How many balloons to lift the Nachoboy?

Saturday brought with it the Nachoboy’s sixth birthday party. I undertook a strategically important job: getting the Nachoboy* out of my wife’s hair while she prepared for the onslaught of 14 kids.

When the boy and I returned from Taco Bell,** the living room was crowded with Helium Balloons. Milo and another small human grabbed the balloons, and the other adults joked with me about the balloons lifting the kids away. So, of course, I had to estimate the number of balloons that could actually lift a six-year-old.

The Nachoboy weighs about 45 pounds, which equivalent to a mass of 20 kg.*** Thus, we need 200 N of lift.

Estimate #1: Buoyant Force Analysis

Archimedes’ Principle states that the buoyant force is equal to the weight of the displaced fluid – so, we need the balloons to displace 200 N (equivalent to 20 kg) of air to lift the Nachoboy. Air has a density in the neighborhood of 1 kg/m³. That makes 20 cubic meters of balloon volume.

Each balloon has a diameter of a bit less than a foot. If we call the radius 10 cm, then the volume of a balloon is .004 m³. (That’s using the equation for the volume of a sphere, (4/3)πr³. It helps to approximate π = 3.) Then, 5000 balloons give us the 20 cubic meters.

Estimate #2: Spring Scale Measurement

I grabbed a spring scale from my classroom. The 13 balloons I could gather in the living room pulled up with about half a newton of force. So, call it 25 balloons to the newton of buoyant force… that gives an experimental estimate of 5000 balloons. It seems our estimates are at least self-consistent.

Estimate #3: Use internet research

First of all, crazy people have in fact levitated themselves with helium balloons for transportation purposes. Most recently, we have a Mr. Couch from Oregon. But that doesn’t answer the question about numbers. In the picture at the link above, it’s possible to count his balloons, but they seem quite large, and inferring a reasonable scale is difficult.

Not surprisingly, the Mythbusters worked on this very problem, except that they levitated an adult. They only needed 6000-7000 balloons, a number consistent with our order of magnitude estimates above. The pictures at their slide show of the demonstration show balloons of approximately the size I was considering.


What have I figured out? Well, this won’t work for use at the science demonstration show that the Atlanta Cracker (Woodberry's AP chemistry teacher) and I do each spring for prospective students. On the other hand, we’re starting to look into the price of helium and balloons. It might be worth spending the time and money to capture us lifting Milo on video, and posting the video online. More on this topic eventually, if we do end up filling 5000 balloons.

Or, maybe we should just levitate the cat instead of a kid.

GCJ

* The Nachoboy is also known as Milo Cebu Jacobs, my six-year-old. The name comes from my other blog, Nachoman's Baseball. Check out some old columns now; I'll be writing there again once the season starts next month.

** The Taco Bell in question is attached to an enormous playground. Funny, I would rebel nastily if someone charged admission to a playground. However, I wholeheartedly support the Taco Bell playground, even though it’s $10 down the drain for lunch every time I take Milo there.

*** Don’t start on me with the “20.45 kg.” We’re making an order of magnitude estimate. I’m happy if I get the number of balloons right to within a factor of 5 or 10. The whole point is to figure out the feasibility of the experiment. If it’s going to take 100,000 balloons, well, we’re never going to actually do that. If it only takes about 20 balloons, we’re having liftoff this afternoon. All numbers here are good to a maximum of one significant figure – and that’s all we need.

Teaching AP Physics? Then give AP tests.

People consider the AP physics exam difficult. Of course, “difficult” is a relative term. Difficult compared to what?

Usually students mean that the AP exam is tough compared with the tests they are used to taking in high-level math and science courses. The College Board agrees:

“Since the complete exams are intended to provide the maximum information about differences in student achievement in physics, students may find them more difficult than many classroom exams.” [p. 16, College Board’s AP Physics Course Description.]

A school’s grading scale usually requires a score of 90% or more to earn an A, and 80% or more to get a B. This requirement should not be onerous on tests that require simple recall. However, the AP exam demands so much more than merely recalling physics facts. On-the-spot problem solving is a far more involved skill than memorization is. Thus, on the AP-1 exam, 70% or so of the available points equates to a top score of 5; the average score nationally is below 50%. No wonder students think the exam hard – in their minds, even the very best students barely managed to earn a D.

