## 5 Steps to a 5: AP Physics C (2016)

### STEP __3__

### Develop Strategies for Success

### CHAPTER 7

### How to Approach Each Question Type

**IN THIS CHAPTER**

**Summary:** Become familiar with the three types of questions on the exam: multiple-choice, free-response, and lab questions. Pace yourself, and know when to skip a question.

**Key Ideas**

You don”t need a calculator to figure out multiple choice questions, even though you are allowed a calculator.

There are five categories of multiple-choice questions. Two of these involve numbers: easy calculations and order-of-magnitude estimates. The other three don”t involve numbers at all: proportional reasoning questions, concept questions, and questions asking for the direct solution with variables only.

Free-response questions test your understanding of physics, not obscure theories or technical terms.

You can get partial credit on free-response questions.

Each free-response section will contain at least one question that involves experiment design and analysis—in other words, a lab question.

Check out our six steps to answering lab questions successfully.

**How to Approach the Multiple-Choice Section**

The AP exam is very, very straightforward. There are no trick questions, no unreasonably difficult problems, no math beyond the clearly articulated scope of the course. The multiple choice questions test your physics knowledge in a variety of ways—a glance through the practice exam in this book, as well as reading through this section, can give you a sense of the types of questions asked.

Until 2015, calculators and the equation sheet were not provided during the multiple choice section. Now, though, you can use calculators and equation sheets on the whole exam.

Important point: *The content and style of questions did not change, even though the calculator policy did* .

The point is, you do not need to use a calculator on the multiple choice section. No multiple choice question requires significant number crunching. More importantly, though, understand that

Physics is NOT about numbers.

Yes, you must use numbers occasionally. Yet you must understand that the number you get in answer to a question is always subordinate to what that number represents.

Many misconceptions about physics start in math class. There, your teacher shows you how to do a type of problem, then you do several variations of that same problem for homework. The answer to one of these problems might be 30,000,000, another 16.5. It doesn”t matter … in fact, the book (or your teacher) probably made up random numbers to go into the problem to begin with. The “problem” consists of manipulating these random numbers a certain way to get a certain answer.

In physics, though, *every number has meaning* . Your answer will not be 30,000,000; the answer may be 30,000,000 electron-volts, or 30,000,000 seconds, but not just 30,000,000. If you don”t see the difference, you”re missing the fundamental point of physics.

We use numbers to represent REAL goings on in nature. 30,000,000 eV (or, 30 MeV) is an energy; this could represent the energy of a particle in a multibillion-dollar accelerator, but it”s much too small to be the energy of a ball dropped off of a building. 30,000,000 seconds is a time; not a few hours or a few centuries, but about one year. These two “30,000,000” responses mean entirely different things. If you simply give a number as an answer, you”re doing a math problem. It is only when you can explain the meaning of any result that you may truly claim to understand physics.

**So How Do I Deal with All the Numbers on the Test?**

You see, in virtually all cases the test authors still assume that you have no calculator. Thus, a large majority of the multiple-choice questions involve *no numbers at all!* And those questions that do use numbers will never require more than the simplest manipulations. Here is a question you will **never** see on the AP test:

What is the magnitude of the magnetic field a distance of 1.5 m away from a long, straight wire that carries 2.3 A of current?

(A) 3.066 × 10^{–6} T

(B) 3.166 × 10^{–6} T

(C) 3.102 × 10^{–6} T

(D) 2.995 × 10^{–6} T

(E) 3.109 × 10^{–6} T

Yes, we know you might have seen this type of problem in class. But it will *not* be on the AP exam. Why not? Plugging numbers into a calculator is not a skill being tested by this examination. (You should have recognized that the equation necessary to solve this problem is

though.) We hope you see that, without a calculator, it is pointless to try to get a precise numerical answer to this kind of question.

**Fine … Then What Kinds of Questions Will Be Asked on the Multiple-Choice Section?**

Fair enough. We break down the kinds of questions into five categories. First, the categories of questions that involve numbers:

- easy calculations
- order of magnitude estimates

Most questions, though, do NOT involve numbers at all. These are:

- proportional reasoning
- concept questions, subdivided into
- “Why?” questions, and
- diagram questions
- direct solution with variables

Okay, let”s take a look at a sample of each of these.

