Email discussion group and an excellent conversation

I set up an internal email conference accessible only to my classes.  Each class has a separate folder, to which I post assignments and commentary.  Students are also encouraged to ask specific questions of each other and of me on the folder.

Getting the students to use this folder properly and usefully is difficult.  Most are too timid to post anything.  Then when someone does post, they say "I can't do #4.  Help."  I have to tell such a student to try again with a SPECIFIC question:  say, "On #4, I drew the free body diagram, but I can't figure out how to get the components written."  Specific questions can provoke excellent e-discussions.

I also use this conference myself to hammer home points that I don't want to make in class; or, points that I have made in class, but need reinforcement.  For example, yesterday when I graded homework I saw some ridiculous free body diagrams; posted the picture above with the subject line "What are the two things wrong with this free body for the boat?"  The body of the message included the statement, "First to post the answer gets candy!"

A few minutes later, I found a student's homework contradicting Newton's second law.  Instead of screaming, I merely posted to the folder, offering another piece of candy:  "What's wrong with the statement 'Since the resistive force exerted by the water is less than the forces exerted by the ropes, the boat can move in the direction of the ropes.' "

I got excellent answers.  To the latter question, student Peter Chen replied: 

"You don't necessarily need to exert greater forces than the resistive force to make it move. What you really need is the same quantity of forces on the opposite direction to the resistive force. If you don't fulfill this requirement, no matter how great the forces are, you cannot move the boat.  eg: Even if you exert 1 billion Newton of forces to both sides of the boat, which are perpendicular to the direction of the resistive force, you will never move the boat. Because the quantity of forces on the opposite direction to the resistive force is 0.

To the question about the free body diagram, I reposted James Moyler's answer with commentary:

1.You shouldn't write 600N on the free body diagram. It is a rope so it should say T1 and T2. You don't put quantitative values on a FBD.

Correct.

2. F isn't enough. F of what? I believe it should be Fr for Force of Resistance.

In this particular problem, the resistive force was DEFINED as "F." So the plain old label "F" is okay here. But generally, Mr. Moyler is correct -- put a subscript or words on the label on a free body.

Another student, Frederic Lamontagne, followed up:

Firstly, there is no normal force when the object is on water. The force on water is Buoyant Force.  Secondly, [this force] would not be acting to the left (as it is indicated in the free body diagram)...it would act perpendicular to the water.

Absolutely correct.

Thing is, everyone in the class read that exchange.  Everyone in the class had done those problems just the day before, so the information was current and relevant.  The five minutes of my time it took to post and reply were worth 20 minutes of lecture time.

New Guidance for Free Body Diagrams on the AP Exams!

Some families argue politics or religion.  AP Physics readers have been arguing free body diagrams.

Many good teachers have differing opinions about the purpose and proper construction of the free body diagram.  The grading of free bodies on the AP exam has been the subject of extremely lively debate for many years.  Everyone, fortunately, has common goals:

* Award credit to students for correct physics

* Do NOT award credit to students for vague or incorrect physics

* Have enough flexibility in the rubric to accomodate alternative but reasonable interpretations of the correct construction of the free body diagram.

Perhaps the loudest of the shouting involves the issue of vector components.  Many of us -- including me -- take it as a matter of faith that a free body should never include components of a force.  Others reasonably point out that since the whole point of the diagram is to determine the magnitudes of the forces, and since one must break down angled vectors into components at some point, such components represent a necessary and important part of problem solving technique.  I see the legitimacy to both arguments. 

In order to quiet the arguments and send a clear message about free body components, the AP development has decided to change the language used to ask students to draw free body diagrams.  The test questions now will SPECIFICALLY forbid components on free body diagrams, and will even remind students to use a separate space to draw components where necessary.  You can see the white paper issued by the development committee here within the College Board's website.

Moral of the story:  Argument settled by fiat.  DO NOT put components on free body diagrams, or you will lose points.  Break angled vectors into components on a diagram separate from the initial free body.

Mailbag: Forces on a Table

From Michael Herrin, from Chestatee High School in Gainesville, GA:

I’m having trouble working a problem. It’s from the Cutnell and Johnson’s book chapter 4, and I am curious if you could help point me in the right direction.

Mr. Herrin actually pointed me to a problem in the 5th edition, but I found a slightly different version in the newer edition. In the diagram shown, all pulleys are massless and the surfaces are frictionless. Find the tension in the rope and the acceleration of the masses.

The problem solving process that I teach for Newton’s second law problems is:

1. Draw a free body diagram.
2. Break angled forces into components, if necessary.
3. Write (up-down=ma) and (left-right=ma).[1]

This is a two-body problem; therefore, we start with not one but TWO free body diagrams: Look here -->

Note the tricksiness of the diagram for the 3 kg mass. The rope is pulling up TWICE on this mass: once from the left side of the pulley, once from the right side. So we put two tensions on the diagram.

Jacobs’ law of tensions says “One Rope Equals One Tension.” That’s why I didn’t label the tensions T₁ and T₂, but just T. The tension will be the same throughout.