Now, most physics teachers recognize the need to prepare their students for the rigorous nature of the AP exam. In April, they give their students practice exams. I submit, though, that giving normal, classroom-style tests all year followed by practice AP exams in April is a recipe for failure.

Imagine a college football team who plays a ten game season. The first nine games are against division-3 doormats, and the team goes 9-0. But, the last game of the year is at the university of Florida, a team sending half of its seniors to the NFL.

How should the coach get the team ready for the Florida game? Perhaps he arranges a scrimmage against Ohio State the week before. Is that going to be enough preparation?

Or, are the players going to be so intimidated at the vastly higher level of physical play that they hang their heads and give up the first time something goes wrong, that they begin to expect failure?

I submit that the only possible way this coach might have a prayer of beating Florida in week 10 is to schedule similar teams all year – even if the team’s overall record goes from 9-0 to 5-4. If the goal is to win the big game, the team must prepare for the big game from the start of the season, not just a week or two ahead of time.

Students who go through the school year from August to March getting 95% on their classroom tests have been conditioned as to what to expect on a physics test. Then, when they take an authentic practice AP exam in April, they are thrown for a loop. Even if they are capable of getting the 70% necessary for a top score, they may well hang their heads and give up 30 minutes in when they recognize that they aren’t performing nearly as well as they had on their classroom tests.

The solution, I believe, is to give AP-level tests right from the start of the year. Pick out authentic questions that cover the topics you have studied in class. Make the students work at the pace necessary for the real AP exam – approximately 1:20 per multiple choice question for physics C (1:50 per question physics 1), one minute per point for physics C free response (2 minutes per point for Physics 1). Then, grade the test on the AP scale! Somehow, whether it be through a curve or (as I prefer) by earning back points with test corrections, make sure that 70% or so converts to an A, 55% or so to a B, and so on based on the scoring from a released exam.

[Edit in 2016: Nothing wrong with giving items from the old physics B tests early in the year, and then moving the focus steadily from problem solving to explaining by integrating more and more physics 1 items.  Either way, you're using authentic AP items with available, external rubrics, on which 90% is essentially unattainable.)

Sure, you’ll get complaints before and after that first test. Everyone will come out thinking they failed, thinking they’ve never seen a test that hard. But, when they see their actual grade, when they get a chance to correct their mistakes and earn credit for those corrections, when they recognize that they are NOT going to fail the exam, they’ll relax. About halfway through the year, AP-style testing will become routine.

The proof is in the pudding. I don’t have geniuses in my class by any stretch. Yet, on the AP-style trimester exam consisting entirely of authentic questions from previous APs, 17 of my 25 students earned 5s, and everyone got 3 or above. They’ll do even better in May. I am thoroughly convinced that my class’s success is not as much due to my teaching skill as to the fact that I make them comfortable with the level and style of the exam throughout the year. Try it. It works.

GCJ

The Jacobs Crusade – NO QUESTIONS DURING A TEST!!!

I refuse to answer questions during a quiz, test, or exam.

Why am I so cruel, you ask? Or, at least, students, parents, and colleagues ask. Thing is, by mid year, no one complains about the “no question” rule. And my colleagues are occasionally envious.

I want to know what my students can do on their own. Daily interaction and coursework provides plenty of opportunities for students to talk to me and to each other, to figure out how to approach the types of problems the class covers. The purpose of a test is for my students and me to see how successful they have been in learning the material. And I can’t effectively evaluate my students or my teaching unless I get an authentic account of each student’s ability.

Think about what kinds of questions students tend to ask during a test…

-- “What is this question asking for? How do you want me to answer?”

This student may be truly confused by the wording of the question; or, the student could be stuck and hoping for a hint. Either way, this is an inappropriate question. I make sure that homework problems are worded in the same style as test problems, so that there should be no surprises on the test. Homework is the time to learn vocabulary, and to get in tune with “what the problem wants you to do.” And if the student is stuck, well, then the test has served its purpose – it’s exposed a portion of the course that the student does not understand yet.

Besides, how am I supposed to answer this? Tell him to read the question again? Or, am I supposed to just solve the problem for him? I don’t think so.


-- “You didn’t give us enough information to solve this problem.”