**Easy Calculations**

These test your knowledge of formulas.

A ball is dropped from a 45-m-high platform. Neglecting air resistance, how much time will it take for this ball to hit the ground?

(A) 1.0 s

(B) 2.0 s

(C) 3.0 s

(D) 4.0 s

(E) 5.0 s

You should remember the kinematics equation: . Here the initial velocity is zero because the ball was “dropped.” The distance involved is 45 meters, and the acceleration is caused by gravity, 10 m/s^{2} . The solution must be found without a calculator, but notice how easy they have made the numbers:

Everything here can be done easily without a calculator, especially if you remember to use 10 m/s^{2} for *g* . No problem!

**Order of Magnitude Estimates**

These test your understanding of the size of things, measurements, or just numbers.

Which of the following best approximates the gravitational force experienced by a high school student due to the student sitting in an adjacent seat?

(A) 10^{1} N

(B) 10^{–8} N

(C) 10^{–18} N

(D) 10^{–28} N

(E) 10^{–38} N

Wow, at first you have no idea. But let”s start by looking at the answer choices. Notice how widely the choices are separated. The second choice is a hundred millionth of a newton; the third choice is a billionth of a billionth of a newton. Clearly no kind of precise calculation is necessary here.

The answer can be calculated with Newton”s law of gravitation . You complain:

“They didn”t give me any information to plug in. It”s hopeless!” Certainly not. The important thing to remember is that you have very little need for precision here. This is a rough estimate! *Just plug in a power of 10 for each variable* . Watch:

*G*: The table of information says that the constant*G*is 6.67 × 10^{−11}N·m^{2}/kg^{2}. So we just use 10^{−11}in standard units.*m*_{1},*m*_{2}: It doesn”t say whether this is Olympic gymnast Shawn Johnson (41 kg) or football offensive lineman John Urschel (137 kg). What do I do? Just use 10^{1}or 10^{2}kg. If you”re really concerned, you can make one 10^{1}kg and one 10^{2}kg. It won”t matter.*r*: The distance between desks in any classroom will be more than a few tens of centimeters, but less than a few tens of meters. Call it 10^{0}meters and be done with it.

Okay, we”re ready for our quick calculation:

(You remember that to multiply powers of 10, just add the exponents; to divide, subtract the exponents.)

You still object, “But when I use my calculator and plug in more precise values, I get 3.67 × 10^{−7} N. Or, if I use both masses as Shawn Johnson”s, I get 1.1 × 10^{−7} N.” Look at the choices again; the second answer choice is still the best answer. We got that without a calculator—and a lot quicker, too.

**Proportional Reasoning**

These also test your knowledge of how to use equations, except that you don”t have to plug in numerical values to solve them.

Planet X is twice as massive as Earth, but its radius is only half of Earth”s radius. What is the acceleration due to gravity on Planet X in terms of *g* , the acceleration due to gravity on Earth?

(A) ¼ *g*

(B) ½ *g*

(C) *g*

(D) 4*g*

(E) 8*g*

First we need to know what equation to use. We know that the force that a planet exerts on a small mass *m* _{1} near its surface is

Using Newton”s second law (*F* _{net} = *ma* ), we know that the acceleration of the small mass is simply

One method of solution would be to plug in the actual mass and radius of the new planet. But no fair, you say, the mass of the Earth isn”t given on the constants sheet. How do I find the mass of the planet?

*You don”t!*

Use proportional reasoning skills instead, so:

*“The mass of the planet is twice that of the Earth. Since mass is in the numerator of the equation for acceleration, doubling the mass of the planet must double the acceleration* .

*“Okay, but the radius of this planet is also different. Radius is in the denominator, so a smaller radius means a bigger acceleration. The radius of the new planet is half of the radius of the Earth. Therefore, the acceleration must be doubled. Almost there … because the radius is SQUARED in the denominator, the acceleration must be doubled AGAIN* .

*“So what is my final answer? The mass causes acceleration to double. The radius causes the acceleration to double, and then to double again. So the total acceleration is multiplied by a factor of 8. The acceleration on this planet is 8g.”*

In the much more concise language of algebra, your reasoning might look like this:

What if the answer choices had been like this:

(A) 2.5 m/s^{2}

(B) 4.9 m/s^{2}

(C) 9.8 m/s^{2}

(D) 19.6 m/s^{2}

(E) 78.4 m/s^{2}

Is the problem any different? (Answer: no.)

