STEP 3 Develop Strategies for Success
6 General Strategies
IN THIS CHAPTER
Summary: This chapter contains general strategies useful for the entire AP Physics 2 exam—multiple-choice and free-response sections. First, let’s talk about AP Physics 1 and what you need to remember. Second, I’ll discuss the tools you have at your disposal (calculator, a table of information, and equation sheet) and how to use them. Next, I’ll investigate what those equations you are given mean, how to relate them to a graph, and how to use a graph to find information. Finally, we’ll work on ranking task skills.
You should dust off that 5 Steps to a 5 AP Physics 1 book you had last year. The skills you learned in AP Physics 1 are going to be needed.
Sure you can have a calculator, but it won’t help you for most of the exam. Only use it when you actually need it.
The table of information/equation sheet is good to have in a pinch, but it won’t save you if you don’t know what it all means.
Each equation tells a story of a relationship. Graphs are a picture of these relationships. Learn to see the relationships.
There are three ways to get information from a graph: (1) read it, (2) find the slope, and (3) calculate the area under the graph.
Ranking task questions show up in both multiple-choice and free-response questions. Some require conceptual analysis and others have numbers.
What Do I Need to Remember from AP Physics 1?
The short answer is everything. The prior skills you learned in AP Physics 1 are expected knowledge on the AP Physics 2 exam. Don’t panic. You won’t be asked any questions about blocks on an incline attached to a pulley. Only the content in AP Physics 2 is tested. However, the information you learned about forces, energy, momentum, motion, graphing, free body diagrams, and all the rest is assumed to be still accessible in your brain. Physics is cumulative. There won’t be any roller coasters going around a track, but there will be charged particles that experience forces, accelerate, and convert potential energy into kinetic energy. All the skills you learned last year will help you this year.
So what do you do if all that past information is fuzzy? Ask your teacher to review the concepts and dust off that 5 Steps to a 5 AP Physics 1 book you had last year.
Tools You Can Use
You can use a calculator on both sections of the AP exam. Most calculators are acceptable—scientific calculators, programmable calculators, graphing calculators. However, you cannot use a calculator with a QWERTY keyboard, and you’ll be restricted from using any calculators that make noise. 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 a few questions on the exam that require you to do messy calculations. The longer answer, though, is “Yes, but it won’t help very much.”
The majority of the questions on the exam, both multiple choice and free response, don’t have any numbers at all.
There are questions that have numbers but don’t want a numerical answer. For example:
A convex lens of focal length f = 0.2 m is used to examine a small coin lying on a table. During the examination the lens is held a distance of 0.3 m above the coin and is moved slowly to a distance of 0.1 m above the coin. During this process, what happens to the image of the coin?
(A) The image continually increases in size.
(B) The image continually decreases in size.
(C) The image gets smaller at first and then bigger in size.
(D) The image flips over.
The numbers in these problems are only there to set the problem up. (The correct answer is D).
Then there are questions with numerical answers but using a calculator is counterproductive. For example:
A cylinder with a movable piston contains a gas at pressure P = 1 × 105 Pa, volume V = 20 cm3, and temperature T = 273 K. The piston is moved downward in a slow, steady fashion, allowing heat to escape the gas and the temperature to remain constant. If the final volume of the gas is 5 cm3, what will be the resulting pressure?
(A) 0.25 × 105 Pa
(B) 2 × 105 Pa
(C) 4 × 105 Pa
(D) 8 × 105 Pa
Using your calculator to solve this one will take too much time. You can do this one in your head: PV = nRT, nRT is constant. So, if the volume is four times smaller, the pressure has to be four times greater! Correct answer (C) 4 × 105 Pa. In fact, many times the numerical calculations are simple or involve ratios that don’t require a calculator.
Here is the big takeaway—use your calculator only when it is absolutely necessary.
Special Note for Students in AP Physics 2 Classes
Many, if not most, of your assignments in class involve numerical problems. What can you do? Start by trying to solve every problem without a calculator first. Be resourceful. Draw a diagram, sketch a graph, use equations with symbols only, etc. Second, work the conceptual problems from your textbook and ask your teacher for the key. Practice the skills that will make you successful on the AP exam.
