 So, check on that, uh, let's see, here's the one with the first test, I don't know, I've read it the last one, let's try to take points off, rather than add points, those two would benefit by loop up. Check to make sure the points total to right, is it entered on Angel the right way? Solutions there. Alright, any questions or comments before we start the new section now? We're doing very much the same general pattern that we did in Physics 1. We started in Physics 1 with the kinematics, particularly of particles. We're going to continue with particles, particle motion, but now we're going to do the kinetics, but still of particles, so we're not worried so much yet with the size of things. There might be a problem that could come up where certain dimensions apply, but in general, what we're concerned with is whatever it is we're working with is represented by a single point. If you wish you can look at that as the center of gravity or something, in fact that may even help when we get to, uh, when we finish up the particle motion and start looking again at the rigid body motion. But that's the type of thing we're going to look at now. Kinematics, if you remember, in general, we really only dealt with four things. What were they? There's four, we've done four weeks already, only dealt with four things. That's one thing a week, that's all you had to remember. One thing a week, that's all I asked. Pat, I asked more of Pat, but he can deliver. What were the four things we've been working on so far? Nothing else, just those four things. Time and velocity, acceleration, and position. Yeah, I'm not one of your favorite students. Position, velocity, acceleration, and the time during which those things occur. That's all we've been looking at. Well, they've been variation, but most of those variations really were just different coordinate systems and different changes like that. So now we're going to look at how we affect those changes. And for the most part, you'll recognize it as Newton's first law. Simply put, that when we have unbalanced forces, that will cause masses to accelerate. Basically these problems are either we have an acceleration we want, so we try to figure out what forces will give us that, or we have forces that are already given, and we want to see what is the resultant acceleration from that. We'll do two other methods just like we did in physics one. This is our first method of solving kinetic problems. Two others will come directly from that if you remember from physics one. At least those of you who had it with me and we certainly did this. We'll also look at the work energy method and the impulse momentum method. But for now our working equation will be, you can do it in whatever form you prefer. I don't care. They all mean the same. They all carry the very simple idea that we need to take into account all of the forces acting on an object. Well, let me refine that a little bit. It's all pertinent forces. There will be some and some problems that just aren't important to us. For example, if we're pushing something along a level frictionless track, then the force of gravity really doesn't come into the problem. It's a force on the object. It's just not a pertinent force in that problem. And so we don't need to concern ourselves with it. So this is our vector representation first law. Actually, I guess technically Newton's first law is that which we use in statics. So I don't see him as different laws anyway, but everybody else does. So we'll play their little game. The second law is actually one that says acceleration. The first law is the one that says if those forces sum to zero, then there will be no acceleration. That's the one we're using in statics and mechanics and materials. In this class though, we're concerned with the possibility that things will accelerate. In fact, there will always be some acceleration in all of our problems here. It doesn't mean that this doesn't apply because we also have the realization that at any time we can have acceleration in one direction, but not in others. And then we have Newton's second law applying in one direction, but not Newton's first law applying in another, if any one of those are zero. So that's a scalar representation then, if you will, of Newton's second law. Newton's second law to the minus one. I guess this isn't two to the minus one, so I ought to put the whole thing there. Newton's second law, the inverse of Newton's second law is essentially that the mass of an object can be defined by the forces applied to it and its resultant acceleration. And in fact, that's just how mass is defined, particularly well in the SI system, particularly badly in the English system. Let's see what that means to us right now. We've got to get the forces right in this class, in this section of the classes. If we don't have the forces right, we're not doing the right problem. So one of the forces we have to get right, and luckily isn't too terribly difficult, is that force that we call weight. It's the force of gravity acting on a mass. So a couple things we have to worry about. One, in this class, and I don't remember anybody doing this wrong in Physics One with me, but I have some guys here. I didn't have Physics One. So let me remind you that this force is down. It sounds kind of obvious. However, I know there are lots of well-meaning high school physics teachers. Old students, if you have a problem on an incline, transfer that problem to a non-incline problem and just incline the force of gravity. Anybody have that for physics, high school physics? You wouldn't admit it now, anyway. It is. It's ridiculous. For