**Concept Questions: “WHY?”**

Many multiple-choice questions involve no calculations and no formulas. These test your understanding of vocabulary and explanations for physical phenomena.

Two identical train cars move toward each other, each with the same speed as the other. When the train cars collide, they stick together and remain at rest. Which of the following fundamental physics principles can best be used to explain why the attached cars cannot move after the collision?

(A) Conservation of mechanical energy

(B) Conservation of linear momentum

(C) Conservation of angular momentum

(D) Conservation of mass

(E) Conservation of rotational energy

The direct answer to this question is B: conservation of linear momentum applies to all collisions. The cars had equal momentum in opposite directions, so the net momentum before collision was zero; thus, the cars may not have any momentum after collision. Kinetic energy is a scalar, having no direction, and so kinetic energy of two moving objects cannot cancel to zero. Mechanical energy was not conserved, because kinetic energy was lost in the collision.

But even if you have a hesitation about the difference between momentum and kinetic energy conservation, you can still get close to the right answer by eliminating obvious “stupidicisms.” Look at E: perhaps you recognize that there”s no such thing as “conservation of rotational energy.” Or likely you see right away that conservation of mass, while a legitimate concept, is usually relevant in a chemical process or fluid dynamics and can have little bearing on the speed of train cars in a collision.

**Concept Questions: Diagrams**

These ask you a simple question based (obviously) on a diagram.

A particle experiences a potential energy *U* as a function of position *x* as shown in the diagram above. At which position is the particle in a state of unstable equilibrium?

(A) *A*

(B) *B*

(C) *C*

(D) *D*

(E) *E*

For these, you either know what to do with the diagram or you don”t. Here you, of course, remember that equilibrium is represented on an energy-position diagram by a horizontal slope and that unstable equilibrium requires the energy-position diagram to be at a maximum. Thus, the answer is C.

**Three Things You Can Do with a Graph**

You could see so, so many graphs on the AP exam… . It”s often difficult to remember which graph means what. But if you know your equations, you can usually figure out how to interpret any graph you are faced with. Why? Because there are pretty much ONLY three things you can do with a graph:

- Take the slope.
- Find the area under the graph.
- Read off an axis.

For example, an AP Physics C exam question described an experiment in which a solenoid was stretched to vary the number of turns per length, *n* . At constant current, the magnetic field inside was plotted as a function of *n* ; the question asked for an experimental value of the permeability of free space *μ* _{0} . Chances are that you”ve never done this experiment and that you”ve never seen this particular graph. But you do remember your equations: the magnetic field of a solenoid is *B* = *μ* _{0} *nI* . Solving for *μ* _{0} , .

The slope of this graph is . Therefore, *μ* _{0} must be the **slope** of the graph divided by the current in the solenoid.

Similarly, imagine a graph of force vs. time on a question that asks for impulse. Since impulse is equal to force times time interval (Δ*p* = *F* Δ*t* ), then impulse must be the **area** under the graph.

Finally, if you”re totally clueless about what to do with a graph, just try taking a slope or an area, and see what happens! You might experience a revelation.

Other diagram questions might ask you to:

- use the right-hand rule to determine the direction of a magnetic force on a particle
- identify the direction of an electric or magnetic field
- analyze the properties of a circuit
- recognize the correct free-body diagram of an object
- interpret motion graphs

Many other diagram questions are possible. Try making one yourself—pick your favorite diagram from your textbook, and ask a question about it. Chances are, you have just written an AP multiple-choice question.

**Direct Solution with Variables**

Because the AP test writers can”t ask you to do any kind of difficult number crunching on the multiple-choice section, often they will ask you to do your problem-solving using variables only.

A pendulum of length *L* is drawn back to position *P* , as shown in the above diagram, and released from rest. The linear distance from *P* to the lowest point in the pendulum”s swing is *d* ; the vertical distance from *P* to the lowest point in the swing is *h* . What is the maximum speed of this pendulum in terms of the above variables and fundamental constants?

