Basic Physics Lecture 23
This is a modal window.
Das Video konnte nicht geladen werden, da entweder ein Server- oder Netzwerkfehler auftrat oder das Format nicht unterstützt wird.
Formale Metadaten
| Titel |
| |
| Autor | ||
| Lizenz | CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben. | |
| Identifikatoren | 10.5446/12934 (DOI) | |
| Herausgeber | ||
| Erscheinungsjahr | ||
| Sprache |
00:00
Optische WeglängeMessungDonnerstagDimmerComte AC-4 GentlemanSchusswaffeAnalemmaMagnetresonanzmikroskopieIonLoggerPulsphasenmodulationÜberschallstaustrahltriebwerkLHCMinuteTinteInterplanetares MagnetfeldVega <Raumsonde>MontagMittwochGleichstromTeilchenStandardzelleImpulsübertragungFahrgeschwindigkeitSchubvektorsteuerungPfadfinder <Flugzeug>DruckkraftAkustische OberflächenwelleTagBuntheitSchaft <Werkzeug>Vorlesung/Konferenz
03:37
WeltraumAntiteilchenGyroskopDonnerstagBergmannGasturbineGeneratorGleichstromLichtSiebdruckTeilchenWarmumformenTakelageUnterwasserfahrzeugSchieneAngeregter ZustandBeschleunigungErsatzteilFaraday-EffektMasse <Physik>PassatPatrone <Munition>SchiffstechnikAbstandsmessungFront <Meteorologie>FahrgeschwindigkeitSteckverbinderInitiator <Steuerungstechnik>TagColourSatzspiegelNanotechnologieCocktailparty-EffektDruckkraftGammaquantSchraubendreherDreidimensionale IntegrationPfadfinder <Flugzeug>Computeranimation
10:25
WeltraumKraftwagenMikrowellenlandesystemElektronen-EnergieverlustspektroskopieTakelageAntiteilchenEisenbahnwagenElektronisches BauelementElementarteilchenphysikGleichstromVideotechnikSatz <Drucktechnik>WarmumformenWasserdampfReglerAbwrackwerftBeschleunigungErsatzteilImpulsübertragungMasse <Physik>RauschzahlSummerAbstandsmessungFahrgeschwindigkeitSchubvektorsteuerungErdefunkstelleSchiffsklassifikationDruckkraftGasballonFACTS-AnlageDrechselnMessungSchmiedSchieneAngeregter ZustandDunkelheitElektronenbeugungSpeckle-InterferometrieWeißLagenholzInitiator <Steuerungstechnik>TagGewichtsstückHadronenjetKofferNanotechnologiePagerKardierenSchaft <Werkzeug>RaumkapselClosed Loop IdentificationComputeranimation
17:12
ImpulsübertragungLenkradKnicklenkungBremswirkungDruckkraftAirbagMasse <Physik>BlechdoseIonGewichtsstückAtmosphäreArmbanduhrEisenbahnwagenElektronisches BauelementGeneratorGleichstromLichtSatz <Drucktechnik>WarmumformenAbtriebswelleAmperemeterFeilenImpulsübertragungMasse <Physik>MolekularstrahlepitaxiePatrone <Munition>RauschzahlWeißAbstandsmessungBremswirkungFahrgeschwindigkeitInitiator <Steuerungstechnik>LenkradUrkilogrammKofferDruckkraftKalenderjahrReaktionsprinzipFACTS-AnlageEisenkernSchaltuhrSeitenairbagStundeEnergiesparmodusElektrisches SignalScheinbare HelligkeitAirbagKoerzitivfeldstärkeComputeranimation
23:21
KugelschreiberStapellaufAnstellwinkelProjektil <Physik>Satz <Drucktechnik>Elektronen-EnergieverlustspektroskopieStehwellenverhältnisLeitungstheorieWeltraumSägemaschineOptischer HalbleiterverstärkerAtmosphäreElektronisches BauelementGleichstromMessungVeränderlicher SternSatz <Drucktechnik>WarmumformenAmperemeterBehälterbauBeschleunigungErsatzteilFaraday-EffektImpulsübertragungMasse <Physik>MultiplizitätPatrone <Munition>Projektil <Physik>RauschzahlStapellaufA6M Zero-SenZylinderkopfFahrgeschwindigkeitScheinbare HelligkeitUrkilogrammTagGewichtsstückGleiskettePassfederSchubvektorsteuerungKanoneErdefunkstellePfadfinder <Flugzeug>WocheTrajektorie <Meteorologie>FACTS-AnlageHubraumMinuteProof <Graphische Technik>Closed Loop IdentificationGasGlasProjektionsapparatRaumfahrtRegenVW-Golf GTIStörgrößeRegelstreckeKartonSchalttransistorFunkgerätBootAngeregter ZustandChannelingFeilenSchiffstechnikWasserwiderstandInitiator <Steuerungstechnik>RegenschirmDrahtbondenMontagProzessleittechnikBlei-209EnergielückeSturmgewehrLinealCHAMP <Satellitenmission>KalenderjahrKommandobrückeKugelschreiberChirpMessschieberGreiffingerNyquist-KriteriumRömischer KalenderWindroseRinggeflechtComputeranimation
