Transcription
Uh, we will be doing today lab number two on Newton's Second Law, as, um, Kerry was just saying. Now, this lab is, at least in the equipment part, may be considered somewhat an extension of the first lab. We will be using some of the, um, things that we have learned in the first lab, applying it here, and then also there will be obviously some new, new things because that is not just kinematics anymore. This is, um, forces in motion and again, specifically Newton's Second Law.
So, the lab itself, it's not long. It's much shorter than the first one. So, it's important that we understand the question and why we're doing this rather than just the calculations itself. Now, again, we're trying to verify with Newton's Second Law of motion holds true for this same case of a cart moving on a or rolling in a truck and being pulled by one of these little masses. And why we're doing that? Well, you know, Newton's Second Law is such a fundamental law. It's important to, um, well, understand how it works and also to make sure that it's not just something you learn about in a text and use some, uh, you know, solve some mock-up problems, but it's actually something that holds true in the real life or not. You know, this is, um, for you to decide once we have, uh, I've done the experiment and you have completed all the calculations.
So, there's a page of page two. It's full of derivations and equations and whatnot. So, uh, Kerry has talked about that a little bit, and you can read, um, more about that on page number two. It's all very detailed how they derive the equations that we're going to use for the calculation of the theoretical, um, acceleration or calculated acceleration and the measured acceleration. This is where our timing system will come into the plate. And basically, what we did in the first lab, we're gonna use some of that knowledge and apply it here as well to measure the actual or observed or experimental acceleration in this lab. So, again, uh, the cart, obviously, it's on a level track, so there's no acceleration unless you're pulling the cord or, you know, have the truck set up on an incline.
So, what we're going to do is we're gonna attach to one end of this cord a small weight, similar to those or mass similar to those we used in the last lab. And this is what's going to provide the tension in the string. And as that mass is falling to the floor, draped over this, supported over this pulley for smoothness of motion, that's what's gonna actually accelerate our cart. Now, in the first lab, hopefully, uh, you have concluded that the motion of this cart when being pulled in a fashion I just described, indeed, it's accelerated motion. This is what you, uh, should have, um, learned or determined from your, uh, extended calculations there in the first lab. So, we're not going to spend much time on that. We're going to assume that this is accelerated because we know that by now, and we're going to focus just on the Newton's Second Law of motion then.
Now, all of your experimental results will go on in a table on page three. Uh, it's a smaller, shorter table compared to what we had in the first lab. And, uh, basically, what we're going to do, we're gonna use one photogate separation. Remember how in the first lab we tested a few to see if that had any effect on the acceleration, uh, different, uh, photogate separations? And again, hopefully, you would have concluded that, uh, truly, no matter how close or far apart you place photogate one from photogate two, it has no, you know, measurable significant effect on the, um, measured value of the acceleration of that cart. Because truly, what it is, we're just taking snapshots on the cart's final velocity at different time intervals, and then the initial velocity, as measured by this one, is always the same if we release the cart from the same spot. So, you know, it is logical that the calculated acceleration shouldn't change regardless where we place the second photogate, right? Even though the final velocity will be different as taken by this key.
Now, um, so we will set up these photogates so that the photogate separation is 0.05 meters or five centimeters. So, essentially, they'll be very, very close. And, um, the photogate flag width, it's all also pre-pre-filled there in the table for you. So, what it is, this black, um, plastic piece that has printed lines on it. These are, if you remember from the last lab, this is what triggers the photogate, right? Uh, there's a light beam, invisible light beam, passing through one end of the gate to the other. And, uh, the clear portion of this plastic, it lets that beam to pass through. But the moment the black area enters into the photogate, that blocks the light beam, and then when it's out of the gate, it unblocks it. So, this is where the timer uses to, um, determine when an object is indicated or not. And essentially, because this is so short relative to the length of the track, essentially what we're getting is an instantaneous velocity of this object at the photogate. So, this is what we're calling the V1 or V initial, and V2, V final, right? So, this is what that 0.025 meters, that's what's referring to. It's the length of this topmost line on this plastic, okay?