The Table of Information and the Equation Sheet
The other tools you can use are the table of information and equation sheet. You will be given a copy of these sheets in your exam booklet. It’s a handy reference because it lists all the constants, math formulas, and the equations that you’re expected to know for the exam.
However, the equation sheet can also be dangerous. Too often, students interpret the equation 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 equation 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 velocity, and you’re not sure how to do that, don’t just rush to the equations sheet and search for every equation with a “V” in it.
If your teacher has not issued you the official AP Physics 2 table of information and equation sheet, download one from the College Board at https://apstudents.collegeboard.org/courses/ap-physics-2-algebra-based/assessment. Exam day shouldn’t be the first time you see these tools.
Get to Know the Relationships
Now that you have an official AP Physics 2 equation sheet, let’s talk about what the jumble of symbols tell us. Take a look under the “FLUID MECHANICS AND THERMAL PHYSICS” heading. See the equation PV = nRT? What does it tell us? It shows us how all these individual quantities are related and what their relationship is. Rearranging the equation for P we get: . T is in the numerator, which means that if T doubles, and all the other variables on the right stay the same, P must also double. Pressure is directly proportional to temperature: P ∝ T. See graph #2 below. If V doubles, and all the other variables stay the same, P will be cut in half. Pressure is inversely proportional to volume: . On a graph, an inverse relationship looks like #4. What other relationships are we likely to see? Shown below are the six most frequent relationships in AP Physics 2.
Kinetic energy . Kinetic energy is directly proportional to the velocity squared, K ∝ v2. It will have a graph like #3. If you double the velocity, the kinetic energy quadruples: 4K ∝ (2v)2.
Rearrange the kinetic energy equation to solve for . Velocity is proportional to the square root of the kinetic energy ; see graph #5. If you double the kinetic energy, the velocity goes up by a factor of .
Electric force: . The electric force is inversely proportional to the radius squared , but it is directly related to the charge FE ∝ q. See graphs #2 and #4. This means that if you double one charge and also double the radius, the force will be cut in half: .
There are always questions on the exam that can be solved this way. Learning how to work with these relationships is crucial to doing well on the exam because they don’t require a calculator and save you time. Put your calculator away and practice this skill all year long.
What Information Can We Get from a Graph?
Gathering information from a graph is another highly prized skill on the AP exam. Let’s spend some time making sure you have it down cold. The good thing is there are only three things you can do with a graph: read it, find the slope, or find the area. But, before you can do that, you need to examine the graph. Look at the x-axis and y-axis. What do they represent? What are the variables? What are the units? Which physics relationships (equations) relate to this graph?
1. Read the Graph
Look at this graph. The data is not in a perfect straight line. This is common on the AP exam, as it includes real data like you would get in an actual lab. If you get data like this, sketch a line or curve that seems to best fit the data.
This data seems straight, so draw a “best-fit” line through the data that splits it down the middle. Your line may not touch any of the data points. That’s OK. Once you have your best-fit line, forget about the data points and concentrate only on the line you have drawn. The AP exam may ask you to extrapolate beyond the existing data or interpolate between points. For example: at a current of 2 amps the power is approximately 6 watts.
2. Find the Slope
In math class you calculated the slope of lines, but most of the time it didn’t have a physical meaning. In physics, the slope usually represents something real. Take a look at the axis on the graph. Power is on the y-axis and current on the x-axis. Ask yourself if there is a physics relationship between power and current. P = IΔV seems to fit the bill. In math class the equation of a line is y = mx + b. Now line up the physics equation with the math equation to find out what the slope’s physics meaning is. Turns out that the slope is the potential difference!
This procedure of matching up the physical equation with the math equation of a line will help you find the physics meaning of the slope every time.
Now that we know the slope represents the potential difference, we need to calculate it. Slope is rise over run. Pick two convenient points. I used points (1 A, 3 W) and (3 A, 9 W). Thus, the slope is (9 W — 3 W) / (3 A — 1 A) = 3 W/A = 3 V.