Well over 90% of the time when this question comes up, the test problem is just fine… it’s that the student is approaching the problem incorrectly. For example, in a conservation of energy problem, the mass term often cancels; an object’s mass is not a necessary piece of information. Recognizing that the mass cancels is a physics skill, one that I often test. But if students are allowed to ask why I didn’t give them the mass, then part of the purpose of the test problem is eliminated!

So what about that rare instance when you should have given an object’s mass, but didn’t? Shouldn’t people be able to ask about that?

No.

Before the first test of the year, I prepare my classes for just this kind of situation. I tell them that if they think I screwed up by not giving them critical information, then they should tell me so in writing on the test… then they should continue solving the problem by making up a reasonable value. There’s nothing wrong with someone writing, “You didn’t tell us the mass of the roller coaster! So, I’m going to pretend it’s 500 kg.” This student will be in good shape… even if he was supposed to solve for the mass some other way, he can still get partial credit for finishing the problem. And, if I truly screwed up, then he’s demonstrated enough knowledge to earn full credit. Most importantly, he hasn’t distracted the entire class with his question.

-- “You made a typo here. You said, ‘find the nass of the roller coaster.’ Did you mean ‘find the mass of the roller coaster?’ ”

This sort of question makes me livid. Do you want me to take off every time your writing is unclear, or every time you make a minor grammatical error? You distracted the entire class for the express purpose of saying, in effect, “Na na na na boo, boo, teacher screwed up!”

Once again, pre-test preparation can prevent this sort of one-upsmanship. Make it clear from day one that you don’t mind any sort of WRITTEN comment on the test. If a student wants to write how awful a question is, or to criticize my spelling or syntax, more power to him, as long as he does it in writing. In fact, I often give long, detailed, polite responses to reasonable criticisms written on a test.

Most importantly, of course, if the student happens to be right about a poorly worded or ambiguous question, I’ve got to be fair in my grading. Once in a long while I just throw out a part of a question, or give a huge variety of answers full credit, because I realize later that the problem wasn’t good to begin with.

In fact, just today someone told me (after the test was over) that multiple choice question #18 included two identical answer choices. It turned out that those choices were wrong, so no one cares. But if the identical choices had been correct, I would have at least counted either choice right, and possibly thrown out the entire question because of the confusion my mistake caused.

But no one asked during the test. All of my students got 120 minutes of silence in which to do their work. I got some grading done. This time of year, if I’ve done my job right, a trained orangutan could administer my tests. And that, I think, is the way things should be in high school.

Rainwater in a cart – why does the cart slow down?

A multiple choice question on, I think, the 1998 AP B exam, asks about rainwater falling into a moving cart. If the rain falls vertically, does the cart speed up, slow down, or maintain constant speed? And is that because of conservation of momentum or energy? (Note that we're not considering a donkey-pulled cart, just a freely-rolling cart.)

The answer is that the cart slows down due to conservation of momentum. Mechanical energy is not conserved in this situation because much of the kinetic energy of the water dissipates as thermal energy upon splashing in the cart. And since momentum is conserved, the additional mass added by the rainwater causes the cart’s speed to drop in order to maintain the overall mass×velocity.

My students often miss the question on first pass. They’re not really sure what’s conserved and why. “Conservation of energy” is so ingrained in their consciousness – both from a physics and an environmental standpoint – that they nearly automatically choose an answer with the magic phrase.

I asked this question on my first trimester exam back in November. Anyone who missed the question had to write a test correction. Problem was, a lot of folks still made poor arguments. Some thought that energy was conserved. Some thought the cart would speed up because of the water’s initial speed – they didn’t separate vertical from horizontal momentum. I knew many of these folks were ripe for making the same mistake again.

I’m not averse to hammering an idea over and over. That’s the main idea of the “Less is More” teaching philosophy – you don’t have to assign that much work, but you must hold students thoroughly accountable for understanding everything that is assigned. So, I told the class to expect a quiz based on this question. Below is the quiz I assigned...



1. An open cart on a level surface is rolling without frictional loss through a vertical downpour of rain. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. Thus, the cart and water can be treated as if they are colliding.

(a) Which of the following is conserved in this collision? Circle all that apply.

Kinetic energy

momentum

velocity

acceleration


(b) What is the horizontal velocity of the rainwater before it lands in the cart?


