2026 AP Physics 2 Free Response #3

Añadido: 2026-05-10

[00:00:00]All right, now on to the experimental design FRQ 2016 AP Physics 2 version J.

[00:00:06]Uh experiment one scientist want to collect data to be graphed to determine the magnitude of B0 of a external uniform magnetic field. The field is directed in the figure as shown here.

[00:00:14]Um between identical parallel conducting plates that are connected to a power supply variable EMF. So this is the voltage. The plates are a known distance D apart, so we know D and D is much smaller than dimensions of the plate. Okay. Each trial device emits a small charged sphere at speed V through the plates.

[00:00:31]E is varied until the spheres uh move undeflected toward the motion detector.

[00:00:35]So we're going to shoot electrons this way. Scientists can vary V between the trials. In addition equipment, scientists have access to a voltmeter, so we can measure the voltage here.

[00:00:43]Um they do not have access to other measuring tools, devices, sensors, or equipment. So we can measure the voltage.

[00:00:48]Um and we can, you know, wait until we get uh get a detector there. Can we vary this?

[00:00:55]We want to determine the magnetic field.

[00:00:57]So we can vary the voltage until uh the the key quantities can be measured using the available equipment that allows scientists to determine B0 using a linear graph. So we got to do some kind of linearization on the experimental design.

[00:01:09]So we definitely um we can measure the voltage epsilon.

[00:01:14]And um we can't vary D.

[00:01:20]Um Scientists can vary V between trials.

[00:01:27]Um Oh oh, I see. We're going to we can vary the velocity. That's what we're doing.

[00:01:33]So we're going to this and we're going to measure this and um uh what else are we going to need? Are we going to need Well, we're going to vary the velocity and we're going to vary the E until it goes undeflected. That's the idea.

[00:01:49]So if we're not sure about what we're Yeah, I think we're just going to could be measured. We just need to measure the voltage here. That's all we need to measure.

[00:01:57]Um we need to know um Let's see. We need to know how fast they're moving though.

[00:02:04]Well, let's see if we need to figure out how much they're not. So, the way this is going to work is we're going to shoot it here and once it's going undetected, right? So, from our free body diagram and we're Are we We're ignoring gravity.

[00:02:14]So, the only forces we're going to have are um well, well, let's see. It emits charged particles.

[00:02:24]Let's assume it's a positive charged particle for the sake of argument here.

[00:02:27]So, there's going to be electric force from the electric field. Okay? And then there to compensate that we're going to want a magnetic force that goes upwards.

[00:02:37]And if that Let's see it was a right-hand rule just to make sure that that works. Yeah. If it was a positive charge, it would be an upward magnetic force. We want the magnetic force to equal the electric force. This is going to be QVB cuz they're already moving perpendicular. That's equal Q times the electric field. So, we don't actually need to know the charge. The velocity is going to be B over the electric field.

[00:02:58]Um so, the velocity we can figure out um So, what are the things that we can quantify? Well, the electric field we know is going to be the voltage divided by the distance there.

[00:03:12]So, this is going to be B over V times D. This is or let's uh let's use epsilon just so we don't confuse it with the velocity.

[00:03:23]And so, this is what we're trying to figure out. Uh we know D. We want this We need to know the speed somehow. So, can we measure the speed?

[00:03:31]It emits a small charged particle with speed V through the regions. It can vary. The scientist can vary V. I think we're just going to have to assume that we're going to know V. We're going to need to know the distance.

[00:03:41]Well, I don't know if you need to measure it, but we do need to know We do need to know the distance. We do need to know the E and we do need to know the velocity here cuz this is the equation that we're going to be using.

[00:03:53]Right?

[00:03:54]To get the B0 part.

[00:03:56]Uh describe a method to reduce experimental uncertainty for the measured quantities in part A. So, you can vary the velocity, vary velocity.

[00:04:07]And um and adjust uh epsilon to you know um detect until detecting the particles.

[00:04:20]Detecting the charged particles.

[00:04:27]And you can also repeat multiple times.

[00:04:33]So, multiple So, I see multiple velocities is one way or you could repeat it multiple times. But we want to do vary the velocities.

[00:04:44]Um so, this is my default one cuz we got to vary it so we can make a straight line graph.

[00:04:48]>> [snorts] >> Okay, uh indicate what quantities could graph on the horizontal and vertical axis. So, if I want the you could uh easiest one is just to say like, well, I could make this my Y variable. I could make 1/epsilon my X variable and then the slope would be B0D, right? So, what quantity corresponds to X axis?

[00:05:09]We could do 1/epsilon. There's a lot of ways you can do this, by the way. This is not the only option.

[00:05:14]Um as long as you just rearrange it and the remaining thing that you have that's the slope is constant. It's not varying in the experiment.

[00:05:21]Uh oops, uh Y variable would be V.

[00:05:25]And then the slope and so the slope is going to equal B0D.

[00:05:30]So, B0 would be the slope of the line of best fit.

[00:05:39]Uh divided by D.

[00:05:41]Okay? So, that's kind of how we would do that one. All right.

[00:05:44]Experiment two, scientists want to use a graph to determine the mass of identical charged particles emitted from the device. Each particle is a charge there.

[00:05:51]Each trial is emitted with the speed V0.

[00:05:54]Uh so they give us a number and they give us the radial path here. In subsequent trials, B is increased and the resulting R is recorded.

[00:06:01]Gravitational effects are negligible.

[00:06:03]>> [snorts] >> So no gravity collected data is given in here. Okay, let label the axis with measured quant or calculated quantities.

[00:06:11]Uh the graph quantities should yield a linear graph that can be used to determine the mass. Okay, so what's the process we're going to go here?