one, it really hasn't changed the problem any, but there's a lot of... Your high school teacher did it? I don't know that you can move the earth over to the side without permission. I think you at least have to clear that with some higher beings. Good. I'm glad we won't see that in... When I taught this class to about 100 at RPI, maybe 10 or 15 did that way. That high school teacher that had him do it that way. They meant well, but it's just... I don't see what it accomplished other than be fuddling the reality of it. And we hate to have reality be fuddled. In the SI system, this is all real easy because we have previously defined our unit of mass, have previously measured the gravitational field strength. A couple of you are taking physics three, right? Talked about field strength yet. Electrostatic fields and the like. This is exactly the same type of thing. That's really what G is. It's a measure of the gravitational field strength. Just like you talked about is the electrostatic and we'll talk about the magnetic field strength. Then this is defined then as the unit of force, of course is one new. Remember the convention is if a unit is spelled out, which it almost never is, it's not capitalized. If it's abbreviated and it's someone's name, it's always capitalized. There are probably a few exceptions, but none leak to mind. So the easiest thing to do is just do it. But this is actually the definition of a Newton. And just to prove that the universe has poetry to it, what's something that weighs about a Newton? I know my physics one guys know. Do you other, your newbies know? Something that just as a common everyday household object weighs about a Newton. Just so you know about what it is. Huh? A thing? A thing. That's too much poetry in the universe. Yeah, it's about an apple. It's about the weight of an apple, depending upon the size of the apple and light. But it's about that. And of course that is the dropping out apple that twig Newton onto what was going on with Bradley back in the 1600s. So that's pretty easy. We just now have essentially what's a conversion factor that one Newton equals, actually, sorry, this isn't one Newton. How come nobody was paying attention? You expect me to? This is 9.8 Newtons. Because we define one Newton as one kilogram meter per second squared. Didn't anybody catch that? Jake, you just out thought it. So we have that definition of a Newton. I was getting messed up here because in the English system, it's a horrible mess, leading to what is probably one of the silliest units ever devised. This was okay. This all worked so nicely because the mass was defined first. The meter and the second were all defined independently and then everything else was defined from there. That's not the way it was done in the English system. In the English system, we still use w equals mg, but the things were defined differently. The things that go with it are defined differently. For example, the unit of force is known as the pound. When we colloquially use the word pound, that's generally what we mean. But if you'll notice, there's a little subscript f on there because independently defined in the English system is the pound mass. A pound force acting on a pound mass causes it to accelerate with an acceleration of 32.2 meters per second squared. Meters per second? No, not meters, feet. Now you're awake. There's also a unit of mass called the slug. That's the amount of mass when accelerated at one foot per second squared requires 32.2 pounds of force to do that. You can just see the awesome beauty of any system that requires a unit called the slug. Quite obviously, I hope, one pound mass is one over 32.2 slugs. Here's what I'd do if I were you with the English system. It almost always works out. There's a few times where in a problem what you're given requires you to make a convergent. But generally, this is what I would do if I were you. Say that we want to find the mass of an object that has a weight of 40 pounds. Just as an example of how we do this. We'll make it simple in that anytime you see pounds we'll take that to be a force in this class. And that's generally the way it's taken in engineering as well. So if we want to find out what the mass of 40 pounds is and we're wondering, gosh, do we do pounds mass? Do we do slugs? My advice is do neither. Just make the conversion. In this case, I use the example of 40 pounds. We know the general gravitational field strength to be 32.2 feet per second squared. That comes out to be what? About 1.24. Then without worrying about whether this is pounds mass or slugs, just leave it like this. And use that as your units for mass because 9 times out of 10 or even more, 95 out of 100, once you've found the mass, you've got to go through the rest of the problem and the units will just work out anyway. You'll go right back into the acceleration or force or whatever it is you're looking at the problem. So that's my advice. Just leave it like that and use that as our units of mass. Don't convert to slugs. Don't forget the pound. Just forget it. Why is it pound second to squared over feet? Is that supposed to be the actual unit of mass? No, it's not an actual unit of mass. These are actual units of mass and these are stupid. This isn't stupid because everything it needs right there, you don't have to make a conversion when you go into a problem but now you have to take that mass and accelerate it when you put those units in there put this in for mass the units work out perfectly and you're fine. If you do this, you're on the risk of converting wrong, getting confused. I don't know. You can do that if you want. I