CAUTION! Never choose a plotted point unless it actually falls on your best-fit line. This will give you the wrong slope. Notice that one of the chosen points was an actual data point (1 A, 3 W) because it was on the best-fit line. That’s OK. The other point (3 A, 9 W) was not a data point.
Let’s practice. The graph (shown above) has pressure as a function of depth. (Watch out for the units on the axis: kPa.) This looks like a fluids problem. The equation P = P0 + ρgh seems to fit. Now let’s match the physics equation with the math equation.
So the slope is the density times the acceleration due to gravity. Using the circled points, we get a slope of 10 kPa/m. This time there is a y-intercept, which is the pressure on top of the fluid, P0 = 100 kPa.
Sometimes the axes are strange. Take a look at the graph, which shows the inverse of current as a function of resistance. Don’t fret! What is the physics relationship between current and resistance? . Now match up this equation with y = mx + b:
The slope is the inverse of the potential difference. That’s kind of strange but if that is the graph they give you, just go with it. The slope = 0.006 (1/A)/Ω. Taking the inverse, we get the potential difference of 167 V.
One last hard one! The graph, shown above, is the inverse of the image distance as a function of the inverse of the object distance. What a mess, but who cares? We can handle it. Image and object distances imply optics: . Now match the equation up:
The slope turns out to equal −1 and does not have any physical meaning this time. The y-intercept is the inverse of the focal length.
Occasionally the AP exam asks that you to take a graph that is curved and produce a graph that has a straight line. This is called linearization. It is the reverse process of above. Take the equation and match it up with y = mx + b to see what you should graph. Take this equation: n1 sin θ1 = n2 sin θ2. Let’s put the θ1 on the x-axis and θ2 on the y-axis. Match the equation. Plot what it tells you to plot, and you get a straight line from your data. Piece of cake.
3. Find the Area
This time we look to see if multiplying the x- and y-axis variables will produce anything meaningful. If so, the space under the graph has a physical meaning. Take a look at the graph above—pressure times a changing volume. That looks like something to do with gases: W = —PΔV. The area under the graph is the work. Calculate the area of a graph just like the area of a geometric shape. Keep in mind that the “units” of our graph area will be Pa · m not a geometric unit like meters squared.
The area of this graph is (6 × 105 Pa)(9 × 10—3 m − 2 × 10—3 m) = 4200 Pa · m = 4200 J. Since our equation was W = —PΔV, our final answer is negative: W = —4200 J of work.
Ranking Task Skills
Ranking tasks are an interesting type of question that can show up in both the multiple-choice and free-response portions of the exam. Here is an example:
A battery of potential difference ε is connected to the circuit pictured above. The circuit consists of three resistors and four ammeters. Rank the readings on the ammeters from greatest to least.
They are not asking for any numbers, and in most cases, trying to use numbers to solve the problem is much more time-consuming than using conceptual reasoning and semi-quantitative reasoning. In this example, we see that ammeters A1 and A4 have the same current because they are in a same single pathway. This is the main pathway that feeds the rest of the circuit. This main current splits before passing through the lower two resistors. The 20-Ω resistor will have less current passing through it than the 10-Ω resistor. Thus, the ranking from greatest to least is A1 = A4 > A3 > A2. No numerical calculations were needed, just physics reasoning.
On a free-response question, make sure you write your answer in a clear way that cannot be misunderstood and designate any that are equal. For example: Greatest (A1 = A4) > A3 > A2 Least. On a multiple-choice question, look to save time. As soon as you figure out the ranking of any pair, look for any answer choices that don’t have that pairing and cross them out. For example, look at the answer choices below:
(A) A1 > A3 > A2 > A4
(B) A1 > A3 = A2 > A4
(C) A1 > A4 > A3 > A2
(D) A1 = A4 > A3 > A2
When you determine that A1 = A4, a quick look at the answer choices shows that only answer choice (D) will work.
There are students who are more comfortable with numerical thinking. If that is the case with you, you can choose a number for ε and work out the currents. But this will almost always take longer.