Transkript: Englisch(automatisch erzeugt)
00:08
We'll go ahead and get started. So we have one more chapter that we're covering, chapter nine. We'll do that today, Friday, Monday, Wednesday will be largely a review in preparation for
00:23
both the final exam and the exam. So here's the last online quiz. Now the section we're entering is 90% review. Most of what we do in chapter nine, we've done already. We just give it a new name.
00:42
The 10% that's new is dealing with momentum conservation, so we'll come up with that. But impulse is really just forces, only we multiply them by delta t, and they're still forces. So this was very interesting to see because, for instance, question number two is basically,
01:04
since an impulse is forced, in any collision, this is key, right? In any collision, the collision, there's just a single collision. It has to last the same amount of time, can't be different. And we already know Newton's third law, which you learned for the last test, tells you
01:22
what about the forces involved in two objects colliding? They are equal and opposite. So they have to feel the same impulse, right? The same, one can't be larger or smaller. And it doesn't matter how long the collision is because it's the same for both of them,
01:40
but that was good. Most people did not answer that. So this is really just a Newton's third law question. So it was mainly review, and you need to go back and do that. The formula ones, people are very good with momentum, particle doubles its speed, what happens to momentum, good. This one, most people got it, but keep in mind, right, if I'm going this way, and
02:03
I'm going to end up stopped and going that way, my velocity changed in that direction. The force is a vector in the direction of your change in velocity. Again, same concept we've had before, impulse is just force times delta t. Everything we learned about forces applies.
02:22
So since I turned around, my force is in that opposite direction. It's not in the direction I was originally moving. So that question, number four and two, caused the most trouble. And those really were just forces. This one, not so bad, but a few of you got tricked by the as the particle stops phrase,
02:40
I have a feeling. To stop, I have to have a change in velocity, I have to go from moving to stop. I can only change my velocity if I have a force. And if I have a force, I have an impulse, because impulse is force times delta t. So there has to be an impulse on me. And again, it's opposite the direction I was moving, because it's stopping me.
03:03
So you want to go back and just double check those if they caused you problems. Which direction was the impulse there? So there wasn't a whole lot in the comments this time around. Some of the standard ones, I'm not really going to go over that today. But the big one here is number two and number four really were review.
03:23
And so you need to go back and make sure you understand why that was a review. Any questions? What we're really doing, as I said, is we're really starting and looking at
03:47
how do we deal with F equals ma in different situations. Now, this equation, which we looked at at the beginning, and I can be a little more careful. I can write acceleration by its definition as dv dt.
04:03
And that's something during the next few days, Wednesday, Friday, next week, you want to pay close attention, because so many of the concepts we've done get reviewed in this chapter. It's very helpful. The key thing about this is this is about a single instance in time.