(c) What will happen to the speed of the cart? Explain in one or two sentences.

GCJ

(Top photo from donchesnut.com.)

Electric fields and potentials of point charges

The electric FIELD produced by a point charge is E = kQ/d². The electric POTENTIAL produced by a point charge is V = kQ/d.

Electric field is a vector. This means that the equation E = kQ/d² gives just the magnitude of the electric field, and therefore the sign if the charge producing the field should NOT be plugged into the equation. The direction of the field is away from a positive charge, and toward a negative charge.

Electric potential is a scalar. This means that the sign of the charge producing the potential SHOULD be plugged into the equation V = kQ/d. Positive charges produce positive potentials; negative charges produce negative potentials.

When more than one charge produces an electric field, the net field is found by vector addition. When more than one charge produces an electric potential, the net potential is found by algebraic addition and subtraction.

I can’t begin to tell you how frustrating it is to go over the above paragraphs 30 times in 15 different ways with 80 different examples… and then to see someone tell me that the electric field due to a couple of charges is “(2-Q)/d.” Aargh!!!

Such is the nature of electricity, though. I have to remind myself time and again how abstract the idea of a “field” is to begin with, let alone potential, the concept of “charge,” the creation of a field or potential… double Aargh!

The only success I’ve found at the physics B level with these topics is through repetition. There is no choice but to ask students quiz questions 30 times in 15 different ways with 80 different examples. If that doesn’t work, give it a rest for a week… then ask a 31st time.

Below are four questions from a fundamentals quiz which get to the heart of electric fields and potentials due to point charges. Can you answer them correctly? (Post a comment with your answer! If you’re wrong, that’s okay… someone will correct you.)

1. What is the electric potential produced by a -3Q charge a distance of 2a away from the charge?

2. What is the magnitude of the electric field produced by a -3Q charge a distance of 2a away from the charge?

3. In the diagram to the right, what is the magnitude of the electric field produced by the two charges at point P?

4. In the diagram to the right, what is the vertical component of the electric field produced by the –Q charge at point P?

GCJ

(Photo at the top from alexhulbert.com . )

Where do you find good multiple choice questions?

Yesterday I described my nefarious scheme for getting students to study for the trimester exam by means of a multiple choice extra credit exercise. I also indicated that the multiple choice portion of the AP trimester exam will include 23 multiple choice questions. During the trimester, I give multiple choice quizzes two-three times a week. And you will find out soon that, next month, my AP class will be plowing through many, many multiple choice exercises in preparation for the May AP exam.

You will find that I BELIEVE in the utility of a well-constructed multiple choice item to evaluate students’ understanding of physics concepts, and to help students confront their own misconceptions. Sure, many physics skills are better tested with free response items; I willingly concede that if the majority of your assessment is done with multiple choice, you get a biased account of a student’s physics ability. Too often, though, teachers and administrators dismiss multiple choice merely as the first and last resort of a lazy instructor.

Such is the pejorative connotation of multiple choice that when I was the first Woodberry teacher to acquire a scantron machine, I hid it in my office in order to avoid the inevitable soapboxing from my colleagues outside the science department. The machine is still in my office… but after eight years it’s become an open secret. At exam time I willingly help out the rebels from humanities departments who sneak down to use the machine.

Now, don’t think that I’m encouraging slack teaching. In order to be useful, a multiple choice question must be well-constructed. Writing good items is not a trivial exercise, as I’ve discovered numerous times. Not much is more embarrassing than going over a quiz in which the correct answer doesn’t appear in the choices, or in which the answers are not clearly different from one another. Initially, the front-end work necessary in finding or writing multiple choice questions cancels out the back-end work saved by grading via scantron machine.

(As an aside, my English department colleague El Molé invented the principle of conservation of exam workload – in writing an exam either you have to spend enormous time writing multiple choice or grading essays. The total time spent on the exam process is conserved regardless of how the exam is structured.)

Perhaps I’ve convinced you of the utility of multiple choice. Multiple choice practice might be useful and wonderful, but this post begs an obvious question – where in the heck do you find enough good multiple choice items for use in your class?

That’s a tough one, but I have a few suggestions. First of all, get good at evaluating the quality of an item. When you assign a question on a test or quiz, rewrite it immediately or throw it out if it didn’t work quite the way you thought. When you happen to see a good question somewhere, write it down before you forget.

