AP Physics Insights Caveat: These are my personal thoughts and not in any way condoned or affiliated with ETS or whatever else. If you disagree with any of my points, please shoot me a comment or respond to the post and let me know your interpretations. I am more than willing to re-evaluate my ideas. These are simply my current conclusions based on evidence I’ve gathered, but I’m quite sure there’s more out there I haven’t seen that could lead to even better insights.
Lab questions have some very common patterns. There’s always at least one lab question in every free response section of every test. They aren’t always design a lab, nor are they always plot/best-fit/slope, nor do they always ask you to discuss errors, but all of those are very, very frequent. So, I want to talk about each for a bit. This is not exhaustive, but it does hit a lot of common themes I’ve seen while grading.
One thing students are asked to do that is straight forward but usually done very poorly is plot some data, draw a best fit line, find the slope, and then relate that to some physical relationship. Advice for doing one of these problems well:
- Do not force it to go through the origin unless there is specifically a piece of data given as (0,0). The AP will often specifically give data sets that do not go through the origin to test whether or not you can analyze that situation and understand what a y-intercept means in a physical sense. Yes, technically, it does mean “it’s the value of Y when X is zero”, but that will not give you any credit on the AP at all. Why is the value of Y something other than zero when X is zero? That is what you must explain using physical examples.
- Draw one straight line all the way to and through the axes, at least in the first quadrant. There are a hilariously large number of ways to improvise a straight edge if you didn’t happen to bring one specifically. Fold a piece of scratch paper in half or quarter. Use one of your extra pencils you definitely should bring. The side of your calculator is probably vaguely straight enough to do. Do not sketch it out in four thousand tiny pen/pencil strokes. Get a straight-edge. Draw one firm line. DO NOT FREE HAND IT
- Do not connect the dots. Not even two of them. Draw a line in the middle of the dots that’s as close as you can get to ALL of them while going THROUGH as few of them as possible. Sure, sure, if you have a calculator, you can run a regression. There’s specific math for all that. But if you’re going to eye-ball it, as close as possible to all while going through as few as possible will get you into a good, reliable ballpark. It’s better to be medium away from two than really close to one and really far from another.
- Calculate the slope from your line, not the plotted points. If you choose just one point, you’re implicitly choosing the origin as the other point. If your line does not go through the origin, guess who just did it wrong? You! You did it wrong! Pick two points on the line that YOU drew and find the slope from there. It is helpful to circle those points to make it explicitly clear. Even better, write the coordinates down next to each point or in the margin somewhere. Make sure you check both axes for units and scale. Sometimes it will be mV and you’ll need to convert to Volts. Sometimes km to m. Sometimes m (x10^-2) to m.
- The slope is not always exactly the variable you are looking for. The slope will always be related to your goal, but it won’t always be exactly equal to it.** On AP C: Mech Q1 this year, a question of this sort was asking students to find an experimental value for g (acceleration due to gravity near the Earth’s surface). One method of solving it ended up with the slope = g/2. Another method had the slope = 2/g. Another method had the slope = g. Another would be slope = 1/g. And there were more than just those four valid methods. Make sure you know what the algebraic relationship is that you are graphing. Anything in your equation that is not on one of the axes should be a constant AND included as part of the slope.
** A note from Ralph von Philp with an excellent correction: “Sometimes the slope is not related to the goal, but the Intercepts are related to the goal. Two examples I have seen in the past are using intercepts to get focal length of a lens, and using the intercepts to get work function and cutoff frequency for photoelectric effect.”
Other common lab questions involve asking students to design a procedure. When I graded P1Q2 two years ago, it was a ‘design your own lab’ question, as is this year’s CM1Q1.
- Figure out what two things you are varying. There are only so many things you can actually measure in mechanics. It doesn’t make any sense to write a long lab procedure about measuring energy. The basic things you can measure are force, mass, distances (lengths/dimensions), and times. Pretty much every single other basic mechanics quantity is a combination of these things. Speed, acceleration, jerk, momentum, energy, rotational motion, torque, frequency, etc. Sure, motion sensors can give you velocity and acceleration, but they do that through calculating them based on the changes in distance during time intervals.
- Don’t over-complicate the equipment. There are a whole lot of mechanics labs you can do with the most simple possible materials (scale/balance, meter stick, stopwatch, ball). It is generally assumed you know how to use meter sticks, stopwatches, scales/balances. There is absolutely no reason to go into excruciating detail about opening up LabView on your computer. If you are going to use sensor technology, you better be very, very careful that you can explain how to use them correctly. If you are “using a motion sensor to measure distance” you better explain how that is going to work. My best advice? Don’t bother with sensors for mechanics labs. **See below for a discussion of E&M labs.