04:26
Or, we do apply it sometimes when we talk about the average, where we've averaged it over time. But it's kind of comparing a single thing.
04:43
We looked at a case where the force acted over some distance, and we realized we had a new concept that we defined called work, and this dealt with a force over a distance,
05:04
and we had kind of an initial state and a final state. And we noticed, if you recall in doing this for just a single particle, that this was related to the change in kinetic energy.
05:24
I don't know why I put a K there. This was our change in kinetic energy, and it had a close connection to our kinematics formula
05:46
because of our connection to F equals ma. So this was, okay, we take our force, only the force in the direction of motion matters, we're not going to worry about changes in direction,
06:01
we're just going to see what happens to our speed between two different locations in space. Well, if I look back at our original F equals ma, it would also be nice to say, well, what if we have an initial and final force in time?
06:23
And that's what this section is about. We now take J, we give it a name, we call it the impulse, and we're going to ask, what if a force acts between two times t1 and t2? This is much easier because we saw, right,
06:48
that Newton's second law allows us to write the force in terms of the derivative of the velocity. So what, we've already said integrals are areas under curves, we said integrals allow you to sum little pieces,
07:01
there's one other meaning of the integral. The integral is the opposite of what? The derivative, it's the anti-derivative, right? So if you take the derivative of t squared, you get what? 2t. If I integrate 2t, I get what? t squared, right?
07:22
So if I integrate the derivative, I get the thing I'm taking the derivative of, so I just get the velocity. So we see, if we're asking about a force acting over time,
07:42
the thing that's relevant is just the change in velocity, v final minus v initial, because when I integrate the derivative of velocity, I just get the velocity. Well, I can make this even more general
08:00
and consider cases where the mass might change and it's the change of the product and that is why we define this nice new quantity called the momentum, which you all used and calculated well in the quiz. And so that's really the big picture situation we're in right now
08:20
and I can get most of it on the screen. We introduced the idea of Newton's law, F equals ma, and we asked about it at single instances or for average forces and then we realized, well, sometimes the force will act over some distance and we asked what does it do when it acts over a distance
08:41
and that's related to changes in energy and that's work and then we said, oh, well what about if it acts over a time and that's just impulse which is our change in momentum. So we have two new definitions we have to remember what momentum is and what impulse is
09:02
and then just like we have the work kinetic energy theorem we have the impulse momentum relation. So this is an impulse causes a change in momentum.
09:24
So it's really important to keep in mind what are our three equations we have that are about causes, that are not definitions, they're causes. We have three now. Can anyone name them? F equals ma, forces cause accelerations.
09:41
Number two. I think I heard it over here somewhere. Work does what? Causes a change in energy and now our third and final one this is the easy one, it's like right here in front of you. Impulse causes change in momentum.
10:02
Those are the three big concepts in the course. The big three. Notice if there is no impulse what would you say about momentum? It is what? Conserved because it does not change. Delta p is zero, that's what we mean by conserved. If there is no work, what can you say about energy?
10:23
It is conserved and if there is no net force, what can you say about the velocity? It's conserved, we use the word constant for velocity we just change it a little bit. So those are the three big ideas. Kinematics is all about describing motion
10:42
and if you happen to have constant acceleration it's describing it with some simple equations. If not, you use the definitions. Velocity is dx dt, acceleration is dv dt. For energy, you have to remember in this particular class how many different types of energy?
11:01
Four. Kinetic, potential energy of gravity, potential energy of the spring and then the internal or dissipated energy due to friction. And how many types of momentum are there? One. Just momentum. That's it. I've just summarized the class in two minutes. This part of the video you want to go back to over and over.
11:25
Now, the only real problem with this notice is that we are back to vectors so we do have to worry about direction and components so just be aware of that.
11:41
So let's go with clicker question number one. I really should have brought some water balloons to throw. That would have been appropriate
12:01
because eggs are a bit messy but you're trying to catch a raw egg it is a good idea to increase the time it takes to catch the egg decrease the time it takes to catch the egg the time is irrelevant. Apparently all the people with the wrong answer were sitting next to each other. It actually is you want to increase the time.