(A)

(B)

(C)

(D)

(E)

“Ugh … too many letters!” you say. We disagree. Solving this problem is no different than solving the same problem with numbers given. In fact, if the variables bother you, try solving with made-up numbers first:

Let”s say the height *h* is 5 meters, and the mass of the bob is 2 kg … well, we use conservation of energy. Energy at the top of the swing is all potential, all *mgh* . So that”s 2 × 10 × 5 = 100 J of potential energy.

At the bottom, all this energy is kinetic. So 100 . Solving, *v* = 10 m/s.

Now how did we get that? We set *mgh* = *mv* ^{2} , and solved for *v* . The masses cancelled, so *v* = square root of 2*gh* . Lo and behold, that”s an answer choice!

**When Should You Skip a Question?**

Never. There is no penalty for guessing, so guess away!

**Some Final Advice on Multiple-Choice Questions**

- Know your pace. Take the practice exams under test conditions (45 minutes for 35 questions, or some fraction thereof). Are you getting to all the questions? If not, you are going to need to decide your strengths and weaknesses. Know before the exam which types of problems you want to attempt first. Then, when you take your exam, FOLLOW YOUR PLAN!
- The multiple-choice questions do not necessarily start easy and get harder, as do SAT questions. So if you suspect from your practice that you may be pressed for time, know that problems on your strong topics may be scattered throughout the exam. Problem 35 might be easier for you than problem 5, so look at the whole test.
- Speaking of time, the AP test authors know the time limit of the exam—you must average a minute and a half per question in order to answer everything. So they are not going to write a question that really takes three or four minutes to solve! You must always look for the approach to a problem that will let you solve quickly. If your approach won”t get you to a solution in less than two minutes, then either look for another approach or move on.
- One other alternative if you don”t see a reasonable direct approach to a problem: look at the answer choices. Some might not make any sense; for example, you can eliminate any choice for a speed that is faster than light, or a couple of answer choices to concept questions might contain obvious errors. Guess from the remaining choices, and move on.
- Correct your practice exam. For any mistakes, write out an explanation of the correct answer and why you got it wrong. Pledge to yourself that you will never make the same mistake twice.

**How to Approach the Free-Response Section**

The best thing about the free-response section of the AP exam is this: you”ve been preparing for it *all year long!* “Really?” you ask. “I don”t remember spending much time preparing for it.”

But think about the homework problems you”ve been doing throughout the year. Every week, you probably answer a set of questions, each of which might take a few steps to solve, and we bet that your teacher always reminds you to show your work. This sounds like the AP free-response section to us!

The key to doing well on the free-response section is to realize that, first and foremost, these problems test your *understanding* of physics. The purpose is not to see how good your algebra skills are, how many fancy-sounding technical terms you know, or how many obscure theories you can regurgitate. So all we”re going to do in this section is give you a few suggestions about how, when you work through a free-response question, you can communicate to the AP graders that you understand the concepts being tested. If you can effectively communicate your understanding of physics, you will get a good score.

**What Do the Graders Look For?**

Before grading a single student”s exam, the high school and college physics teachers who are responsible for scoring the AP free-response section make a “rubric” for each question. A rubric is a grading guide; it specifies exactly what needs to be included for an answer to receive full credit, and it explains how partial credit should be awarded.

For example, consider part of a free-response question:

*A student pulls a 1.0-kg block across a table to the right, applying a force of 8.0 N. The coefficient of kinetic friction between the block and the table is 0.20. Assume the block is at rest when it begins its motion* .

*(a) Determine the force of friction experienced by the block* .

*(b) Calculate the speed of the block after 1.5 s* .

Let”s look just at part (b). What do you think the AP graders are looking for in a correct answer? Well, we know that the AP free-response section tests your understanding of physics. So the graders probably want to see that you know how to evaluate the forces acting on an object and how to relate those forces to the object”s motion.

In fact, if part (b) were worth 4 points, the graders might award 1 point for each of these elements of your answer:

- Applying Newton”s second law,
*F*_{net}=*ma*, to find the block”s acceleration. - Recognizing that the net force is not 8.0 N, but rather is the force of the student minus the force of friction [which was found in (a)], 8.0 N − 2.0 N = 6.0 N.
- Using a correct kinematics equation with correct substitutions to find the final velocity of the block; i.e.,
*v*=_{f}*v*+_{o}*at*, where*v*= 0 and_{o}*a*= 6.0 N/1.0 kg = 6.0 m/s^{2}. - Obtaining a correct answer with correct units, 9.0 m/s.