The best source of multiple choice items is the College Board itself. A number of full-length AP exams have been released. Go attend an AP physics workshop, contact an AP physics consultant, or go to collegeboard.com and look for released exams. (Neither I nor anyone else is allowed to post content directly from an AP exam, as that would infringe on the AP program’s copyright and a plague of lawyers would descend upon me.) The College Board also writes the SAT II physics test, which consists of well-written and vetted multiple choice questions. Take a look at a sample test and use some of those problems.

I do not recommend most commercial AP or SAT II preparation books. It’s rather pathetic how out of touch most of these books are with the level or content of the exams, or sometimes even with what physics is all about. Similarly, I strongly recommend against fly-by-night companies such as the ubiquitous “D&L marketing” who send flyers peddling AP physics multiple choice tests.

Two books, though, are in fact useful. One is my own, 5 Steps to a 5: AP Physics B & C by Greg Jacobs and Josh Schulman. Yeah, I had better recommend my own book. One other good source is the older book published by Kaplan, written by Connie Wells and Hugh Henderson. Connie and Hugh are both AP readers, both former members of the Test Development Committee (the group that writes the AP test each year), and both should be on any list of the top 10 physics teachers in the USA. It’s worth finding a copy of the Henderson/Wells book – the newer Kaplan book has different authors, and I have not evaluated its quality.

Each year the American Association of Physics Teachers sponsors the Physics Bowl, a 40-question multiple choice contest. Old tests from 1994-2000 can be found at the PSRC website. Some questions are good, some aren’t, some won’t cover the topics you want; but one way or the other, Physics Bowl questions are an awesome resource.

The AAPT sells CDs of Physics Bowl tests and solutions from 2001-2007. They also sell a couple of other multiple choice tests on CD. These are worth the money.

If you’re looking for below-AP level multiple choice, a terrific source is the National Science League. Their contest is rather silly – my top 10 students in AP physics would have no excuse not to get a perfect score. But for my GENERAL physics class, the NSL test provides solid review questions. I’ve been buying this contest each year for a decade now, and so I have a large bank of basic questions for lower-level students.

Got a good source for multiple choice questions? Post a comment.

GCJ

Preparing for the Trimester Exam

It’s nearly trimester exam time! In AP physics, my 2-hour trimester exam will consist of 23 multiple choice questions in 30 minutes, followed by a full-length 90-minute free response section consisting of authentic AP exam questions. The general physics exam is an eight question free response test designed to be 2 hours long (but I allow three hours for everyone). The exams will, of course, cover everything we have discussed all year.

(Students always wonder if the exam will be cumulative… why wouldn’t it be? Why did I bother to teach back in October if you’re just allowed to forget what I taught you? Are you saying that the material I taught isn’t worth remembering? And in AP physics, the May AP exam is cumulative, so I would be doing you a disservice if every test were not cumulative. Now quit asking silly questions.)

With the exam upcoming, prepare for a series of posts about exams. Today, I discuss exam “review.”

I refuse to enter into conversations about what specifically will be on the exam, or to run a “review session.” If I’ve been doing my job, and if students have been paying attention, then exam preparation should be nothing special. Daily homework, quizzes, and discussion are exam review.

Woodberry holds a “consultation day” before each exam period, during which teachers hold court in their classrooms, and students can visit whomever they want to ask questions. I don’t want consultation day to degenerate into “so, want to tell me what’s on the exam?” But I want to encourage my students to stop by. I dangle bait for my class in the form of extra credit.

Yesterday I distributed a sheet with 20-30 multiple choice questions (a different sheet to AP physics and general physics, of course). The extra credit assignment is to do these questions if they were a test – no books, notes, or collaboration. Then, on Sunday’s consultation day, they can come to my classroom to scan their answer sheet. Showing up on Sunday is the first requirement for extra credit.

The second requirement is corrections. For each question they missed, they must explain how to get the correct answer. Corrections must be done on the sheet displayed to the right. (I hope the quality is good enough to read... if you want a ms word version of the sheet, email me.) The standard of evidence for the correction is high – if they don’t thoroughly convince me that they understand the problem, they don’t get credit. The corrections are not due until next Thursday’s exam; but, since collaboration is allowed and encouraged on the corrections, most students stick around on consultation day because so many folks are around to discuss the problems and to help each other out.