12:21
How many of you have ever been in an egg toss contest? Or a water balloon toss contest? Do you catch the water balloon like this? Or do you catch it like this, gently? Increasing the time at which you catch the water balloon as if somebody threw you a baby. Please don't do that.
12:40
Now, this is one of those times where the formula makes it very obvious. Our change in momentum is our impulse which is our integral of f times dt. Now, one of the things that's very common
13:01
the force will vary a lot during the interaction. When you first start to catch it the force increases then it decreases at the end. So there will be some graph and this is basically the area under the force-time curve.
13:21
The other thing it turns out to be which is more useful in a lot of the applications we do is the average force just times the total time of the interaction. And that's giving us our mass times our change in velocity. And the piece I think that is most often overlooked
13:44
and I refer you to Spiderman Tech you can find it on YouTube where Professor Denham discusses the situation in which Spiderman is trying to save Gwen Stacy and breaks her neck versus saving whoever he saves.
14:02
Aunt May I think is the example that's used where he does it correctly and does not break her neck. It's a very exciting video. And it serves as a good advertisement for that course Physics 12 that you should tell your friends about in the summer summer session one to sign up for.
14:21
Yeah, how is that for shameless advertising? But if you notice your mass doesn't change. That's usually set. And in fact in most collisions this is set, right? Because v final is generally zero. That's not an option. And v initial is whatever it is, right?
14:45
You come in with some initial velocity and we're going to try and stop you. What you control and this is the piece that people don't realize at first what you control are these two.
15:01
And the point of this and what Newton's Law tells us is if I can make this as long as possible then this gets as small as possible. And in a given collision
15:21
or given interaction the amount of damage that happens to the object is related to the force. It's not related to the total impulse. So this is a place where we can take advantage of the physics to minimize damage by minimizing the instantaneous force at any given point.
15:41
Because most objects break not due to some average force applied to them but due to how big the maximum force gets to be. And if you make the time longer the average force goes down and then the maximum force at any point goes down. And so it really helps. This is a lot like when we took advantage of doing work
16:00
where we lifted the object up the ramp. We used a longer distance so we did the same amount of work but we got to use a smaller force which from our muscle point of view is really where all the energy and effort comes from. Any questions on that? I won't ask the question because it does tend to reveal more about your psychology
16:22
than your knowledge of physics but I would often follow this up with as you're skateboarding down a hill out of control would you rather run into a brick wall or a haystack to stop? I find when I ask that question I get about 50-50 split. Go figure.
16:41
But another question to think about that's a little more serious and we'll maybe come back to it is would you rather have a car that in a collision doesn't break or a car that in a collision shatters like modern cars do with their crash zones? So think about that one as we go into our first example problem.
17:01
Any questions before we do that? By the way, all the remaining problems that will happen in lecture are now posted on the web. So there's that. We increase the time it takes to catch the egg. So here's our example. You're driving your car 27 meters per second.
17:22
You slam on the brakes and you hit the steering wheel. And the collision takes, because you're hitting the steering wheel, it's hard object. It stops you pretty quickly. It takes five milliseconds. Now, we want to compare that average force to what happens when you slam on the brakes.
17:41
Your airbag deploys and because it's a nice soft cushiony object it takes you half a second to stop. So that's what we want to do. And we know your mass is 80 kilograms. Notice some key words to start looking for.
18:02
We have a collision. Now, in this case, we're given the time. What you will find, collisions will tend to make you think very strongly of momentum and impulse.