- Keep the steps as simple as you can. The basic procedure for literally any lab is “set up [equipment] to let me vary [this] and measure [that] while controlling [these]. Then vary [this]. Then measure [that]. On P1Q2 a few years ago, the procedure could be as simple as “Drop the ball from various heights and measure how far it bounces back up for each different height.” That’s it. Tell me what you are doing, what you are varying, and what you are measuring.
- Be explicit about what you control. This means list things you could vary but are not that could potentially affect your outcome. For instance, if you are rolling a ball down a ramp from different heights and measuring the time, you could talk about controlling the angle of the ramp and the release and the mass of the ball, etc. You don’t have to talk about controlling the lights in the room. You don’t have to control whether the window shades are up or down. You don’t have to control whether your ramp is on the table or on the floor (assuming both are level). Worry about the things that could affect what you are measuring (the time) that aren’t specifically different release heights.
**I’m still learning about E&M lab development at the AP:C level, so I don’t have a lot of hard advice for that. What I do have for the AP1/2 level? Say you are using a multimeter^ to measure things. You’ll get no points if you say you’re using an ohmmeter to measure voltage. Here are my best guesses regarding common equipment for E&M labs. BEST GUESS. Most circuit labs will probably involve wire, a power source, something to do a thing (resistor, heater, light bulb, speaker, capacitor, etc), and a multimeter. Electrostatic labs will be about measuring forces, so it basically becomes a mechanics lab. Labs with induction involve either a loop of wire or a magnet moving around in most cases. Things that move? Hey! We’re back to mechanics! Seriously, we can measure time, distance, force, mass, current, voltage, and resistance. That’s about it. These quantities are related to pretty much every single other thing you learn about. Whether mechanics or E&M, keep your labs as basic as possible. (^Thanks to James D Von Steen for this insight) **
The other most common piece of a lab-based question is error analysis. Students come up with all kinds of wacky possibilities. Good examples of bad reasons for errors:
- THIS IS A BAD REASON: “human error” and “our measuring tool was broken” and “bad equipment”, etc.
- THIS IS A BAD REASON: “Drawing a bad best-fit line” or “miscalculating the slope”
- THIS IS A BAD REASON: You waited too long to look at your measuring tool, so the value changed
- THIS IS A BAD REASON: The multimeter shorted out/couldn’t handle that high of a load/the resistance was too high
- THIS IS A BAD REASON: My partners copied the measurement down wrong
- THIS IS A BAD REASON: Almost any phrase involving “should have”, “could have”, “maybe”, or “might have”. The ramp should have been straighter. The table could have been crooked. The ruler might have the wrong markings. Maybe the scale wasn’t zeroed.
No. These do not count as explanations for experimental error. These are reasons you and your group are bad at labs. That’s not experimental error. Experimental error has something to do with the setup, a variable you couldn’t or didn’t control for, an object or phenomenon that was assumed to be one way in your model (frictionless, massless, stretchless, ideal in any way) but in actuality was not that way. You have to think about the assumptions you made going in and how those assumptions being wrong will affect your final result. Here are a few examples along those lines.
- The spring does not follow Hooke’s Law (the radius of the windings change with the length, it ended up close to the elastic limit, or similar).
- The resistor does not follow Ohm’s Law.
- There is actual resistance in real wires.
- The battery has internal resistance.
- The pulley has mass and friction.
- The string has mass and stretches some.
- The wheels have friction.
- The transition from the heavy string to the lighter string is not perfect.
- The insulator does conduct some heat, so the system is not actually isolated.
- The water is from the tap, so it has some impurities that affect the density.
OK, that last one is stretching things pretty far unless your tap leads straight to the Dead Sea, but I hope by this point you recognize that experimental errors are about disagreements in behavior between the perfect, ideal model of the system you developed using Newton’s Laws or other first principles compared to a real system that exists in messy, messy reality. It’s not about what YOU DID during the experiment. It’s about what YOU MISSED in your model.
That’s what science is about in its entirety. What do we know? What are we looking for? What assumptions are we making? Uh oh! Our results didn’t match our prediction! What did we miss? Oh! This assumption didn’t apply! Guess we better look into that or find a way to control for it! Yay science!