Now, write Newton’s second law twice, once for each block. The direction of acceleration will be to the right for the 10 kg block, and down for the 3 kg block. (We can see that by imagining releasing the masses from rest, and seeing which way the blocks speed up.)

T = (10 kg)a and (3 kg)g - (T+T) = (3 kg)a

Now, the PHYSICS IS DONE: I have two equations and two unknowns, a and T. Everything else is a known value. All that’s remaining is mathematics.

I think it’s easiest to solve by addition – multiply the first equation by 2, and add the equations together. This cancels out the tension terms; solve to get a = 1.3 m/s²? . Plugging back into either equation, I get T = 13 N. That’s reasonable: the tension is less than the weight of either mass, but is on the same order of magnitude.

Now, ask your students: what would happen to the acceleration if we were to give the 10 kg mass an initial shove to the left. Would the acceleration be greater than, less than, or equal to 1.3 m/s²? Post YOUR answer in the comment section.

GCJ



[1] Well, okay, sometimes we write (right-left=ma), not (left-right=ma). How to know which is which? Determine the direction of acceleration, and start with that direction.

AP exam review: 2004 B1, Roller Coaster

It's time for that final AP exam review. Today's post gives a multiple choice review exercise based on an old AP exam question; tomorrow I'll describe my final classday activity.

As I've discussed before, just doing an AP practice problem does not provide sufficient review. Practice problems must be followed up somehow. Usually I have students do corrections on what they missed. But for a fun change of pace in the spring, I get out my classroom response system (my "clickers") and run a little contest for extra credit.

Before I go on, please note that (a) this contest works just fine without "clickers" -- just have the groups write their answer really big on a piece of paper and hold it over their heads. And, (b) this type of review is not confined to AP physics. AP questions can be carefully selected, or edited, for use with your general high school physics class. You can use this as final exam review.

How the contest works

This contest is based on problem 1 from the 2004 AP physics exam. For lawyerly reasons I can't post the actual question here, but you can get it via this link: http://apcentral.collegeboard.com/apc/members/exam/exam_questions/2007.html#name04

First, I have the students do this problem to the best of their ability on their own. This usually means as a quiz.

Next, I use http://random.org/ to divide the class into teams of two. Each team gets one clicker

Now, I ask the multilpe choice questions that you see below. I ask them one at a time, giving at least 60 seconds for the teams to discuss the correct answers. After the 60 seconds, I collect responses, and then go over the correct answer

Scoring: Each team gets one point for the correct answer, and one more point for each group who doesn't get it right. There are a bazillion ways to score a contest like this... I've found that this particular scoring makes students less willing just to listen to the smartest students without thinking for themselves. I get good arguments amongst the class, which is what I'm after.

Here are the questions I ask:

1. At which labeled point does the car attain its maximum speed?
(A) I
(B) II
(C) III
(D) IV
(E) V

2. To calculate the value of the car’s maximum speed, do we use kinematic equations (vf = vo + at and so on) or conservation of energy?
(A) Kinematics must be used
(B) Conservation of energy must be used
(C) Either kinematics or energy conservation may be used
(D) Neither kinematics nor energy conservation will produce a solution

3. What general formula for potential energy do we use here?
(A) mgh
(B) ½mv²
(C) ½kx²
(D) qV
(E) (3/2)nRT

4. What general formula for kinetic energy do we use here?
(A) mgh
(B) ½mv²
(C) ½kx²
(D) qV
(E) (3/2)nRT

5. To calculate the speed at point B, which of the following formulas is correct?
(A) mg(90 m) + 0 = 0 + ½mvB²
(B) mg(50 m) + 0 = 0 + ½mvB²
(C) mg(40 m) + 0 = 0 + ½mvB²
(D) mg(30 m) + 0 = 0 + ½mvB²
(E) mg(20 m) + 0 = 0 + ½mvB²



Which of the following free body diagrams correctly represents the forces acting on the car when it is upside down at point P?
(A) A
(B) B
(C) C
(D) D
(E) E

What is the weight of the car?
(A) 700 N
(B) 7000 N
(C) 700 kg
(D) 7000 kg

What is the magnitude of the NET force on the car?
(A) mg
(B) Fn
(C) Fn – mg
(D) Fn + mg

What is the magnitude of the car’s acceleration?
(A) 0 m/s²
(B) 28 m/s²
(C)[(28 m/s)² / (20 m)]
(D) 10 m/s²

What is the direction of the car’s acceleration?
(A) Down
(B) Up
(C) Left
(D) Right

Imagine changing the (still frictionless) track such that point B is still 50 m off of the ground at the top of a circular loop, but the circular loop has only a 15 m radius. What happens to the speed of the car at point B?
(A) It is smaller than before
(B) It is larger than before
(C) It is the same as before

Consider the same track with NON-negligible friction. What is true about the speed at point B now?
(A) It is smaller than 28 m/s.
(B) It is larger than 28 m/s.
(C) It is still 28 m/s.

How could we adjust the track with NON-negligible friction so that its speed at point B is the same as we calculated previously?
(A) Make the radius of the circle smaller
(B) Make the radius of the circle bigger
(C) Make point B closer to the ground
(D) Make point B higher off the ground