won't count it wrong This I found you just don't get wrong. I found students when they try to think whether they're supposed to be in pound mass or slugs, whichever they make mistakes as often as not. When you do it this way, just leave it like that and then it comes right back out. Two seconds later, you're fine. You don't really need to know, I guess, but is it slugs or...? That's my point. Who cares? One point two four right? It's pounds, seconds squared per foot and then you don't have to worry. You say slugs, you say pounds of mass and then you roll out in the hallway having a fist fight over that. It's not worth it having a fist fight over something important. Leave it like that. Forget this stuff and you'll be fine. That's my advice. I'm just trying to make it easier for you. You don't like easy? Do slugs and pound mass. Slugs and pound mass are very, very rare even in industry. Barely used. The law is that the mass and the force were defined independently in the English system where in the SI system mass was defined first and the force was defined from that. That's my advice. I'm your advisor. This is a reminder of the types of forces we're going to be working with. Applied forces. Those are the ones that show up in a problem as pushes, thrusts. Anything where something outside of the object is acting upon the object. Also of course, poles because you can push an object as easily as you can pull on it. Remember though that in general, strings, tables, games, ropes, basically anything you'd find in your bedroom. There are forces only away from the object. They only can pull. You can't push anything with a rope. You're welcome to try for extra credit and they only pull along their own length. That's good for us because it means of two possible unknowns in a problem involving a pole, one of the unknowns is already figured out. The angle and the direction are figured out. All you'd have to figure out then is the magnitude. Let's take care of the units that go with it. So that's good. All you have to worry about with poles is the magnitude. Pushes could be different. Pushes, we might have to figure out both the magnitude and the direction. We also have normal forces. Those are the forces exerted by inert objects as our object is being forced upon it. The other example is if we have some object sitting on a table and doing nothing else, we know that there must be a force opposing that. Otherwise it would accelerate down. That force we call the normal force and it's actually the resistance of the material itself to this object trying to come through it. It's the molecular forces pushing back on the object. A couple things to remember. Don't forget them. And it's easy to do. This is a contact force. If you don't have two surfaces in contact you don't have a normal force. A lot of times odd students in a problem will put in something and say that's the normal force but there's nothing else in contact and they have an account of four in some other way whether it's a pusher or a string or something. It's only a contact with some other object. It's always perpendicular to the surfaces. That's where we get the word normal. In physics and engineering normal means perpendicular. So it's perpendicular to the surfaces a push on the object in question. It's always directed towards the object from the surface. I hear this it almost looks like it's pulling on the object but that's just because it's long enough to go through the object that can make them any length they want. Try to make them big enough to see. That's good too because if we have normal forces in the problem we already know their direction. One less unknown to worry about. Is the magnitude of it. When looking for the normal forces use a free body diagram. Pink Fox it's that. Use a free body diagram. We'll work on some of those again here as a reminder for most of you it's been a while since physics won't work. There are I think a free body diagram free zone. How about that? What else are we going to work with? Friction forces again like normal forces this is a contact force. Even if it's air in contact with an object as the air goes over that object that's still a contact force. So if we don't have two objects in contact we're not going to have friction for the most part in this class. It's always parallel to the two surfaces in contact which means it's always perpendicular to the normal force at those two surfaces. Opposes the motion of those two surfaces or impending motion if they're not actually doing it yet. That's when students have a little bit of trouble with sometimes because in general the object might be moving but the two surfaces are not. For example when you drive your car without skidding the car is moving, the wheels are turning, the wheels are moving but where the wheel is in contact with the surface of the road those two surfaces are not sliding, not moving in respect to each other. There's no motion of the two surfaces. You have to look at the surfaces and sometimes disregard what the object itself is doing and it always opposes the motion of those two surfaces one surface tends to slide to the right with respect to another surface friction will oppose that and be to the left. Again, that's good news because we know the direction generally we know we know the angle, generally we know the direction of the two surfaces and if you remember it depends upon the coefficient of friction and the normal force because this is the force holding the two surfaces together there's a clamping force if you wish it's the force that's got one surface connected to the other surface between those two surfaces