Can a normal force do work?

At the first-year physics level -- absolutely a normal force can do work.  If an object moves parallel (or antiparallel) to a normal force, then the normal force has done work.  

But how can that be?  A block slides to the left on a flat surface, say.  The normal force is upward, movement is left, so the motion is not parallel to the normal force.  No work is done by Fn.

That's correct.

Even for a block sliding up or down an incline, the normal force does no work.  The normal force by definition is perpendicular to the surface, and the block slides along the surface; no component of the normal force is parallel to the motion.

That's correct, too.

So how in the sam hill can a normal force possibly do any work?

What if the surface itself is moving?

Consider a person standing in an elevator.  The normal force is the force of the elevator floor on the person.  As the elevator moves upward, so does the person... so the normal force is parallel to the person's motion, doing work.  If the elevator moves downward, the normal force is antiparallel to the motion, and so does negative work.

Now I leave you with this... what if the elevator is slowing down as it moves upward, such that the normal force is less than the man's weight.  Does the normal force do positive work, negative work, or zero work?  I'll answer in a few days in the comment section.

Mail Time: Does electrostatics show up on AP Physics 1 or AP Physics 2?

Erika Sherger of New Jersey writes in with a question I've been asked before:

Is electrostatics in AP Physics 1 or 2?  The website lists it as a 2 topic but the two sample curricula for AP Physics 1 contain it.

Electrostatics in some form is on both exams.

In AP Physics 1, Coulomb's Law for the force between two electrical point charges will show up -- but that's it.  No mention of electric field, no electric potential, no vector addition for the force exerted by multiple point charges.

AP Physics 1 will also cover simple DC circuits.

In AP Physics 2, all of the algebra-based electrostatics you can think of will show up: fields and potentials due to multiple point charges, due to parallel plates, due to a dipole, electric field mapping (with vector fields, NOT with traditional field lines), capacitors, problems including electrostatics in combination with magnetic fields or other forces, more complicated DC circuits even sometimes including steady-state capacitor behavior...

I know it's a pain in the Dan Snyder to parse, but try searching the electronic copy of the curriculum framework for "point charges" or "Coulomb's Law."  The learning objectives are pretty clear as to what is expected in each course.

And, of course, buy McGraw-Hill's "5 Steps to a 5: AP Physics 1" when it comes out this summer!  :-)

greg

Grading AP Problems: Wrong, but Consistent

Joseph Rao, from Massachusetts, writes in:

I had a grading questions regarding the AP. I noticed on the scoring keys that usually a response is given full credit if it is using the correct approach, but with an answer that was calculated incorrectly.   I had a student on my recent exam who asked if she should receive points if she used the wrong approach on the first part, then calculated the second part of the question with another approach that was wrong, but made sense for the initial approach used.  When in doubt should I just following the scoring key for if they specify to use the answer from the previous question? I chose to not award points because neither approach helped get any closer to an answer. 

Joseph, you chose... wisely.

Now, before I even start answering this question, remember there's no such thing as a "typical" or general rubric.  You've gotta follow each one independently.  And the understanding among readers about how to deal with difficult responses will change on every problem, every year.  Teachers get themselves tied into all sorts of conundrums repeating memes like  "Oh, the AP awards points for substitution, but not for the answer."  That may have been true on one or two rubrics, but neither that nor anything else is a universal rule for AP rubrics.  Each rubric is designed independently.  You cannot game the test.

But to answer your question as best as I can:  If a calculation from part (a) must be used to answer part (b), usually credit is awarded just for the recognition that the answer from part (a) is used, whether that answer is right or wrong.  I call it "wrong but consistent" -- a calculation that leads to an incorrect answer, but which is consistent with previous work, I mark as "WBC."

Don't let students lawyer up, though.  Exceptions exist.  The most obvious exception is when a previous answer renders a future answer ridiculous (as in a car moving 1500 m/s, or the mass of a proton being 500 kg).  Or, if a previous answer renders future work trivial (i.e. calculating a force of zero newtons in part (a), meaning parts (b) and (c) would also answer zero somethings).

Sometimes, credit is awarded for a correct (not consistent, CORRECT) answer -- in this case, WBC work might earn partial credit, but not full credit.  

When in doubt, follow the rubric and use your physicist's spidey sense.  If you feel like you're awarding credit for bad physics, DON'T, regardless of how your student argues the rubric.  If you feel like you're not awarding credit for good physics, DO.  (And your student probably won't complain.)

In the case you describe, I can't imagine this student earning credit.  "Wrong but consistent" doesn't mean compounding error upon error.  It means, someone did everything right in one part of a problem, but not the other; we're going to credit the correct physics, and dock the incorrect physics.  If it's all incorrect, there's no room for credit.

And as a final note, one that I have to give every year to multiple students:  They are not allowed to go to Kansas City with the AP readers in order to serve as counsel for their test.  Grade the test, give it back, and don't accept any arguments about the rubric.  If you need me to serve as a final arbiter, you know where to reach me.

GCJ

Block on an incline -- trig identity or pythagorean?

Joel Houghton from Raleigh writes in about a problem I use in my AP class.  The block shown sits at rest on an incline.  The coefficient of static friction is 0.30.  What is the angle of the incline, and what is the normal force acting on the block?

(As an aside, usually this question is phrased with "maximums":  The MAXIMUM static friction coefficient is 0.30, so what is the BIGGEST angle at which the block can stay at rest?  I assign this problem in week 2 of my AP course, so I ignore the issue of maximums... as I stated it, the problem is still technically correct.)