Now, we”re not suggesting that you try to guess how the AP graders will award points for every problem. Rather, we want you to see that the AP graders care much more about your understanding of physics than your ability to punch numbers into your calculator. Therefore, you should care much more about demonstrating your understanding of physics than about getting the right final answer.

**Partial Credit**

Returning to part (b) from the example problem, it”s obvious that you can get lots of partial credit even if you make a mistake or two. For example:

- If you forgot to include friction, and just set the student”s force equal to
*ma*and solved, you could still get 2 out of 4 points. - If you solved part (a) wrong but still got a reasonable answer, say 4.5 N for the force of friction, and plugged that in correctly here, you would still get either 3 or 4 points in part (b)! Usually the rubrics are designed not to penalize you twice for a wrong answer. So if you get part of a problem wrong, but your answer is consistent with your previous work, you”ll usually get full or close to full credit.
- That said, if you had come up with a 1000 N force of friction, which is clearly unreasonable, you probably will not get credit for a wrong but consistent answer, unless you indicate the ridiculousness of the situation. You”ll still get probably 2 points, though, for the correct application of principles!
- If you got the right answer using a shortcut—say, doing the calculation of the net force in your head—you would not earn full credit but you would at least get the correct answer point. However, if you did the calculation
*wrong*in your head, then you would*not*get any credit—AP graders can read what”s written on the test, but they”re not allowed to read your mind. Moral of the story: communicate with the readers so you are sure to get all the partial credit you deserve. - Notice how generous the partial credit is. You can easily get 2 or 3 points without getting the right answer and 50–75% is in the 4–5 range when the AP test is scored!

You should also be aware of some things that will NOT get you partial credit:

- You will not get partial credit if you write multiple answers to a single question. If AP graders see that you”ve written two answers, they will grade the one that”s wrong. In other words, you will lose points if you write more than one answer to a question, even if one of the answers you write is correct.
- You will not get partial credit by including unnecessary information. There”s no way to get extra credit on a question, and if you write something that”s wrong, you could lose points. Answer the question fully, then stop.

**The Tools You Can Use**

You can use a calculator. Most calculators are acceptable—the acceptable calculator list is the same as for the SAT or the AP calculus exam. The obvious forbidden calculators are those with a keyboard, cell phones used as a calculator, or those calculators that make noise or print their answers onto paper.^{ }^{1}^{ }You also cannot share a calculator with anyone during the exam.

The real question, though, is whether a calculator will really help you. The short answer is “Yes”: you will be asked questions on the exam that require you to do messy calculations (for example, you might need to divide a number by *π* , or multiply something by the universal gravitation constant). The longer answer, though, is “Yes, but it won”t help very much.” To see what we mean, look back at the hypothetical grading rubric for part (b) of the example problem we discussed earlier. Two of the four possible points are awarded for using the right equations, one point is awarded for finding the magnitude of a force using basic arithmetic, and the last point is awarded for solving a relatively simple equation. So you would get half-credit if you did no math at all, and you would get full credit just by doing some very elementary math. You probably wouldn”t need to touch your calculator!

So definitely bring a calculator to the exam, but don”t expect that you”ll be punching away at it constantly.

The other tool you can use on the free-response section is the equations sheet. You will be given a copy of this sheet in your exam booklet. It”s a handy reference because it lists all the equations that you”re expected to know for the exam.

However, the equations sheet can also be dangerous. Too often, students interpret the equations sheet as an invitation to stop thinking: “Hey, they tell me everything I need to know, so I can just plug-and-chug through the rest of the exam!” Nothing could be further from the truth.

First of all, you”ve already *memorized* the equations on the sheet. It might be reassuring to look up an equation during the AP exam, just to make sure that you”ve remembered it correctly. And maybe you”ve forgotten a particular equation, but seeing it on the sheet will jog your memory. This is exactly what the equations sheet is for, and in this sense, it”s pretty nice to have around. But beware of the following:

- Don”t look up an equation unless you know
*exactly*what you”re looking for. It might sound obvious, but if you don”t know what you”re looking for, you won”t find it. - Don”t go fishing. If part of a free-response question asks you to find an object”s momentum, and you”re not sure how to do that, don”t just rush to the equations sheet and search for every equation with a “
*P*” in it.