where friction is happening review for the most part yeah? I hope get friction in your life with your parents when you get on with your parents profession good things, statute of limitations is up that's mostly a review and a reminder we got to get the normal force right the best way to do that is with a free body diagram otherwise you're going to cut corners simplify it too much make simple mistakes so for a simple warm up reminder problem mass sitting there upon which we are exerting a force kinetic friction 0.3 what's it mean that I gave you the kinetic friction? means in this case the two surfaces are indeed sliding over it there is motion between the two surfaces alright got some numbers on these 300 newtons the mass will make 60 kilograms and you want to find the acceleration there's something called a kinetic diagram where you also draw in the acceleration or maybe expressly draw in the acceleration to help with the solution problem obvious oh yeah simple warm up one nothing more than what you had to do with physics one some of you just weeks ago draw the free body diagram here's some free body diagram advice it's one student to know this and they wouldn't be doing it wrong free body diagram the object in question free of any other objects with all pertinent forces applied as best you can in the direction you can remember at any point on your free body diagram if you look at it and it's clearly not doing what it should be doing for example this one has got to be accelerating down because of the way it's drawn you know that there are forces missing normal force perpendicular to the surface friction parallel to the surface now remember we're not worried about the size of this object so exactly where the forces are is not a concern to us we're not considering the fact that there might be some moment caused as drawn these are particles we just make them big enough to see your free body diagrams big right? I think there's big that is big and simple because we're thinking football player big and simple you're not that big apply that your love of that to your free body diagrams alright everybody's doing the same problem we should have the same general solution remember we're looking for acceleration in that direction just as we know what's going to happen with the surface because of the surface sliding on if you do draw the kinetics of the problem or the kinematics of the problem draw the acceleration make it a different vector so you don't accidentally add it into your solution or confuse me with it let's see we're expecting acceleration the x direction sum the forces in the x direction little portion of the applied force in the x direction and some little portion that's why we need these diagrams to be nice and big what is that? f cosine 30 minus the friction which is in the opposite direction and that's all going on the x direction isn't it? that okay so far? the kinetic friction product of the coefficient and the normal force so we need the normal force that we find from summing the forces in the y direction paying attention to the obvious factor we don't expect it to accelerate in the y direction so we've got all the up forces then I've got equal all the down forces up we have the normal force down we have f y which is f sine 30 that's it right? helps the nice big diagram we've got all those pieces what'd you get for the normal force? what'd you get? 739 for a bunch of different things were you each throwing out one digit best way to find the normal force is with the free body diagram too many students just assume the normal force is equal to the weight and it's not true in this case it's increased by the downward force we're applying as the table itself tries to push back by that greater amount with nothing to do but put the acceleration the normal force up there we've got the acceleration what'd you get? 0.64 simple as that nice warm up of course we're not doing any more problems that easy those are physics 1 problems this is physics 1.5 alright let's look at a different problem one that's got a little bit more to it a little bit more of the type of thing we need to do in here here's a maybe an accelerometer or something diagonally across it is a frictionless with a sliding collar on it this collar can slide up and down anywhere along that bar you have to find the acceleration such that the collar neither slides up or down that bar stays right where it should be if your acceleration is too small it'll slide down the bar a little bit if it's too great it'll slide up the bar so find A such that that collar stays put that body diagram is going to be vital to this I think some of you can do it without them but you are 27 gallons no of course it's got for yourself the acceleration well that's going to come from the forces in the x direction since it's x acceleration only and to get all the forces is a free body diagram free body diagram of what such that this collar doesn't go up or down on this frictionless bar it'll stay right where it is a free body diagram of what people are drawing a free body diagram of the cart couple are drawing a free body diagram of the collar free body diagram of the cart is we've got the weight of it whatever that is we don't know what the weight is so we don't know what the normal force is we weren't even asked to find the force that's doing the accelerating all we were asked to find is the acceleration itself so a free body diagram of the cart is not going to do it it's not going to do it for us it's not going to help it just doesn't deal with what we're given and what we're asked for so a free body diagram of the car that's the