18:20
There will be times where it's actually energy that you'll be thinking about and the real signal of the difference is often whether or not time is involved. Time is fundamentally pointing you to the fact that we're going to use momentum and impulse, whereas distances would tell you
18:42
that we're looking at work and energy. Those are kind of the key words. We're given our mass. We're given our velocity. So momentum is pretty much set. This is what I would call the basic core momentum-impulse problem. This is the little nugget that will show up in a much bigger problem
19:01
that you really want to be good at and recognizing when it shows up in a bigger problem. And what you want to know the difference between is whether you're being asked for impulse or a force. Because if you're being asked for the impulse, you won't need the time, usually. If you're being asked for the force,
19:21
you'll generally need the time of the collision or you won't be able to figure out the force. So that's kind of the differences here. Here we're being asked for the average force and luckily we have the two times. So that's kind of our first reaction to reading the problem. Any questions on that?
19:44
So let's look at it. Like I said, it's fairly straightforward. Just like with energy conservation, as soon as you have any collision or explosion or interaction and you're looking at a change in momentum,
20:04
remember that's final minus initial. Two decisions. One is do I need components and two, let's make a table of the initial and final.
20:20
Now in this case, we're just moving in a single direction so we'll make the right positive and we'll make that the direction you're driving. So yes, I'm doing components, but I don't need x and y, I just need the one and I can work with minus signs from there. So now I have my final and my initial
20:42
and I'm looking at just the momentum of my car. The final is zero because I'm stopped. The initial is a positive 27 meters per second times my 80 kilograms. So that's just my mv or vm in this case.
21:00
So my delta p and notice this is what caused people some issues on the quiz. Since that's zero, my delta p is a minus 2160 kilograms meters per second. So, delta p is that way.
21:24
And so my impulse is to the left and I believe I asked for the magnitude of the force, but if I was asking for the direction and I was traveling to the right, the direction of the force is to the left, which it must be to stop me. Now, if I was hitting a wall and I was asking for the direction of the force on the wall
21:42
due to the collision, then I get to use Newton's third law. I almost always compute the force on the object that is obviously doing the moving, in this case the car, and then when I want to know the force on the wall, I have to use the third law and use the fact that it's equal and opposite and switch it. So we'll see that in some of the problems. So you want to watch for that.
22:04
Now, I need to turn this into a force and we were given two situations, right? So J, which is delta p, we know is f average delta t. So f average is just delta p over delta t.
22:23
And in the one case where I hit the steering wheel, it's 432,000 Newtons. And when I hit, so that's the steering wheel and that's the airbag. Because remember, in one case delta t was 0.005 seconds
22:44
and in the other case it was 0.5 seconds. And so that's the difference between the two. So a huge difference in the force from hitting the airbag instead of the steering wheel and that's why we have the airbags.
23:01
Any questions on that kind of most basic of problems? So now we get to move right on
23:21
to problem number two. And this is where things start to get more fun. And you can see, hopefully you'll start to see like we had last week, a projectile motion with a conservation of energy problem. Here we're going to have a projectile motion
23:41
with a momentum impulse. Next week in discussion section, we will add, you'll get to do a problem that has conservation of energy followed by projectile motion, followed by collision, followed by conservation of energy again. It'll be a lovely four-part problem. But you'll have a lot of time to do it. So here, what I would like you to take a minute to do,
24:07
okay, is think about the physics in this problem because we're going to answer it in this way. So talk to the person next to you. I'll start the clicker question.
24:24
So remember, we're going to launch a cannon and it's going to hit a castle wall. Okay, now what I want to do,
24:42
that's excellent, so most people went with more than one. So let's try and refine it a little bit. Let's do it this way. Two types from the list, three or four.
25:05
So vote on that. You went more than one. Do you see two here that are relevant, three that are relevant, or four? So now, this is interesting. Most people went with two or three. So given that you went with two or three,
25:22
which is the one that's definitely not in this problem? Circular motion. What is in this problem that's definitely here no matter what you pick, whether you pick two or three? Projectile motion because it's flying through the air. Why is it so critical to distinguish between
25:42
projectile motion and circular motion? Everybody's part of it, but what's the fundamental physics difference between the two? And what about the acceleration?
26:01
More than the specific type. What type of acceleration occurs in projectile motion? Constant. That's the key. Gravity is the cause of it, but the key factor is it's constant acceleration. Is circular motion constant acceleration? No.