[00:06:19]Um it's a circular motion, so we're going to do a free body diagram, do our forces. So we have force here. This is the centripetal This is the force the magnetic force. It's going to use it from a right hand rule.

[00:06:29]Um that's the only force acting. Nothing else is touching it. So and then we have a centripetal acceleration directed towards the center of the circle. So when we do Fnet equals MA, just our Newton's law, it's the this is going to M times the centripetal acceleration.

[00:06:43]The magnetic force is going to be QVB.

[00:06:47]The charge is capital Q, V0, and then um B, and that's equal to M V0 squared over R.

[00:06:57]So the one of the V0s cancels and what are we trying Oh, we're trying to find the mass. So we have QB is equal to M over RV0.

[00:07:06]So we would like to know or let's do V0 over R times M.

[00:07:13]So we could uh we know V0, we know this number, so you could do um V0 over R.

[00:07:21]Okay, so that that would be one a possibility. So we could make this X if you wanted to.

[00:07:26]Um you can make this Y.

[00:07:29]Um do we know the charge of this thing?

[00:07:31]Yeah, we do know the charge. So you could make that Y.

[00:07:34]And then the slope would be M.

[00:07:38]That's one possibility. If you just want to do it with these guys and not calculate as much, and be a little bit lazy, then you can solve for B. B is going to be V naught over QR times M. And then we could do 1 over R.

[00:07:52]So V naught M over Q and then make it 1 over R. Just rearranging some of the variables. This is why the And then you could then say like, "Oh, make this Y."

[00:08:02]Great. I don't have to recalculate anything. And then this is going to be X. So you could do um B on the Y axis. So this is B and then that would mean units of Tesla.

[00:08:12]And then you could do 1 over R, which is meters -1. So they're just leaving them right there, like that for you. Okay? And then the this guy would be the slope. So the slope would then equal V naught M over Q. And we know V naught and Q, those are constants. So then you could just solve for M from your line of best fit.

[00:08:29]Okay. So now we want to plot this data.

[00:08:31]So let's do all the 1 over R calculations, and then we'll move it down to the graph. 1 / 1.8 0.56.

[00:08:40]1 / 1.2 is going to be 0.83.

[00:08:44]1 / 0.5 is 2. 1 / 0.4 is 2.5. And 1 / 0.3 is going to be 3.33.

[00:08:52]Okay. So now, just for simplicity, I'm going to make a copy of this.

[00:08:57]Move it down here so I can plot the data. Now, how are we going to label the axes?

[00:09:02]So on the X axis, we want to go from 0 to 3.33. So 1 2 3, that's not going to That'll be easy, barely the half. We have 1 2 3 4 5 6.

[00:09:12]So we couldn't make them 0.5s because um that would uh that would not cuz that would make this three over here, at least if we started at zero. We don't have to start at zero because we don't care about the Y intercept, so we could start at 0.5. Make this 1 1.5 2 2.5 3 and 3.5. Then each of these little lines is 0.1.

[00:09:34]That sounds That sounds pretty nice to me. Y axis, we're going to go from 0 to 0.2. That's 1 2 3 4 5 6. We got to go up to 0.2 / 6 is like 0.3, but maybe if we just make it 0.5 or 0.05. 0.05 0.10 0.15 0.20.

[00:09:56]We use up 0.04 from here to here. That's exactly half. Not my favorite, but probably we'll just go with that just because um But you do want to try to use at least half the vertical axis. But we're going to go from about here to 0.2, which is here, which is technically more than half. So we just stick with it.

[00:10:18]All right. Um so then the X value is 0.56.

[00:10:23]So um actually each of these is 0.02.

[00:10:28]So 2 4 6 and then 0.04.

[00:10:32]Like that.

[00:10:33]And then 0.83.

[00:10:36]Uh 5 2 5 4. No. What am I doing?

[00:10:40]That's not right.

[00:10:42]They're each 0.1.

[00:10:44]0.56 is going to be about there. And then 0.04 is going to be about is going to be right on that line there. Okay.

[00:10:52]And then 0.83. So this is 1 0.9 0.8 0.83 and then 0.06. It's going to be right around there.

[00:11:02]And then two and then 0.14 or two and then 0.14.

[00:11:08]And then 2.5 and 0.16.

[00:11:12]And then 3.33. 1 2 3. Little past there.

[00:11:16]And then 0.2.

[00:11:18]So three. 1 2 3.

[00:11:21]Yeah. And then about there.

[00:11:24]Okay, cool. That looks pretty good. So let's draw a line of best fit now.

[00:11:30]I don't know.

[00:11:31]Something like that.

[00:11:33]Let's pick two points that we can easily read off the graph. So, we'll pick this point here. This point here is 3.4, 0.21.

[00:11:41]Let's pick this point here is what?

[00:11:43]0.567, 0.7, 0.05.

[00:11:50]Okay.

[00:11:51]Cool. Got our points. Now, let's calculate the slope of our best fit. So, the slope which we said was equal to V0 M over Q is going to be 0.21 - 0.05 the Y values over 3.4 - 0. S S uh 0 Sorry.

[00:12:15]0.7. Yeah.

[00:12:18]And then, we're just going to multiply I'll just do it. We'll We'll multiply is going to be this number times Q over M the Q over V naught. So, 0.21 - 0.05 divided by 3.4 - 0.7 that's going to give me 0.059.

[00:12:35]So, we're going to do 0.059 times Q over V naught. The Q we're going to plug in What was the number?

[00:12:44]6.4 * 10 to the 19 -19 and the V0 was like 3 * 10 to the 6.

[00:12:56]So, we're going to do times 6.4 e - 19 divided by 3 e 6. And that's going to give me the M is equal to 1.26 * 10 10 to the -26 kg. Don't forget the units there.

[00:13:10]Okay.