to meters.  The most common mistake on this quiz:  620 nm can be written as 620 x 10^-9 m, or as 6.20 x 10^-7 m, but NOT as 6.20 x 10^-9 m.

GCJ

A red laser with wavelength 620 nm in air shines through two slits which are separated by 0.50 mm. On a screen 2.0 m away from the slits, the laser makes an interference pattern. The brightest spot is located directly in front of the two slits. You are asked to find the location of the nearest bright spot to the central maximum.

1. What is the relevant equation?

2. Assign a value to the following variables. USE UNITS OF METERS FOR ALL DISTANCE QUANTITIES!!! Indicate the variable that is not given in the problem statement; don’t bother to solve for it.

d =


θ =


m =


λ =

Magnetism Introduction: Assigning reading, a reading quiz, and personally handwritten notes

I ask students to read their textbooks very, very rarely.  Textbooks can be excellent references, they can provide sources of problems, examples of problem solving processes in action... but it is rare that a first-time physics student can simply read and understand a section in a textbook.

Well into the school year, after I have hammered the class about the difference between physics and math, when the students themselves are demanding demonstrations and physical (rather than mathematical) explanations of new topics... then and only then will I consider assigning some reading.  And even then, that reading must have a clear and useful purpose.

One reading assignment I've used repeatedly is to introduce the magnetic force on a charge and the first right hand rule.  Serway's presentation is pretty good, though equation-heavy and technically written.

If I were to present this topic in class, I'd be stopped with questions at every turn:  "Is a magnetic field the same thing as an electric field?  What does the θ mean in F=qvBsinθ   ?  Does a negative charge get forced the opposite way as a positive charge?  Why doesn't a charge experience a force if it moves along the magnetic field lines?  Why do we use B for magnetic field, not M?"  I'm quite proud of my class for their inquisitiveness, I'm pleased that they expect these sorts of questions to be answered.  There have been numerous times in class when I've encouraged, nay, DEMANDED such questioning.  It's difficult for me to communicate "Shut up right now and listen for ten minutes while I just show you the fundamentals.  You'll have time to play with these new ideas on homework and in class tomorrow, but for now, I just have to feed you this information.  So be patient and quit buggin' me."

I assign the brief section of text in which the equation F=qvBsinθ and the right hand rule is introduced.  Sure, this is pretty confusing, even to my experienced AP students.  But now they know what questions to ask.  And the text answers many of these questions, so I can go straight to a presentation on the right hand rule, followed by several demonstrations in which I use a manget to deflect a beam of electrons in the direction predicted by the right hand rule.

Here's how I set up the reading assignment.  Instead of two homework problems on, say, Thursday night, one of the problems is replaced by the reading assignment.  Here's what I say:

Problem 2: READ Serway chapter 19-3, about magnetic fields. Magnetic fields are different from electric fields. I expect you to know equation 19.1, including what each term means; and, you should look at how to figure out the direction of a magnetic force. Friday's quiz will be basic questions about this reading.  You will be allowed to use your notes on this quiz if the notes were personally handwritten by you.

Note that I've referenced the only relevant equation in the section, though Serway provides others that are not particularly relevant.  Also note that by promising a quiz I ensure that a student who has difficulty doesn't just throw up his hands and say "I don't get it."  He's welcome to say that, but he'll fail the quiz.

(I'm particularly fond of the "you may use personally handwritten notes" proviso.  I credit Haverford history professor Roger Lane for this idea.  Half of the course grade in US History was based on periodic pop quizzes based on the assigned reading.  We were always allowed to use our notes, but only if these notes were handwritten by us, not xeroxed or highlighted.  So we all took pretty good reading notes.  And, the quizzes weren't so hard, 'cause we had paid such good attention to the reading, 'cause we had taken such careful notes.  Insidious, that Roger Lane.)

Anyway, here's the quiz.  Note that questions 3-5 are as much about knowing when a magnetic field DOESN'T produce a force as about the right hand rule.

1. What are the units of a magnetic field?

2. State the equation for the magnetic force on a charged particle. Define each variable.

3. A positive charge moves to the right in a magnetic field that points toward the top of the page. State the direction of the force on this charge.

4. A negative charge moves to the left in a magnetic field that points to the right. State the direction of the force on this charge.

5. A positive charge is at rest in a magnetic field that points toward the bottom of the page. State the direction of the force on this charge.

Big Butt Electricity Fundamentals Quiz

We're just now finishing with electricity concepts -- fields, potentials, resistors, capacitors.  Coincidentally for me, we have a couple days off for "long winter weekend" starting tomorrow.  This is the perfect time to attempt to cement the tough-to-remember rules we've learned over the past month. 

On Monday, I announced the forthcoming "Big Butt Electricity Fundamentals Quiz."  (Why "Big Butt?"  A 17 year old boy is more likely to pay attention to and study for a quiz with this silly, memorable, and quasi-profane name than just another fundamentals quiz.)  The quiz itself is 25 short questions to be done in eight minutes.  Feel free to use it in its entirety, or in portions. 

Follow-up to multiple choice test corrections

Those of you who have attended my workshops know that, in Jacobs Physics, test corrections are one of the two most important components of the course. Sometimes, though, even the test corrections need correction.

Instead of assigning another round of “correction corrections,” I tend to just give the whole class a quiz when I find consistent misunderstandings. For example, consider the two multiple choice questions below. These were originally AAPT Physics Bowl questions, I believe…

1. A 2 kg object initially moving with a constant velocity is subjected to a force of magnitude F in the direction of motion. A graph of F as a function of time t is shown. What is the increase, if any, in the velocity of the object during the time the force is applied?

(A) 0 m/s

(B) 2.0 m/s

(C) 3.0 m/s

(D) 4.0 m/s

(E) 6.0 m/s

2. A deliveryman moves 10 cartons from the sidewalk, along a 10-meter ramp to a loading dock, which is 1.5 meters above the sidewalk. If each carton has a mass of 25 kg, what is the total work done by the deliveryman on the cartons to move them to the loading dock?

(A) 2500 J

(B) 3750 J

(C) 10 000 J

(D) 25 000 J

(E) 37 500 J

Many students showed an iffy grasp of these two questions on their test corrections. So, I posted to our class folder early last night. I noted that we would take a follow-up quiz today on these problems. I wrote the quiz to address specifically the mistakes that I had repeatedly seen on the first attempt at corrections. Here’s the quiz:

1. (a) What’s wrong with the statement “Work is done both up and to the right in order to move the boxes up the incline?”

(b) What is the direction of the force necessary to carry one box up the incline at constant speed? Justify your answer. Your justification should include a free body diagram.

2. (a) Explain why the average force during the time interval t = 1 s to t = 5 s is NOT 1.0 N.

(b) How do you get impulse from this graph WITHOUT trying to find an average force?