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

Collaboration rules for AP problems assigned for homework

This time of year especially, I like to assign AP questions as homework. But when I do, the collaboration rules change.

Up until now, I've asked students merely to approach the problem individually, spending at least 5 minutes and showing me some kind of reasonable start. After that, collaboration is freely allowed and encouraged. I award full credit for a correct answer whether or not the individual work was on target.

Early in the year, I'm happy if someone merely copies the question and the diagram on his own; at least he's thought about the problem, and has context for the subsequent discussion with his friends. After a couple of months, I insist on a bit more... I start taking off unless the student does SOMETHING on his own, even if he's wrong.

Now, though, my students know how to learn physics. They no longer should be hesitant to approach a problem. Furthermore, an AP free response question always has several distinct parts -- if part (c) is hard, they should still be able to get full credit for parts (a), (b), and (d). Now is the time to practice this kind of approach to AP questions.

Throughout the school year, I nudge my class gradually toward becoming more independent physics students. Now it's time to take the final step. Many will be surprised how well they do on their own after relying on friends' input for much of the year. Others will expose blatant gaps in their knowledge; but they'll be forced to confront their lack of understanding, giving them incentive to figure out what they don't know.

Instructions for AP problems assigned as homework:

* Do the ENTIRE PROBLEM on your own before seeking assistance. Do NOT discuss the problem at all until you are completely finished. This should take no more than 15 minutes.

* If you make any changes, these must be in a DIFFERENT COLOR of ink or pencil. Cross out (do not erase) your original wrong work.

* You will earn full credit for your final answers, unless you fail to follow these collaboration rules.

GCJ