Pythagorean Method:  Joel created a triangle out of force vectors. The 150 N weight acts straight down.  The normal force acts perpendicular to the incline.  The friction force (equal to 0.30 times the normal force) acts up the incline.  Thus, the weight is the hypotenuse of a triangle -- look at the diagram to the right, which Joel sent me.

Joel applied the pythagorean theorem to get an equation in a single variable:

(150 N)² = Fn² + (0.30 Fn)²

Joel solved for Fn to get 144 N.  Then he used the cosine function to get an angle of 16 degrees for the incline.

Vector Components and Trig Identity Method:  Joel's method is complete and correct.  I don't personally like to teach students to use a pythagorean approach here, though -- it is very difficult for first-year physics students to see, understand, and be able to create the triangle of force vectors.  Instead, I encourage an identical approach to every problem:  Break angled forces into components, then (for equilibrium) set up=down, left=right.

The weight breaks up into components down the plane (mgsinθ) and perpendicular to the plane (mgcosθ).  The two equilibrium equations become:

(0.30)Fn = mgsinθ
Fn = mgcosθ

Solving for Fn requires the trig identity that sin/cos = tan.  I tell my class that this is the ONLY trig identity they will be expected to use in AP physics... but this identity is in fact used relatively frequently.  Here, dividing the equations by each other yields tan θ = 0.30... which means, the angle of the plane is 16 degrees.

You solve this problem your way.  I merely pose two possible approaches.

The economics of late work

Teachers are often hung up on grading policies, especially those for late work.  We tend to model our approach after that of the English department: typically, an English teacher might subtract a letter grade for each day late.  So we do something similar, creating a sliding scale of credit, a scale whose complexity sometimes rivals that of the tax code, and adjusting the policy over the years in response to complaints and lawyerly arguments.

Stop.

What is the overriding goal, the most important purpose, of your homework "policy"?  You want your students to do their homework carefully, and to turn it in on time.  That's because well presented homework leads to learning physics well, which leads to success on tests, which leads to happy and smart students.

When you're structuring your homework "policy", then, don't think in terms of "what is a fair consequence for late work?"  Think instead about how to best accomplish the goal of receiving timely, well-done problems.

I don't think the English department is the best model for us as physics teachers.  English essays are -- usually -- assigned days or weeks in advance, and are due only occasionally.  If an essay is due every fourteen days, and won't be graded for another week after it's turned in, then one day doesn't really make so much of a difference.  In fact, I've had English teachers explain they'd much rather have a three-day-late but good essay than a poor essay turned in on time.

Physics is different.  I assign work every day at my boarding school.  At the day school, problems were due twice a week.  Problems are returned within a day or two in order to provide continual feedback, showing students where they do and don't understand new material.  Unlike the typical English teacher, I would prefer finished work to correct work.  The point of homework is to engage with the material, not to show mastery.  The goal of my homework "policy" is to produce that engagement.

A story... Can't cite it, but read it in (I think) the Wall Street Journal:  A daycare service in a large city was having trouble with clients picking up their kids well after the appointed pickup time.  Employees had no choice but to stay late, sometimes very late -- you can't just leave a 4-year-old on the doorstep and say "Mommy will be here soon, sit tight, bye now."

The service revised their policies to provide monetary penalties for late pickups.  That didn't help.  They made the fines for late pickup ever bigger... and yet, the rate of late pickups continued to increase.

Finally, the service tried something different -- they ELIMINATED MONETARY PENALTIES for late pickup.  Instead of a page in their handbook listing crimes and punishments (Late 5-20 minutes = $50, late 20-60 minutes = $200, etc.), they merely wrote that daycare employees expected to leave promptly in order to join their own families for the evening.  Repeated lateness was not considerate of the employees, and would not be tolerated.

Hah!  Late pickups were virtually eliminated.  The article I read speculated that by fining parents for late pickup, they had in the parents' minds created "late pickup" as an economic good which could be bought and sold.  The parents would do a cost-benefit analysis... is picking my kid up late worth the fine?  If so, I'll just pay the fine.  I can afford it.  And why are the employees so grouchy at me when I show up two hours late?  I'm paying them a bloody fortune for the late pickup, they should be happy for the money.

But without the fine, late pickup became not a saleable good, but a sin.  The frowning from the employees was no longer interpreted as ungratefulness for the opportunity to earn overtime pay; instead, the late parents were embarrassed and apologetic.  "I'm so sorry I took time away from your own family.  This won't happen again.  Please continue to watch my child and take care of him with love... I promise to respect your time in the future."

I think of homework the same way as late daycare pickup.  If I assign a sliding scale of grade penalties, I'm encouraging students to weigh the cost against the inconvenience of actually doing the work.  If a student is happy to settle for a C, he can decide to do just enough for that grade.

However, if I present missing homework as a sin, awarding no credit and requiring the homework to be done in any case, the rate of completed homework skyrockets.  Even half-arsed problem sets allow a student to engage with the material, and improves that student's understanding.  Since I've gone to some version* of "no credit for late work, period" I've had few complaints, and very few late assignments.

* In upper level classes, I allow two no-excuse-necessary extensions per marking period.

Anecdote from Burrito Girl:  Some physics teachers will say that they couldn't possibly give no credit for late work, because they'd have to deal with so many complaints from students, parents, colleagues, and administrators.  My wife and sidekick Burrito Girl used to teach English.  She took points off for late work according to a sliding scale.  She says that she got way more complaints about her policy than I ever get about mine.  Students, parents, and colleagues argued that the grade penalty shouldn't be as steep for a particular assignment, or that the policy should be adjusted, or that extenuating circumstances should apply...

In other words, you're going to have perpetual arguments whether you take off 10% or 100% for a late assignment.  Why not give a shot to the method that is most likely to convince students to engage with their physics problems on a regular basis?