26:21
And in fact, there is a radial component to the acceleration that's always v squared over r that you immediately know. That's changing in direction all the time. And that's why it is so important in these physics problems to recognize the types of motion. Because once you know the types of motion, it gives you a large step forward
26:42
in figuring out what equations you'll use to solve it. That is so key. Now, I think the reason we split between two or three is whether or not you thought both of these were in the problem or only one. Now, it turns out both are in the problem. We launch the thing with an explosion
27:00
and it hits the wall, which is a collision. But the problem is only asking you about the initial explosion, right? So depending on how you were thinking about, this is why I don't ask these sort of multiple choice questions on the test, but you want to be aware of that. When you look at this problem, oh wait, actually, I didn't want to stop it,
27:21
but I'll just go here. When you look at this problem, you might think about, okay, I've got to worry about what happens when I hit the wall, but I'm talking about the impulse on the cannon when it was fired. So I probably don't have to worry about the fact that it hits the wall because I'm going to be using the projectile motion in some sense to figure out something
27:42
about the initial state. Now, it could be a problem. Suppose I asked you for the impulse on the wall, right? Then you might need both stuff about the initial launch and the hitting the wall. That's more likely to need both because to get the final velocity that you hit the wall with,
28:01
you might need to know the initial velocity you were launched with. And so it can be, when you're hitting the wall, you may need more of it than when you're being launched. That's just the way these problems often work. Does that kind of make sense? A little bit? A few people nodded, good. I got five of you to understand.
28:21
So let's look at this problem. Always a good idea to sketch it. And actually, on Friday and Monday, we'll be firing bullets and launching things out of cannons. So those are kind of the interesting days. Today we just get to solve a problem. But, you know, it's Wednesday, it's the middle of the week. It's kind of the boring day.
28:41
So it gets launched, and here becomes a notation issue, right? From a kinematics point of view, I have some initial velocity. I'm going to fly in the air, and I'm going to land five meters up, and I'm going to land 200 meters away.
29:01
That's how I would draw the kinematics problem. Now, from the cannon point of view and launching, if I was to make a table of final and initial, and I'm going to look at momentum now,
29:21
what is my initial momentum in the cannon? Zero. Why is it zero? I haven't fired, I'm just sitting there in the cannon. And that is a key piece to recognize. Almost never do we tell you
29:41
it was not moving before it was fired. It was not moving after it hit the wall and stopped. That's the piece you have to recognize from knowing how the real world works. So here, the initial is zero. Using the variables in my picture, what's the final momentum of the cannonball?
30:03
So this is what's happening in the cannon. And we're looking at the momentum of the cannonball. So what is it? V naught times, not the weight, mass.
30:21
We've got to be careful because the weight is mg. That will give you an extra g, you don't want that. So the final is mv naught. Now, I could have called this v, I could have called it v launch, v sub l. There's lots of different ways you can label it. But you want to be aware that as you do these more complicated problems, there's always a connecting step.
30:45
That's what you want to look for. Where a variable goes from one part of the problem to the next. In this case, it is v naught as our connecting variable. And that's a very helpful way to think
31:06
of these more complicated problems, is to ask yourself right at the beginning, what connects the different pieces of the motion together? Now, in this case, I do have to be a little bit careful, right?
31:23
Because I do have a what going on? V naught has what? Direct, remember, it's a vector, right? So it's a villain with both magnitude and direction.
31:44
Remember your Despicable Me. If you haven't watched it yet, it's very important as part of your studying to go watch that for just that little section on vectors. So we do have to keep track of the direction. Because our original question is what's the impulse?