Students appreciate my approach, and not just because they get extra credit. Think about how your students will prepare for a physics exam. OCD-style students might think that they must study for hours… and those hours are too often unproductive. Lazy students might not normally prepare at all. But the extra credit multiple choice assignment helps both of these student phenotypes. The exercise helps the OCD folks focus their studying, so that either (a) the questions they missed inform them about what topics need special attention, or (b) they feel like they’ve studied, and so they don’t waste any more time preparing for the exam. As for the lazy folks, the extra credit might well lure them into doing something when they might otherwise have done nothing.

If nothing else, just getting my students physically in my and each others’ presence is a productive exercise, because conversations invariable turn to physics. Extra credit can be an amazing attractor. (I note that food often works as well. First trimester consultation day is well known as Nacho Day in the physics classroom. I sometimes wonder whether the ample supply of official Nacho Man Nachos or the extra credit does a better job of bringing in the sheaves.)

GCJ

(Picture at the top courtesy of falconsscience.wordpress.com.)

Lenz's Law quiz

I was on duty last night. For those of you out of the boarding school loop, this simply meant that I had the privilege of hanging out on dorm for a few hours after dinner, making sure the guys were studying during the study periods, and supervising check-in and dorm cleanup.

Dorm duty is a useful physics teaching time. I advertise to my students when and where I'll be on duty, so occasionally a group of students will show up to ask questions and to talk physics. If nothing else, I get caught up on my stack of papers to grade.

Problem was, the dorm I was on last night doesn't have internet access for the duty master. Thus, you're stuck with a very short post about Lenz's law.

The multiple choice question above is based on the diagram from Serway and Faughn, 8th ed. It was one of eight similar Lenz's law questions I asked on today's beginning-of-class quiz.

Textbooks will define Lenz's law with complicated verbiage... consider S&F's definition. "The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit." AARRGH! What first-year high school student can deconstruct that sentence?

I suggest teaching Lenz's law from the practical standpoint of finding the direction of an induced current, as would be useful for today's quiz. The process is straightforward. Here are the steps:

1. Point the right thumb in the direction of the magnetic field.

2. Ask, "Is the flux decreasing?"

2a. If the answer is "yes," then you're done -- curl your fingers, and they point in the direction of the induced current

2b. If the answer is "no," then flip the direction of your thumb. Curl your fingers, and they point in the direction of the induced current.

That's it. Don't you like that better than what the textbook said?

To answer the quiz question above, point the right thumb into the page, because the current I creates a magnetic field into the page by the second right hand rule. Is the flux decreasing? NO. Flux is increasing, because the current producing the field is increasing. So flip the thumb, curl the fingers, and the current runs counterclockwise, right-to-left through the resistor.]

Know your fundamentals

Pitchers and catchers have reported to spring training. Woo-hoo! Spring is just around the corner, as is spring break here at Woodberry. My family will be heading to Jupiter, Florida, where the St. Louis Cardinals hold their camp. The Nachoboy, my almost-six-year-old, has decided that he is a Cardinals fan, mainly because he could recognize the bird on their uniform since he was about two.

What will the Cardinals be doing in Jupiter, and what relevance does that have to a physics blog?

The Cardinals will be drilling their fundamentals – pitchers covering first base, ground balls to the infield, cutoff throws from the outfield, and so on. You know, the same things that the middle school baseball team works on at practice. Sure, the Cardinals are professionals, and are some of the best ballplayers in the world. Yet, they still work hard on their fundamentals.*

Advanced physics students may not think they need to drill physics fundamentals, but they often do. Simple recall of equations, units, and definitions can lead to stronger test scores. Drill must be handled carefully, though. On one hand, advanced students will turn off instantly if they feel they are being made to do “busy work.” On the other, less-than-advanced students must not be made to think that success in memorizing formulas is equivalent to success in truly learning physics.

The balance I have struck is never to include recall-style questions on homework assignments, but to give regular “fundamentals quizzes” in class. These recall quizzes are weighted heavily in the students’ grades; I also give rewards such as pieces of candy or exemption from future work to those who do well on fundamentals quizzes.