thing we're trying to control this was a very simple type of accelerometer a free body diagram free body diagram means it's free of all other objects to sum the forces whether it's in the x or the y direction or both we've got to have all the forces so it's vitally important we get all of the forces in the problem we have a different problem if we have too many forces we're doing a different problem so give me one force known or unknown as long as it's pertinent to the problem weight weight of course so whoever speaks up first gets the easy one I said it was frictionless this bar is frictionless collar slides on it without friction so don't over complicate these things read them carefully I know sometimes I forget to put something on the board but ask for it any other forces well there must be because right now there's no way this is going to accelerate in that direction it only has a force in the y direction we couldn't possibly get any x acceleration out of it so you can look at the diagram and just tell you're not done normal force it's a contact force it's two surfaces in contact so what are the two surfaces in contact as it accelerates with the cart it's going to push on the collar so the surface in contact would actually be depending on how tight that collar is how tight that collar is it actually be that upper surface there as the bar pushes on the collar how do I draw the normal force then perpendicular to the bar so if the bar goes like that it's perpendicular to it true Jake no it's not that it's perpendicular to the collar it was shorter what's that force remember we need to have all the forces in the problem Jake says no sooner or later we're done with the free body diagram we call some of the forces but if any forces are missing there's no sense doing the sum of the forces if we're not done you just waste an effort you guys never waste an effort you're efficient clean running machines yeah there's a force pushing the cart but this isn't a free body diagram of the cart force of acceleration hang on here's a rule here's a rule for us in this class and we will not violate this rule you will try but I won't let you all forces all forces in this class by something something concrete something real something tangible something you can touch with your hand can you touch the acceleration Jake because it took to the collar all forces are caused by something real which means if you give me a force I can say what causes it and you have to tell me an object that causes it what causes the normal force contact with the bar the bar is causing it what's causing the weight I knew it was something like that no air resistance because this is in the vacuum of academe that was a joke it might not actually be moving yet we're just getting ready to do it just let go of the collar just got it accelerating so air resistance isn't a concern yet what other forces go on here caused by something something real I can't put this force on it because that's a force on the cart this is a free body diagram of the collar that force whatever it is a jet engine or your hand or who knows what isn't touching the collar doesn't mean it doesn't affect the collar but it's not touching the collar yeah got it that's the normal force here on the collar until we're done with this there's nothing else to do it makes no sense to know some of the forces if you're missing it for some reason I think there might be one that is in the opposite direction down there I'll put it up there if you can tell me what it's caused by well if the cart is moving by some force that's right there I have some force in the opposite direction the collar anyway the carts this force pushes on the cart part of the cart is that bar that means the bar starts pushing on the collar and that's there there isn't any what what acceleration must the collar have not zero must be exactly this acceleration because if it goes if the cart accelerates with A but the collar moves up it's accelerating at less if the collar moves down it's accelerating at more it must have exactly the same acceleration and in fact that's what we're trying to find what's acceleration force causes acceleration acceleration doesn't cause force acceleration isn't something you can put your hand on so you're going to need this rule here to stop you you're going to sit there and look at the problems I just feel like there's something more I've got to put something more in here but if you can't think of what real thing is causing it you might have to think you're done because sooner or later you are done and you have all the forces are we done with that free body diagram we are we are there's nothing else in this problem that could cause any force on that collar it's only in contact with the earth and in contact with the bar we've got all that there's nothing else going on there's no friction no electrostatic no nothing there's your free body diagram now some of the forces it's up to you if you want to incline the x y axes your choice of whether you do or not it's not going to affect the physics so do so if you think it's easy don't if you don't want to generally put the axes in the direction of the unknown we're asked to find the acceleration so generally put the axes in that direction it just makes the algebra a little bit simpler but it's not required pull with all the forces on there make sure that's different give it two arrow heads or something see it's blue I don't want you accidentally adding that acceleration vector into the other vectors somebody else might and you got to help people TJ got it? check with Frank Frank's always done first don't shout it out