32:09
The impulse has direction. If you don't include the direction in your answer, you will get it wrong. Now, this is a nice one, because we already know the direction
32:20
right from the beginning, right? We were told it's being launched at 30 degrees. So that's my 30 degrees. So the direction is 30 degrees up from horizontal. So what I see here is since impulse
32:46
by my impulse momentum relation equals change in momentum is just m v naught minus zero It'll just be m v naught, which will have a magnitude of mass times v naught
33:01
and it'll be 30 degrees up from the horizontal. So all I need to do is find v naught and I'm done with the problem. And notice this piece of it was exactly like that first warm-up problem I did. So as we move to these more complicated problems, the key is to remember all the little pieces of problems
33:21
you've done for single types of motion and then just put them together. Now, how do I find v naught then? So again, here's our picture. What I want you to do now,
33:41
take three minutes, find v naught for me. See if you can find v naught in two minutes or less. So just out of curiosity,
34:02
has anyone drawn something that looks a little bit like this yet? Just a thought that might help you.
34:23
Another option of course is to go right to components. What are our two relevant equations for this? No, just our general equations. Delta x equals what?
34:53
Excellent! T squared. I love it. And the other one? v final v naught plus a t.
35:08
Be more general, right? So this equation I represent graphically by that. Now, this is a case where you might have thought, oh, we just wrote it down today, so I remember this one.
35:25
But notice, does this really help you? Not in this case, because remember, it's telling you just about limited components here. So you would be able to figure out
35:40
possibly the y component because the acceleration is in the same direction as the y displacement. But it wouldn't really tell you anything about the x component velocity, which you need. So you might think this one, but do we know anything about v final? No, we just know it hits the wall.
36:01
So this equation, we can see, v naught's unknown, t is unknown, but that's only two unknowns. And if I have two unknowns in my triangle, I can always get two equations out. Coming back to you now, slowly, right?
36:25
So what two equations might I do for this one? You know, it depends on kind of where you're interested in stuff. I would probably try and get the time right away from tangent 30 is one half g t squared plus five meters over 200 meters
36:45
because now when I solve that, I will get t squared equals 200 times tangent 30 minus my five meters divided by g times two,
37:01
which will give me a time of 4.7 seconds. And then the cosine of 30 is 200 over v naught t, which tells me v naught is my 200 over cosine 30 times t, or 246, wait, no, sorry,
37:26
49 meters per second. And now I take that and I plug back into here, and I get my final answer that my impulse is
37:43
245.7 kilograms meters per second, or you can also use the units newtons times a second, either one works, and 30 degrees up from the horizontal. And this is the impulse
38:01
on the cannonball. So before I ask some few final questions, any questions on that? And notice, you do have to really remember your kinematics. Tomorrow in the discussion section, you will have a slightly different variation on this,
38:23
where you also do some kinematics with an impulse, just to practice it. But any questions on this before I ask you my questions? Okay, now, let's suppose I want you to think about this problem, do the same problem now in your head
38:41
if I asked you for the impulse on the cannon itself. What is the impulse on the cannon during this process? We found the impulse on the cannonball, what is the impulse on the cannon? Anyone tell me?
39:03
Okay, so it's 245.7 kilograms meters per second, 30 degrees down. Okay, we actually have to be careful depending on how you define down. 30 degrees up from the horizontal is kind of 60 degrees down from the horizontal, right, because it's back to the left
39:21
and we make our 90 degrees. Oh, no, no, it is 30, sorry, 30 degrees down and back to the left. It is 30 degrees down. You have to be careful, talk right and left. Now, let me ask you this, one final one before you go. What if I asked you for the impulse on the castle wall?
39:41
What is the impulse on the castle wall going to be? What do we have to do? Now we have to find v final, right? The impulse on the castle wall we hit with v final, right, and delta p, now,
40:02
delta p on the cannonball, this is the initial velocity at this point, yes. No, here's the trick. You might think you need to know the mass of the wall, but what you do is you find the impulse on the cannonball again.
40:22
And then it's the equal and opposite. The impulse on the wall is the equal and opposite. So that, notice, that's why I pointed it out. There's usually one object in the problem that it's easy to compute the impulse on. Often, we ask you for the impulse on the object it hits,
40:42
where you won't know that other objects mass. You won't know that other's object initial or final velocity. And it's all computed by using Newton's third law. And this is problems where the third law becomes critical. Any questions? I guess we're done.