Since my AP class is preparing for their trimester exam next week, I thought it a good time to hit the fundamentals quizzes hard. The 45-minute lab portion of today’s class was devoted to fundamentals. I had four 10-question quizzes prepared. Everyone took the first quiz; the students traded and graded. (I certainly did not provide a key… they had to look up and/or argue about anything they weren’t sure of.) Anyone who got 9/10 or better could leave.** Everyone else got to take the second quiz, and so on and so forth.

As it turned out, 4 of 15 students got to leave early. Everyone else got the benefit of taking four different fundamentals quizzes. I have no doubt that these folks are much better prepared now for next week’s exam.

Below is a typical fundamentals quiz, for which I allot 5-7 minutes. In a future post I’ll make some suggestions about how to write your own fundamentals quiz.

* And, some would say professional ballplayers should work even harder on fundamentals, especially if they’ve ever watched the Cincinnati Reds defense.

** Leaving early from lab is a major perk, one that has not yet been extended to anyone in the class this year.

1. Two masses are connected by a string over a pulley. How many free body diagrams do you make?



2. A car smashes into a tree. The driver of the car is not held in place by a seat belt or any other restraining device. Just after impact but before the driver hits any part of the car:
(a) How do you know the driver’s velocity?

(b) How do you know the driver’s acceleration?


3. A block of mass m slides down an incline of angle θ . What is the component of the block’s weight parallel to the incline?

4. Write the ideal gas law. What are the standard units that should be plugged in for the P term?

5. Which of the following quantities is always conserved in a collision? Circle all that apply.

Velocity
momentum
acceleration
kinetic energy


6.
(a) Where is the velocity of an oscillating mass on a spring largest? Circle one.

At the equilibrium point
at the maximum displacement
(neither of these)

(b) Where is the acceleration of an oscillating mass on a spring largest? Circle one.

At the equilibrium point
at the maximum displacement
(neither of these)

7. A wire carries a current I to the left. What is the direction of the magnetic field at point P?

P.


I

8. What is the equation for the magnitude of the magnetic field produced by a wire?

9. What is the equation for the magnitude of the magnetic force on a wire?

Finding a spring constant in five seconds

In my general physics section, we’re studying springs: force of a spring, energy of a spring, and the mass-on-a-spring as an example of simple harmonic motion. Laboratory exercises with springs are useful and fun, especially because it’s easy to get good, reliable data. Before I introduced springs formally in class, I assigned a lab exercise in which they determined the spring constant of a spring. The experiment I assigned is detailed here via collegeboard.com.

Today we began a different experiment involving the spring in simple harmonic motion. Thing is, in order to use the equation

,

each lab group has to know the spring constant of their spring. Usually they know k because they use the same spring from the first experiment. But, I forgot to have them label their springs for later use. I was too caught up in the physics tournament and lab cleanup, I guess.

I asked the students to make a “quick and dirty” measurement of k just using a few weights and a measurement of how far those weights extended the spring. But I don’t yet trust my general students to do quick and accurate lab work. Estimates of k were varying by 40% within the same lab group on the same spring! What to do?

Fortunately, I had the force probe and motion detector hooked up from my in-class demonstration of the force of a spring. The setup is in the picture to the right, though I admit the picture isn't so clear. Some mass hangs from the spring, which is attached to the force probe. The motion detector sits on the table beneath the mass. The mass is allowed to vibrate, and logger pro takes force vs. distance data.

It takes only about 5 seconds to acquire a graph like the one you see in the screen shot. Press the “slope” button at the top of the screen, and you get the slope of the force vs. displacement graph – voila, the spring constant!

I’ll leave it as an exercise to the reader why the graph has a negative slope. Feel free to post a comment with the answer.

Falling behind...

It's been busy busy at Woodberry. Last week we held the US Invitational Young Physicist Tournament on campus (about which more later). Raffles Institution, from Singapore, defeated Woodberry Forest in the final.

As far as the Woodberry team was concerned, the best part of the tournament was the final evening's party at the Holiday Inn Express. Although all the teams socialized, the Woodberry guys* seemed to slather their attention heavily on the team from Brisbane Girls Grammar School. (They're GIRLS! And they have Australian accents!)

We all had great fun for the weekend. The cost of that fun, from my perspective, was a week of falling behind in my classes as I took care of details as tournament director. I have next to me this morning a stack of papers 7.5 cm high... and that's AFTER I spent two nights this week grading papers on dorm duty.
What do you do when you're so hopelessly behind that you will certainly not catch up before next week's end of the term?