**Math and the Physics C Exam**

Physics C students often worry about the math they”re expected to know for the AP exam, because some of the material covered in the Physics C curriculum involves pretty complicated calculus. Maxwell”s equations, for example, involve concepts that are well beyond the scope of most high school calculus classes.

Whether or not you are carrying an A in your AP Calculus course is irrelevant. Most importantly, you must have a strong understanding of the physical meaning behind the mathematics. The problems that might seem to involve calculus—those that use an integral or derivative equation from the equations sheet—can often be approached with algebraic methods. Remember, an integral is just the area under a graph; a derivative is just the slope of a graph. If you have to, set up an integral and don”t solve it. Or explain in words what your answer should look like. Also, note that many of the equations that appear on the equations sheet as calculus expressions rarely or never need calculus. For instance, Gauss”s law has a nasty integral in it, but when used correctly, Gauss”s law rarely requires any calculus. Whatever you do, it is *not* worth the time and frustration to focus exclusively on the tough calculus—this isn”t a math exam, and the point distribution in the rubrics reflects this fact.

**Other Advice About the Free-Response Section**

- Always show your work. If you use the correct equation to solve a problem but you plug in the wrong numbers, you will probably get partial credit, but if you just write down an incorrect answer, you will definitely get no partial credit.
- If you don”t know precisely how to solve a problem, simply explain your thinking process to the grader. If a problem asks you to find the centripetal acceleration of a satellite orbiting a planet, for example, and you don”t know what equations to use, you might write something like this: “The centripetal force points toward the center of the satellite”s orbit, and this force is due to gravity. If I knew the centripetal force, I could then calculate the centripetal acceleration using Newton”s second law.” This answer might earn you several points, even though you didn”t do a single calculation.
- However, don”t write a book. Keep your answers succinct.
- Let”s say that part (b) of a question requires you to use a value calculated in part (a). You didn”t know how to solve part (a), but you know how to solve part (b). What should you do? We can suggest two options. First, make up a reasonable answer for part (a), and then use that answer for part (b). Or, set some variable equal to the answer from part (a) (write a note saying something like, “Let
*v*be the velocity found in part (a)”). Then, solve part (b) in terms of that variable. Both of these methods should allow you to get partial or even full credit on part (b). - If you make a mistake, cross it out. If your work is messy, circle your answer so that it”s easy to find. Basically, make sure the AP graders know what you want them to grade and what you want them to ignore.
- If you”re stuck on a free-response question, try another one. Question #3 might be easier for you than question #1. Get the easy points first, and then only try to get the harder points if you have time left over.
- Always remember to use units where appropriate.
- It may be helpful to include a drawing or a graph in your answer to a question, but make sure to label your drawings or graphs so that they”re easy to understand.
- No free-response question should take you more than about 15 minutes to solve. They”re not designed to be outrageously difficult, so if your answer to a free-response problem is outrageously complicated, you should look for a new way to solve the problem, or just skip it and move on.

**Lab Questions**

It is all well and good to be able to solve problems and calculate quantities using the principles and equations you”ve learned. However, the true test of any physics theory is whether or not it WORKS.

The AP development committee is sending a message to students that laboratory work is an important aspect of physics. To truly understand physics, you must be able to design and analyze experiments. Thus, *each free-response section will contain at least one question that involves experiment design and analysis* .

Here”s an example:

In the laboratory, you are given a metal block, about the size of a brick. You are also given a 2.0-m-long wooden plank with a pulley attached to one end. Your goal is to determine experimentally the coefficient of kinetic friction, *μ _{k}*

_{ }, between the metal block and the wooden plank.

(a) From the list below, select the additional equipment you will need to do your experiment by checking the line to the left of each item. Indicate if you intend to use more than one of an item.

(b) Draw a labeled diagram showing how the plank, the metal block, and the additional equipment you selected will be used to measure *μ* _{k}_{ }.