Right, so the next thing we need to know is obviously the mass of the cart and the mass of the standard falling mass. So, what we're going to use for the mass of the cart is actually, it's been measured before and written on the cart. So, we'll just write it down and trust that it's correct. So, I have 0.547 kg. That's the mass of the cart, okay? And for the falling mass, let's use, uh, 20 grams. So, that would be what? 0.02 kg, right? I think we used 10 in the last lab. Let's use 20 this time. So, what I will do then, I will attach this mass at the end of this cord. Or, nope. And now, of course, the, um, this length of cord or rope that we're using, the mass of this, it's not, uh, negligible. We are choosing to ignore it because it's rather small relative to the mass of the cart itself. But when you're talking about the sources of error later on, you may want to think or consider this as one of them. I think someone asked the question before, uh, to, I would consider including the tension, the loss. So, this answers your question in a way. We're not considering the mass of the string in this lab at all because it's so small, okay?
So, this is essentially what the starting position of our cart looks like at the start with the experiment. When I release the cart, the mass is gonna fall to the floor, and then it's going to pull the cart with it. And this is the motion that we are going to look at today and investigate and see if Newton's Second Law holds true for the case of this cart rolling on this truck. Now, there's one thing that we haven't done yet. It is the photogates. So, I will return the cart to its, um, starting position and put this here. Now, we are given the photogate separation, which is, uh, zero, zero, 0.05 meters. So, it's rather close. Now, they're not giving us exactly how far from the, um, starting position of the cart to position the first photogate. So, I would say, um, let's, since it's not given, it probably doesn't matter. So, I'll just leave the first photogate where it is. Just gonna position it sort of, see, maybe here, just so it's a nice even number. And then this one, we're going to position five centimeters from the first one. So, it's, I'm just trying to see the, okay, it's about here. So, essentially, what's going to happen, our initial velocity is measured here at photogate number one, and then final velocity is measured almost, uh, immediately after. Okay.
Now, so we have written down the mass of the cart and the mass of the falling mass. So, essentially, we're all set. Uh, the last thing that we need to do is set up our timer. Now, the timer, if you remember, um, it, um, truly, it deals in the units of, uh, time, right? But then anything else that it outputs, it actually calculates, uh, for us. So, the velocity, it doesn't measure velocity directly, right? It measures velocity from the time and the length of the object that is passing through the photogate. So, it does some of the calculations for us. Although we could have taken, you know, just the time and do those calculations manually, but we're choosing not to because, why not? If the timer can do this for us, we know how to calculate velocity, right? So, no need to, uh, do that. So, I will set up the timer. So, what we need to tell the timer, essentially, it's just the length of this object. So, it's 2.5 centimeters. So, I will, let me just move so that I can see what I'm doing. So, I will click on the mode and then I'll just scroll up to set that object's length in centimeters. It says 2.5. I'm going to press the mode again. We're going to ignore this. We're not using it. And then the timer is set up and ready to go. So, then the moment I press the start/stop button, those dashes in front of the zero disappear, and the timer is, um, the timer is ready to record, um, those timing events. So, now, let's say if I move my hand through the photogate, immediately you see that the reading on the screen has changed, and there's a number associated. So, you know, for instance, my hand was there for three-point-something seconds and photogates. So, this is what we're going to use essentially to, uh, measure the velocities of our cart at the two photogates. So, let's reset this. So, we don't need to. Okay.
So, what I will do, I'm thinking I will have this, um, timer, gonna set up in front of you on this, uh, let me just slide it under the track so it's not actually blocking the cart. Um, so this timer, we'll just set it up like this so you can see what's going on. I don't have to hold it, and hopefully these cords are not going to pull it. Should have prepared something for this, but I didn't expect it to be this unstable. It just doesn't want to stay upright. Foreign of course. Okay, so let's find a spot and where it's not gonna. Okay, it looks like all right. So, hopefully you can see, uh, what's on the screen, um, and the glare is not, uh, distorting that. If it does, then I'll just, uh, say it out loud. Okay, perfect. So, again, I'm going to move the cart to the starting position. I will activate the timer and erase whatever maybe in its memory. All right, and then we're good to do the first run. So, there's three things that we're going to record. Uh, so the P12, that's sort of the timer speak, uh, for the transit time between the photogates. So, essentially, it's the time that takes, uh, the cart to, uh, travel between these two gates. And then V1, that's the initial velocity of the first photogate, and then V2, and we call it the final, is the velocity at the second photogate. So, those are the three things that we'll record in each of the five, I believe, runs. And, um, yeah, so once we do the first run, it's, uh, all very straightforward. It's just more of the same, essentially. And again, we're doing these five runs, remember why? Because we want to make sure that we're getting consistent, reproducible results, right? So, you can draw conclusions based on good, uh, experimental data. So, let's, uh, then do the first run. Timer's set up, and then all I need to do is release the cart. All right.