tell him no you didn't don't fall for that he's trying to trick you TJ don't let him we don't know this guy very well what? it does have a number we'll give us acceleration we're looking for and we do have some force in that direction if we didn't that'd be a big worry because there wouldn't be any force available to give us that acceleration we've got at least a little bit there call that I guess nx which in this case is n sin direction so going to give us our x acceleration we know neither n nor m we have some of the force in the y direction because we've also got some stuff going on there see what happens in the y direction what should the acceleration be should be easier we want this to accelerate stay at the same level not go up not go down so all the up forces equal all the down forces so that means n cosine 30 equals mg is that right I mean three unknowns two equations all the masses will cancel out the masses will cancel out in fact the mass of this color doesn't matter the acceleration wouldn't be the same no matter what the mass of the color if that bar is frictionless if it wasn't frictionless which of course in real life wouldn't be you're going to need some kind of acceleration some kind of mass on it now let's just substitution let's do one equation in the other the masses cancel can you see that now it's true sometimes I forget to give you the masses but I was putting clear here put it into there the easiest thing to do I think is to solve for n here put it into there and the masses cancel don't they what did you get because it's one time one second squared actually that's assuming SI system which we didn't need to assume but when given the choice we do I hope to be careful of your intuition the feeling that something else is going on your intuition isn't that mature yet so trust it to a point but then beyond that you have to trust the physics to get out of the class question gets it and I'm having delivered my new white screen TV velocity 7 78 oh sorry kilometers per hour so I'm stopping distance I have to come to a stop without the crate sliding am I missing anything I think I'm missing the fact that my cars are always red I like that thing Joe I mean I'm stopping distance so that the crate doesn't slide stop shorter than that you need to put on the brakes too hard the crate's going to slide some into the back of the truck stop longer than that and you know I'm minimal there's a minimum distance allow us to find just what it takes to stop the crate without sliding so again a free body diagram let's see don't check nope no mass of the crate it's going to be the same for any crate if you have a ton of feathers or a ton of lead in there two science jokes in the world the minimum stopping distance well we've got initial velocity final velocity we're trying to find delta s then we better have some other unknown what maybe the acceleration of the truck because that's what's going to go that distance oh and that's got to be the same as the acceleration of the crate since they don't move in relation to each other no sliding that was the criteria that we're going to get from I think some of the forces that's going to come from a free body diagram so there's our problem GPS we can sum the forces get the acceleration from the acceleration we can get the minimum distance because we'll assume no sliding that'll minimize the distance automatically we don't have to take the derivative and set it to zero or any of that kind of stuff not on this one free body diagram of what yeah so you're doing the wise thing by not actually writing it down anymore are you leaving out your units? is that why you're so fast? yeah and making a really small free body diagram is quicker and always assuming the normal force is equal to the weight that's quicker too always to save time of course you lose it you have to take the class over again but if you're right it's a get out of class question you can go you got it I know you didn't take it from me check your transcript free body diagram of what free body diagram of the crate will give us the acceleration of the crate that's automatically the acceleration of the truck so free body diagram of the crate get all the forces on it such as who goes first? gets the weight gets the easy one let's sit back now DJ normal force perpendicular to the surfaces in contact is the crate with the truck bed other forces since we're dealing with particles if you want to draw it like that that's fine I tend to put it at the surface itself just to remind me that is it in that direction? is it in that direction? well there's only three possibilities where we stop at just the right distance the other one lets see if we stop too hard in that case the crate would be sliding forward and then the friction force is correct the other case is we don't break hard enough the crate still wouldn't slide it's tendency no matter what is to slide forward if we didn't break enough it doesn't change the direction of friction it means we just don't get our minimum distance here so that's got to be the direction of the friction that will give us the acceleration of the crate that will give us the acceleration of the truck then we have one, two, three things we know one thing we don't we can assume the acceleration is constant and then use constant acceleration equations so we've got two minutes before we can get out of class Frank can go but he doesn't want to he's afraid he'll miss the second physics joke ever on get out of class questions with each other because then all of a sudden magically everybody's got the answer and here we go so now you all have to stay not leaving