Start by recognizing that you're NOT going to catch up with every assignment. In a marathon grading session, it's not worth starting at the beginning of the stack and intending to get to the end. Accept that your work will be incomplete. I picked out a few homework problems at random to grade. It's late enough in the school year that grading papers is unlikely to uncover anything new about a particular student. The diligent ones will still be diligent, the lazy ones still lazy, and the smart ones still smart. The whole purpose in grading now lies in checking up, sending the message that "I'm still watching you!" Just a few spot checks can do wonders for making sure the class keeps up with their work.

The other aspect to catching up with grading is to add as little as possible to the stack. My class starts each day with a short quiz. On Friday, I wrote a 5-question multiple choice quiz about one of the problems from the night before. Don't expect that I'll be grading that problem, now -- this quiz has evaluated their homework, and saved me considerable time.

* Woodberry is an all-boys boarding school, so in this case "guys" is not a gender-neutral term.

Here's one of the three homework problems that were assigned for Friday, which I think I got from the 1997-vintage Zitziewitz-Merrill text, but I'm not sure:

A fisherman’s scale stretches 3.9 cm when a 2.7 kg fish hangs from it.
(a) What is the spring constant of the scale?
(b) What will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down?

And, below, take a look at the multiple choice quiz. Notice I've changed values so calculators are not necessary. (Why do the questions start at #15? Because multiple choice quizzes for the whole term go on the same scantron. That means I only have to grade multiple choice quizzes every 50 questions or so!)


A fisherman’s scale stretches 4.0 cm when a 2.0 kg fish hangs from it. The spring is pulled down 2.5 cm more and released so that it vibrates up and down.

15. What is the spring constant of the scale?
(A) 0.05 N/m
(B) 0.5 N/m
(C) 5 N/m
(D) 50 N/m
(E) 500 N/m

16. What is the amplitude of the harmonic motion?
(A) 4.0 cm
(B) 5.0 cm
(C) 6.5 cm
(D) 2.0 cm
(E) 2.5 cm

17. The period of the harmonic motion is 0.40 s. What is the frequency of the harmonic motion?
(A) 0.40 Hz
(B) 2.5 Hz
(C) 4.0 Hz
(D) 0.25 Hz
(E) 5.0 Hz

18. In a new experiment, the spring is pulled down 5.0 cm instead of 2.5 cm to begin the harmonic motion. How does the new period compare with the period in problem 3?
(A) It doubles.
(B) It remains the same.
(C) It is cut in half.
(D) It is multiplied by √2.
(E) It is divided by √2.

19. In a new experiment, a 4 kg fish is attached to the same spring and pulled down 2.5 cm to begin harmonic motion. How does the new period compare with the period in problem 3?
(A) It doubles.
(B) It remains the same.
(C) It is cut in half.
(D) It is multiplied by √2.
(E) It is divided by √2 .

What is this blog, anyway? (FAQs)

When I lead workshops and institutes for the College Board and others, folks are always asking for resources. Not fluffy, overly general resources, but specific stuff. People want quizzes, problems, lab ideas, assignments... and they want to borrow teaching ideas and techniques. This blog is intended to serve both physics teachers and students, whether at the high school or college level. If you have specific requests, like "do you have a good quiz about PV diagrams?" feel free to email me or to post a comment. I can also use this space to explain answers to confusing problems. I won't do your homework for you, but I'll certainly answer specific questions you may have about homework.

Frequently Asked Questions:

What level of physics do you teach?
I teach introductory physics -- AP physics B, AP physics C, General Physics, and Research Physics -- at the high school level.


What kind of school do you teach at?
Woodberry Forest School is the nation's premier boarding school for boys. We are located in central Virginia, about 40 miles north of Charlottesville. I live on campus (not on dorm) with nearly 400 boys grades 9-12.


Where can I find out more about your course and your methods?
The overriding philosophy of Jacobs Physics is Less is More. I assign an extremely light volume of work to my students, but I attempt to hold them thoroughly accountable for everything they ever do. Take a look at the article (entitled "Less is More") I wrote for collegeboard.com via this link. Be sure to click through to read the ENTIRE 4-part article.