So, now the timer has recorded all those events that we need for to transfer into our table so you can do the calculation. So, what I'll do, I'll stop the timing, and then I can scroll through. It's flashing some numbers, but let's don't record that because it does it in, um, kind of odd way. So, we'll just scroll through them manually until we see what we need. So, that's P12, again, that's the timer speak for the transit time. We call it T transit 1-2. So, let's write that down, and that's in seconds, okay? Uh, then we need the V1, right? Now, in your table, that's the last column, right? I think they did it just for convenience so you, it's like in the formula, right? By the timer outputs, uh, V1 first, and then V2. So, this is your VI, in other words. And those units, those square brackets, those are for the units, and these units are meters per second. You probably can't see that because it's all tiny in the corner of the screen, but it's there, okay? And then V2, or VF, as we call it, that's the final velocity of the second photogate, all right? So, now that we've got that, that was our first run. Then we need to do four more. So, what I will do, I will erase this. The timer has been armed again. You see that zero, uh, without the dashes in front of it, so it means that it's ready to, ready to measure. And again, I'll just, now I'm not pushing this cart too hard into the, um, too hard down, basically, into the track or into the barrier, so as not to, uh, potentially affect our results. I'm just holding it very lightly with my finger. So, the moment I release it, it starts rolling, and that's our second run. Okay, so second run, T transit, VI, the initial, and VF final. Okay, now round number three. Okay, so this is round number three out of five. T transit for round number three, V initial, and V5. Okay, accidentally turn it off. All right, uh, and then number four. Well, actually, I can activate this now. Okay, so round number four, then. All right, round number four, T transit, the initial velocity VI, and the VF. Now, as you can see, there's a great, uh, field of consistency in these, uh, measurements, trial to trial, and this is what we are expecting to, uh, see, right? If we're performing this in identical conditions, we expect to see, um, identical or very close measurement results. So, this is an indication that we're doing it right, essentially, and then there's no source of consistent error that is affecting our results, okay? Right, and then the last, uh, run, I believe that, uh, we need to do. Round number five. Okay, so for round number five, the transit time is this, the initial velocity of the cart in the first gate for round number five, and then the final as well. Okay.
So, essentially, what we have done, we have, we did five runs of the cart, uh, through these two photogates and measured the, the timer has measured the time events and then converted into velocities for us using the length of this, uh, object that we provided, entered it into its memory. So, now we have five velocities, five, uh, or five sets of numbers, essentially. Uh, the handout explains, uh, then how you reduce that to just, uh, one number in each group. So, you'll need to calculate the average transit time, average initial velocity, and any average final. So, you can operate with just that. If you don't have to do five calculations every single time you are, you know, answering any of those questions. Now, you may, you may notice that we're not calculating the, um, percent variation this time. You know, it was more of an exercise in the first lab. This lab, and I think the few, uh, labs down the road, will just use our best judgment. We'll look at the results and see if they agree, if those trials agree with each other or not, to our best judgment. And then, if any trials are clearly outliers, uh, then it will just drop those, you know, and assume that something had happened during the experiment that may have affected our measurements. So, it looks like we have, you know, a great deal of consistency there between the trials, so our data looks good, I think. But, you know, you'll be the judge. So, you know, if something's not looking good to you, you can always drop that, but then always explain why you did that, right? We don't just drop, uh, experiment cell runs randomly just because. Okay.
So, I think the rest of it is explained, uh, in the handout, the calculations and so on. And Kerry may, um, again, spend some time, uh, on that as well. So, I'm gonna talk about that. So, if you have any questions about the experiment, uh, I'm available for the next couple of minutes. And then after that, there's, there will be a video, so you may watch it, uh, later on if you missed parts of this. But, uh, yeah, thank you so much for joining us, uh, this morning for this lab. And, uh, Gary, I'll turn off the camera so you can share your whiteboard.