(c) Briefly outline the procedure you will use, being explicit about what measurements you need to make and how these measurements will be used to determine *μ* _{k}_{ }.

To answer a lab question, just follow these steps:

**Follow the directions.**

Sounds simple, doesn”t it? When the test says, “Draw a diagram,” it means they want you to draw a diagram. And when it says, “Label your diagram,” it means they want you to label your diagram. You will likely earn points just for these simple steps.

**Exam tip from an AP Physics veteran:**

On the 1999 AP test, I forgot to label point *B* on a diagram, even though I obviously knew where point *B* was. This little mistake cost me several points!

*—Zack, college senior and engineer*

**Use as few words as possible.**

Answer the question, then stop. You can lose credit for an incorrect statement, even if the other 15 statements in your answer are correct. The best idea is to keep it simple.

**There is no single correct answer.**

Most of the lab questions are open-ended. There might be four or more different correct approaches. So don”t try to “give them the answer they”re looking for.” Just do something that seems to make sense—you might well be right!

**Don”t assume you have to use all the stuff they give you.**

It might sound fun to use a force probe while determining the time constant of an RC circuit, but really! A force probe!?!

**Don”t over-think the question.**

They”re normally not too complicated. Remember, you”re supposed to take only 15 minutes to write your answer. You”re not exactly designing a subatomic particle accelerator.

**Don”t state the obvious.**

You may assume that basic lab protocols will be followed. So there”s no need to tell the reader that you recorded your data carefully, nor do you need to remind the reader to wear safety goggles.

**Now Put It All Together**

Here are two possible answers to the sample question. Look how explicit we were about what quantities are measured, how each quantity is measured, and how *μ* _{k}_{ }is determined. We aren”t *artistes* , so our diagram doesn”t look so good. But for the AP exam, we believe in substance over style. All the necessary components are there, and that”s all that matters.

**Answer #1**

In the laboratory, you are given a metal block, about the size of a brick. You are also given a 2.0-m-long wooden plank with a pulley attached to one end. Your goal is to determine experimentally the coefficient of kinetic friction, *μ* _{k}_{ }, between the metal block and the wooden plank.

(a) From the list below, select the additional equipment you will need to do your experiment by checking the line to the left of each item. Indicate if you intend to use more than one of an item.

(b) Draw a labeled diagram showing how the plank, the metal block, and the additional equipment you selected will be used to measure *μ* _{k}_{ }.

(c) Briefly outline the procedure you will use, being explicit about what measurements you need to make and how these measurements will be used to determine *μ* _{k}_{ }.

Use the balance to determine the mass, *m* , of the metal block. The weight of the block is *mg* . Attach the spring scale to the bulldozer; attach the other end of the spring scale to the metal block with string. Allow the bulldozer to pull the block at constant speed.

The block is in equilibrium. So, the reading of the spring scale while the block is moving is the friction force on the block; the normal force on the block is equal to its weight. The coefficient of kinetic friction is equal to the spring scale reading divided by the block”s weight.

**Answer #2**

In the laboratory, you are given a metal block, about the size of a brick. You are also given a 2.0-m-long wooden plank with a pulley attached to one end. Your goal is to determine experimentally the coefficient of kinetic friction, *μ* _{k}_{ }, between the metal block and the wooden plank.

(a) From the list below, select the additional equipment you will need to do your experiment by checking the line to the left of each item. Indicate if you intend to use more than one of an item.

(b) Draw a labeled diagram showing how the plank, the metal block, and the additional equipment you selected will be used to measure *μ* _{k}_{ }.

(c) Briefly outline the procedure you will use, being explicit about what measurements you need to make and how these measurements will be used to determine *μ* _{k}_{ }.

Determine the mass, *m* , of the block with the balance. The weight of the block is *mg* . Attach a string to the block and pass the string over the pulley. Hang masses from the other end of the string, changing the amount of mass until the block can move across the plank at constant speed. Use the motion detector to verify that the speed of the block is as close to constant as possible.

The block is in equilibrium. So, the weight of the hanging masses is equal to the friction force on the block; the normal force on the block is equal to its weight. The coefficient of kinetic friction is thus equal to the weight of the hanging masses divided by the block”s weight.

^{1}^{ }Does anyone actually use printing calculators anymore?